Give some examples of everyday vibrating objects. Which exhibit SHM, 9cpj2/f zri;p7xue 7zv s2v2dat least approximat 22e 2zp9ic7/v7dux vpfz ;jsrely?

Is the acceleration of a simple harmonic oscillator ever zero-b gu +gejo(b3fq a-y8? If so, where?

Explain why the motiog 8opjatsv358rvn ; 4e9w/gsq n of a piston in an automobile engine is approximately simple hvsv;4 83 9nsrqat/egp gw5oj8armonic.

Real springs have mass. Will the true period and frequency be lorhqt b;d*-pus r *a/xa)83krarger or smaller than given by the equations for a mass oscillating on the end of oark u**r;qa d8xs/pt-b)3 rhan idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscill rf1tdz: x b:hkcv5l,0ator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spr/lhz mrrnm(4z57 p:d ding scale, and then is released. Dehp mdd/5zm(7 :l 4zrrnscribe the scale reading as a function of time.

If a pendulum clock is accurate at5sx+j9xsde;m 0p t9q3 8chjs q sea level, will it gain or lose time when taken to 90 sc;qx3j9h5p +tdej xmss 8qhigh altitude? Why?

A tire swing hanging from a bram/wst(t.0u6g-yd8t ed2gg (sprg p /anch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stop2-mawt(e(r0st. 6d gtppys8/dug / gg watch?

Why can you make water slosh back and forth in a pan only if mwn2xodpdt1830 ,alf you shake the pan at a certain0f do2xdlp3 1, wtna8m frequency?

Give several everyday examples of resj:a8seems2:c x+ ho u/onance.

Is a rattle in a car ever a resonance phenomenon?-c( pkon,wu;j9b 1hzj8rc6o92vx j wc Explain.

Is the frequency of a simple periodic wave equal to the frequency of it;u/f8n kmv ul(xh6;v ds source? Why or whyd(vufkv uh ;; /6xmn8l not?

Explain the difference bekv fhp- 53djqg x1q9 c.ao.72 ad/imcztween the speed of a transverse wave traveling down a cord and thcpkaz3 vo /cd.iq2g5q -.xm91jf adh7e speed of a tiny piece of the cord.

Why do the strings used for the lowest-frw:on sy-9 w2 62ba ad,ik*eqcyequency notes on a piano normally have wire wrapped aroqw6oa 22 9ib :,*necdy-swkyaund them?

What kind of waves do yousi10j1 *gotv0 ju a)dq think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontallo1d1q*)svja0 jgitu0 y parallel to its length?

Since the density of air decreases with an increase in temperax02xxgo:glg )n/iroiq(/t /;xlk7 h pture, but the bulk modulus B is nearly independent t lx)nk;2x/ /gi go(x h7:ql/p g0oixrof temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amp-7l oxcse)c*u3tma s;5yg 7vflitude as they travel away from the source.y* s7fsx actl7-m;3u ge5) ocv

Two linear waves have the same amplitude and speedwmmnj2p 67q5w , and otherwise are identical, except one has half the wavelength of the other. Which tpjm5mww6 2qn7ransmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sect1dc/.vj:71f l 4uezily m,7 fe7kb:(b uodsfb ions of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocib,u e4dd(m1.lo i eff c1bv:sf zb7u7/:k l7yjty do change). Explain why.

If a string is vibrating in three segmentsbx8 ku7jn0 qe yh3.*rm, are there any places you could touch it with a knife blader8jkbqhy 0xem u37n*. without disturbing the motion?

When a standing wave exists on a string, the vibrat c2o;lubis1z.*402 oi jxijx yions of incident and reflected waves cancel at the nodes. Does this mean that eneruzsl;b2o *4o2 ix cxijyi 1.0jgy was destroyed? Explain.

If we knew that energy was being transmitted tlhr;z:p/ s :efrom one place to another, how might we determine whether the energy was being carried by particles (materialpeh; r: t:/zsl bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total dis8;luae82gb xptance it travels in one pe xe;88 ugpbla2riod?    m

  An elastic cord is 65 cm lon *ng16grz/zz2b c 7oqug when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs fro761zu/gzo 2 bcnrz *qgm it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car vei. , c py(oe .ix9qeaxg9 :a,c w+swf*u(za0compress 5.0 mm when its 68-kg driver gets into the drapasu*x:e09 wwc aygqxf,e+ eo .cii (,.(z9viver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs froj7ux1 gu o7 8jz.uzu0nm it. (a) What iuu0 go. z1u7jju87nxzs the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with ag0,4w j vdzs6xx)9pw g frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What iswsx9xd)0 w6v zgg ,jp4 its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating thguj, jvn p7qs2-e cw;.e position x of the mass in Fig. 11–2 at times t = ,w 2qcv7-jg jpn.eu; s0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. Tcs1 uk;b6roe i4u; 9ylhe web vibrates predominately wit4;uey1uos9rlkb i6;c h a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequey 9 -d01lpnuotb2mqd )ncy of 0.88 Hz. When an additional 680-g mass is adopydm- 9)ldb u2nqt 10ded to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of e)6qek9c1khx a spring vibrates 3.0 times per second with an amplitude96) ehq1 ekxck of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is txojba, 9t ,*jgzuf fh1yo5:, hhe speed of a SHO half the maximum valuexy:1 bo jjzohhg*tuff9 ,,5,a?$\approx$    A

A mass attached to the end of af/u 0gb2c9f zm spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is str .f;dw(c 7 ):ofyxeua;e(3l,hroke wu etched an additional 07yw . ef(:,( );fd3ohaxw keruluce o;.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness y:ky) jy(jj )yconstant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equiy) yy:)jjyk (jlibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy p 1lw5b 14ono fe* 2 +lk9xmdnd02yezdeopgun 0.200 m to “load” a 0.ddfol5b2w1e2o0lm xy e +4ne9*1nzk d180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one enqhbf,c/n l, (ap,i hk4d of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass e/, h,cfpa4 b(hilnk,qxperiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the e7fztpt p;(w94q s qp-lquation x = 0.45cos6.4t where x is in mett7pt zs-w 9pl fq4q;(pers and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is 0/s(t af-c6da o(gok0pm: m cpthe energy of a SHO half KE and half PE?pomdtm a(/g 6f- :0kpccso a(0 ±    A

  If one vibration has 7.0 times the,kjcn6n5rbea r1 x 5w1 energy of a second, but their frequencies and masses are the same, what ie1w51,kbr ajx nn5c6rs the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangii 5qg+t g:i8wkng light spring once every 0.65 s.qk i gg8t5+:wi
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical cygvcgt :n7 y) +3*bwbparallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration? ) bc c+y3:btv* g7wgyn

  A 300-g mass vibrates according to the equation xaw b 9x(2qn8miv,(4yyqy5v s x = 0.38sin6.5t where x is in meters and yyq( wvs,q8 nx5ma94y(x 2ibvt is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples 1 jd z:u b6if(.5k+rh y,jw5t-nqcvsk of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124h92ccwgf j 8x2 N/m) is struck by a hammer, which gives the massc82fc2hwg xj9 an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with aadk4 e:r(,zu+dkhln :uok( t:n amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equidhz(kk:k,:e4dno ru t: lua(+librium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to t;lzpzb0, a+cq wo springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal spring 6n3j cz;1kzp wwhose spring stiffness constac316kzzn wj p;nt is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65o w;l-7d fgjslh2(2e l.0 kg jumps from a high bridge. After reaching his lfolw 2d s 7h(jllg2e-;owest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibra;-hul (hs0 hthpu0s0ftions in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulumi57b q k7y v/4d impo.z-b/oie be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly o p/kzqdii-m ybo7/5 . 4ie7vb2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wh xnb4sqmg4b9ga(o j8 6ere the acceleration of gravity is about 0(mbgjxqba48g n9o 6 s4.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lo fil uan+ ax)mi+1w)u0ng
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a cz9 k7eho9do0mass of 365 grams,d70o9zh9ke oc and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m njqf5)oi, x4f. If the clock loses half a minute per d) f,njqoi45xf ay, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for ;32 8apffva ,zqett+bthe maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at (i2zxw+*3 kkpnj fk;ca frequency of 2.5 Hz. At it is released from rest start2icn+ p*3kk kfzwx;j( ing at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that waveefk;m3yyzk-; 0 m f42flj9vpx crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two cy;0fm;2em9 3k lzx yf-fjvpk4rests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequendkoi9( /a itby6m7q+ 0i( vrsacy of 262 Hz and travels with a speed of 343 m/sqdvbit9+i/( oi6am(s7 ar0ky How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have faol) myiwapo5l5, *v 1requencies between 550 kHz and 1600 kHz (kilohertz) and tap5o o *)iy l5al,v1wmravel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal wb d, tmi;/t:mfg, h2io)inec;aves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as v6rxotdouj8 9o)wy 23the other. In which rod 6 jtuy8)owxdo9ov3 2r will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched bbge gsery18p3r jpbx6/g *f2.etween two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel frox/gsb*8pb g3rypejf 6 2.re g1m one support to the other?    s

  A ski gondola is connected to the)q*6 c)y o:b 4xma* cjmphki7k top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comekq*a4 x mc*cpiho6 7)mkyjb ):s to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the suka-cdu01*p*z- *elrrxsr *yv.mb a(drface of the sea. He hears the echo of the wave reflected from thae*bad -rryk u**spzcx( m 1dv0-l.*re ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at differebmu)ha)5pxhxy /c -n 9nt speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took plau/) 9 x)pnmy5bxhcha- ce).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface :706 zwikl* vkrvxvq/cny,z+ry(sj) wave can be approximated by a sinusoidal transverse wave. Assuming a freq+l vzkj7vivcxy y/s,)r(*w6 :0krn qzuency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of k .y/fzi: r2txoi+ ap-an earthquake P wave passing through the Earth and detec2i /+ra.z: p f-otixkyted at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured tbk6orobe 0)k1qq/ una*a9q.no be oa.0b*kn9 r enq61k /)baqquo$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through *6lijph7 e 8emwbhd+; the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of th67w h+p belji;eh8d*m e two waves?   

  Two waves traveling along a stretched string have the same frequ8p,a3vp kh -j2 obzm0s qq99trency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two waves?0qptmkvbho 9-9a,zs8qpr2 j3   

  A bug on the surface of a pond is observese /+ v*e5ai )-sztmcrd to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor ssri+mz)-a5te/ v c *edoes the bug’s maximum KE change?   

The two pulses shown in Fig(f(y3 q dun: a8z4qlav6b .dpb. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass u8lqa b:fqvby 3z(. d(a 6p4dneach other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz +7et 0gtpk0i aas its fundamental frequency, what are the tkp0 g0a7 et+ifrequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what fros)nkki2v gw oq,.(oyg yv 0lj+1 k((jequency will it vibrate if it is fisqg,((k1 0gkv j(yk ol .2+y ni)ovjwongered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency ofph e7;0zy;min8iy b, w 280 Hz. Name at least three other frequencies at which it7n wb i;e8i;mph0 ,yzy will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing w 1p/g 0vyi249jxaap vie,u-o hc61 lepaves is 475 Hz, how far apppl6-1yo1auv94hv xjie0ai/p g ,c2eart are two adjacent nodes?   m

  If two successive overtones of a vibratin p8k5bvsy (n*ng string are 280 Hz and 350 Hz, what is the freque5kn*n bsyv 8(pncy of the fundamental?    Hz

  A guitar string is 90 cm long and has*,ohotc2if+s a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string ,oco+ sfthi2*is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibratepkv.z urpb5gu;+g(9 m at 200 Hz, but it is measured to vibrate ;r .( b+ pvpugz95mgkuat 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar sgrh hxt/67 8udtring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shohx867 d/tghu ruld the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanic0uf77l ; /, pdcqwr2ikp5zpgvg 5tnm7al 60-Hz vibrator. Thcupk5,0;5n7v gzrplw7dq ipft 2 g m/7e string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pulley. If2xb9 ,.vwccwu:+ye w,+l4dg o iq;snf the hanging mass m is fixed at 0.080 kg, how many different stu9,2,cbw iyvl ;c+wf+n: qw g.x sdeo4anding wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a pe94ts 5xbx9itub at just the right frequency, the water 94 xp5t9be xsialternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundarn(fb u4dgb z-;y within the Earth between two kinds of material. If it approaches the boundary at a( b fbn;-gz4dun incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from kz8ags 8ex :p:2.8 m/s to 2.1 m/s If the incident wave crests make: ke sg8:pa8xz a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of coldk)tm5+/kel, .izqpy 4p s aiu1, dense air. If the sound wave hits the cold air ip y)uke/q ,ila51.4p+msiztknterface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary yb.( ndrt/.4vr8mm34mqfdiubetween two types of rock at ar/bqm 3y nu t4dmv4f.m8d.(ir 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diamet/, w bph k3jpd7gobwxbnw(33 1er. According to the user’s manual, the dish has to be pointed in th(w w go7dw,b/3kbhj 3np13pxbe direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km an2kdkt,y8x +ewcc /zz,d velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence ke,wc8kctz/ x ydz+2 ,of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring scn4q / pb 79yn,,mlk-p i4fcaitiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides lf4, 4qp/9i pki,-7nn cabymc with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window tr,72fl v7uj bjo a fire net 18 m below, which stretches the net 1.1 m. Assume that the net rjbf ,lv772jubehaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end )kwz4 ind qqe.5 ul7 samrvrqcd78h(y:g;w0/ of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise:.4wi8rvh) l;rqsm0ec q/ kna dzu5qw(77gyd. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 2f dts2)dezssx2r3y.72 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the sprindsex3t7 r2sfz2y)ds .g stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter )ikos;;nbmi.22h hw i4) d nrz8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–52wr2d;hz.)nn ho kmsib; i)i45). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm fr+e u +k:o2b:zcoykv)-k8ms6z t9yg vcom the center of a 33-rpm phonograph record 6mge 2- +s k:oy:tuv)+ckcyvb 98 kzzohave a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is2g* z)vd8rmrt in meters and t d2trz8vmr )*g in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if itbms/ rl k h. dz4o+t/6:zowyg- accelerates at 0.50g (a) o .+bz4mry-dk : /h6z g/olwstupward,    f
(b) downward?    f

  A 220-kg wooden raft floata:mygjtsvorl97l- cj jo-l(t08j9 p( s on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he gsj jj7jot:9l0o(-pm t yl ar9c vl8(-steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play ap1z-gaz cmt ze; 8ju9f 2h,bt3t 392 Hz (G) and 440 Hz (A). 9;zza-t1ejz8m fpt 2 h3cb,ug
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 11–33. D- a-f+q5h 46n3 nm cav)*taoakhctjg4etermine a formula (a) for the ratio of the speeds of the wave in the heavy section versus thatj3a5 ta)h*aa-ccv qg 4n6nf h+mkt o4- in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip o8pctmqy5q7p el q/4g ,f each prong moves 1.8 mm to e,8cqmype5tl p7 4gq/qither side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillp( /7k/we 1rvli9 ztn a(bme)kates with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order aei7 epr1wt( v)l (zmnk/bk/9 that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can sugfvzsf+b lo).n.r6 dw 02vv8lide without friction on a vertical pole (Fig. 11–57). Determine the .r v8fvdsgw)l 2o+. b0nfzu6vwavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way sw*acmsg2wf kn pfe*8w+27,r zeing takes 1.000*7rk,+e8mag cnf 2pf2ze*sww s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can ohm.13vx:8xwza)uv t j scillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the pejm )a xvw3.zvt:u8hx1riod of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 12/ 3v// t(u ;jn5 wtu14nh a1whwv,qd tdqb.cue3 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulseh1 we ;hjw.q1/ 5 ttd ab3 uuv,4ntnu/cdq/(wv is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended fr-e9nto.rs,,h9 a 07c t3z xsfiuj-5 d8veuefcom a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. Wha5.rt3efvs 9z,9,o- jxce7 c8 d fu0 sn-haeitut is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a*)m;s oxd a9xp 1200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameo9ax xmp;s*d )ter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a platerhwm: s)*2 so7fr(l il as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating )(h72i rwmlfr:s*slo on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz