Give some examples of everyday5bt(* d6yaai v vibrating objects. Which exhibit SHM, at least approa5 t ay(dvi*b6ximately?

Is the acceleration of a simple harmonic oscillat5) n-p8s gvhbecy1i6 uor ever zero? If so, where?

Explain why the motio64v eue7x x3szn of a piston in an automobile engine is approximately simple harmonz7 xxve 6se4u3ic.

Real springs have mass. Will the true period and frequency be cqa :,ey50 uoropa-(tlarger or smaller than a5q ctupr-ooa0y (,e: given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simplm8/ ivw9km)a we harmonic oscillator (SHO)?

A 5.0-kg trout is at(heep1)ml m irj94w6 btached to the hook of a vertical spring scale, and then is released. Describe the scale reading as a functi(1ehwlre9jm6i bm4)p on of time.

If a pendulum clock is accurate at sea level, will it gain or lose tu (j8i;// zt0 srrpyig/r)fc time when takeyti;gr0t)irjpu rc f///s z8 (n to high altitude? Why?

A tire swing hanging from a branchz( q8:db7rujt6sjym 8 reaches nearly to the ground (Fig. 11–48). Hou8:ts yd7j8m(q6j rbz w could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shakethm2b, by93 wm the pan at a certain freb,h2w y9tm bm3quency?

Give several everyday examples of resonann:;u9h g5tgum5z,1jti+qg ej ce.

Is a rattle in a car ever a resonance phenomenon? Exp rz d4ub,zj /k5yiorw*2h/h 5clain.

Is the frequency of a simple per4er .o74sq if vrz ,kg/0nag6wiodic wave equal to the frequency of its source? Why or whvs.rgo,fa0i4/ewzn7kg4 q r6y not?

Explain the difference between the speed of a transverse wave traveling down a s*rq ntj 9p)4acord and the speed of a tin r*)pnqa4stj9 y piece of the cord.

Why do the strings used for the loweste c 25l( r9*0qzhxwlfj-frequency notes on a piano normally have wire wrapped around themc0fl*52rx j9lhzeq (w ?

What kind of waves do you think will travel down a horijmm+ z3+2 cvguvwd)/m1 c zd3nzontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its leng u3mz3c)dz vm +d1gj2m /w+cvnth?

Since the density of air decreases with an increase in temperatu*n;ig jym t4cw n,92ukre, but the bulk modulus B is nearly independent of temperature, how would you expec*4ujc,w2yt9 ;kn mgi nt the speed of sound waves in air to vary with temperature?

Give two reasons why circula +96alvg b/igbr water waves decrease in amplitude as they travel away f/6g9 b lg+ibvarom the source.

Two linear waves have the same amplitu)xgmtsza4 3fbq9m t12 de and speed, and otherwise are identical, except one has half the wavelength of the other. Which transtbqz21am)fm93 4tg xsmits more energy? By what factor?

When a sinusoidal wave crosses f8yr7tfwu i/+the boundary between two sections of cord as in Fig. 11–33, the frequty frfw/i+7u 8ency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any pluzt6*)0ok ; cmfg9jllaces you could touch itc9o0 * ;ukmgz jfl6tl) with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflectln*v4u4 .xaqj ed waves cancel at the nodes. Doe j4auxl4n.*v qs this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, wwy+;if4 s5;ahij6gf how might we de5yi;4w;+jif6wh gfas termine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 q212eesx k7 ljm, what is the total distance it tek2q7sel 12jxravels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 -6ksxmdo4t53;o vlhkl9szk5 ize+ oo3j4 f6z cm long when a weight of 180 N hangs from it. What is the “spring” constant k 49+-5;t36 d lo46oek 3 slhvxksjikfoz mz5ozof this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its cw3qls) 2z3bld*,cq l 5snhp4mzy/4p68-kg driver gets into the driver’s seat. If the car goes ,43dyzw/ sllspcpn3q4qc z *2mb)5hlover a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stqp -jq;p66nx crv 6,dxretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffnepr,d q6;6 vxxp jq-n6css 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 vibrac9 e56zn0q lvuy08 bdftes with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from itudcfz5v09en6 08lyq b . What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating thz g,dtf.* +i fs/crp3ze position x of the mass in Fig. 11–2 at times t = 0,t = gtcz+/3s z*fidr. f,p$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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. The we fv9zsw 46ukh vuz)zmif19n 49b vibrates predominately with a frequency of 4.9zhu fm9vn6if zsz9kw 41v4 u)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 frequency of 0.88 Hz. When anltq 3/rbuz26,x w ig apb9+o.g additional 680-g mass is added to i923ort/g wbl6 za.+xgu, qb pm, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vjdwao2o n0 )7oudp5(k ibrates 3.0 times per second with an amplitude o0oadoo5w nu72jk)p d(f 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 frlcu63z 0ceoqu9a3u g, om equilibrium is the speed of a SHO half the maximum value?q3,culu90e aguoc6 3z$\approx$    A

A mass attached to the end of a sprinpf8yhgb; i-s+ 1zi: xhdn,g*bg 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 isyv; eupxcj 318 stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium3xpjuvye 8;1c position again?    s

  An object with mass 3.0 kg isk19s4gaem5r,a 6 lealu gq+ca r7k8( x attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from i 65r e+9aa(kga,7xukqma8l er1g4c slts equilibrium 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 popgun 0.20ew6n y88 9rmz aqrls(5 mfzt(zp+ctq3b( ;4db0 m to “load” a 0.180-kg ball. With what speed will the ball lea(8ab m 6 lspq8w m5by dqretz4;f3n+z(tz 9(crve the gun?    m/s

  A mass sitting on a horizontal, frictionlessj k:wv2 +4jj,rr/x)i)mq fdax surface is attached to one end 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 spr4a j :jqd k/vij xw)x)2fmr,r+ing compressed, the mass experiences 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 vibrar* 3i:+dpuj zftes according to the equation x = 0.45cos6.4t where x is in meterzj* +:fpudr3is 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 the energy of a SHO r;dcta 8:uuheo/mx+( half KE and half PE? ± h+e(a8t rod muu;xc: /   A

  If one vibration has 7.0 times the enecvtm,l redp q:. .+l)grgy of a second, but their frequencies and masses are the same, what is the ratio of their amr t. :gl el.c,dp)mqv+plitudes?   

  A 2.00-kg pumpkin oscillates fr*ywattoq6;hy 9,k2u yqs2o9rom a vertically hanging light spring once every 0.65t ,92oa2 9yuk yshoqr*;qwty6 s.
(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 parallel vertic 8x/xtd2 0ntabal springs, each with spring stiffness constant k (Fig2 t8/at 0bxdxn. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates aca+v-/oc kr/qacording to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Dete/ca a+v /qkor-rmine
(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 of SHdt.j+ ym 4y.4noq zbw q9 nws-ura0,8hM, 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 1vgui nce)2l4 a horizontal spring (k = 124 N/m) is struck by a hamml)ecgi2n 1u4ver, which gives the mass 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 stiffne6dr ns) 8w(2 kom8ylyiaz;u g:)8rmfpss constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. Theso6z8;ym l nu)):d2yp ( rfma krw8i8g mass passes through the equilibrium 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 two springs, with sprioicq-zfmi 1r 9y 5e5+rng 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 horizonsms mm3e,gb9t0ww/0etal spring whose spring stiffness c9e/ b,03sgmet wmms w0onstant 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 65.0 kg jumps from a high bridge. After rnu *6/ n3pchwlo )kc4teaching his lowest pointc6k u*h/ 3c)n4lptow n, 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 h )y;)8pwup oqe 2l7dmvibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing/ 3 .v9 x:r, aoq 2vu)vza3hnnq,j .dxwrfue3v per second? (That is, one comp:z h ).3av3rje9,xwqv2udfvo.van x3 ,/qnrulete vibration takes exactly 2.0 s.)    m

  A pendulum has a period ofkyqmzshms 3()ry,:mg m -uf 9e9g4x2 q 0.80 s on Earth. What is its period on Mars, where the acceleration zmh(qkmmry9f s) gx 9e g u4-qs2y3m:,of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long l:5,h kf c3qifld1 o u3*hkscmz(n;p6
(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 mass of 36am( mezb25u xb*6wmd v7gby gw,o,8h35 grams, and it is released at an am5eo68gg (hdwmbyvm*3bxaw b 7u, 2z, ngle 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. If the cb+- rwk k0 vbo(jui;x2lock loses half a minute per day, how should you adjust the length of the pendulum? shortened byb-ikkx j;+b0(v orwu2    mm.

Derive a formula for the maximum skdz8(s;r-dq ppeed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is reb 9jcsbau53;oleased from rest starting at an an a3ubs 9ob;cj5gle 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 wave crests pass the bow of his anch(h;dors6kl l tb2z b10ored boat every 3.0 ss(b0 l l1 tobz26hdr;k. He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed ojgv0mhc*nq/c 3lu/b)7hc g k0 f 343 m/s How far apart are b0jugl /c0 37 c*nqhkgv) mh/cthe wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) ao g3n1a(hjtc4 nd travel with a spc g3h o1j4(nateed 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 wavesr0xcj p-gdn0+i,is : kiqi/8wsncixw*,2 *t l in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twiced j 2jdcp(+sj, as dense as the other. In which rod will the speed p sj+d2j(c,djof longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two sup)qeweqf: 7m nk 5a6g3ejz5d0hports 28 m apart. If the tension in the cord is 150 N, how long wizdng)wmeeaq6qkf h 3 0 75ej5:ll it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hil: 2ekgp u2o-/5zrpu mzl by a steel cable of length 620 m and diameter 1.5 cm. o/:m-5zg ur2k up 2epzAs the gondola comes 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 surface of the s/ nmr3bnxbm. ntas);+ ea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at thism.bns+x/r;mnt )a3b n point?    m

  P and S waves from an earthquake travixo;0hqxncnn+ l4 9u:el at different speeds, and this difference helps in locating the earthquake “epicenter:ux;nl09hqncxoi 4+n ” (where the disturbance took place).
(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 sul (o8jr2, klkfsvgk7: rface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which arl27vlj ,k8 k (s:fogkctually 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, 4skniu6 j)dw4c+qp 6bu xpl:9and (b) the amplitudes, of an earthquake P wa b4: pcni jqp+l )sdk6wu649xuve passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthgmfep851- *j gfwm0qfquake wave passing through the Earth is measured to be mqf5w gpjef8- 0 mf1g*$ 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 tr dygh(b/hb+ psi1yk- 5avel through the same portion of the Earth, but one is carrying twice the energy.5/yy(k h- p sbh+1dibg What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but o+ ,hutb:j0x/ rdjsd. vne transports three times the power of the other. +uhvjx/:s0br.d td,j What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and downy5(p1c.wrdi f5xb, v k a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease tibwycpvxd5 ,(f15k .r o 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward eac-ilnvhg3u h21 4pgbl8h 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 hi uh8b1l3 2-l4pnggv pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as i 64,hfhos7gxuxlx .ca*+fu ,v s(n(f wts fundamental frequency, what are the frequencies of the firsxuw.xaxfgv,o7*n, fl6us(( +4s hfcht four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrate9nnz6g) ,/rm: d39e9:qyxuwmcu ycwo lf71 qws at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standin o)9w7::wfy ,c96uxz/ 3d y9mgcqen1wru mlqng wave.)    Hz

  A particular string resoc0wp6wtuu2j;s)r ;;al*na fy nates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it wu * ts)0;yf 6 prjwunac;w;la2ill 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 waves is k+vbw3p7r 7dj 475 Hz, how far apart are two ad3bk+wdv7r pj7 jacent nodes?   m

  If two successive overtones m rri6t0e0wy (of a vibrating string are 280 Hz and 350 Hz, what is 6et00 m( yrriwthe frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass cnnf 5hxo .oeocc1qk( 4fh2+1of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtocehq+2 oh kc(nnc15ff1 oox .4nes?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it t)ypx * 3aweus 4/:3fmnl3vbsis measured to viw:mf us3 )x y /leba3pnv4t*3sbrate at 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 string is suppo +x3 aqlht,:bb6 7sqohsed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased byaosq3l tbh+,6h: b7 xq    %

  One end of a horizontal string is attached to a small-amplitude mech886uk e( eui9 wt2sskkanical 60-Hz vibrator. The string’s mass pe9ekisust 882e(6u wk kr 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 srh 4;zgohc8*adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave parsg z*h4oc;8h tterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right bsfc:rm do:1ec*+ yu (frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a stad bco*:u:s mc+(rf 1eynding 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 travelfc.a3sm wrx wr(iy/)ap(b) o ;ing at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approabw3 a )m)ocy.p/arsf(wx i;(rches the boundary at an 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 fek33y.-fl d ogrom 2.8 m/s to 2.1 m/s If the incident wave crests3k y -e3.dlgof make 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 cold, emz9cmx z. a1p0tz)ye(v+t,mdense air. If the sound wave hits the cold air interface at aazz tz9tm(m evy ec mp)1x.0+,n 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 bet5z3kufzcby/ r0 1:u 8b46 h0 psopoegeween two types of rock at a 38z:e uy bgps/z4 f pk0h8cuoo0er 53b61 $^{\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 diameter. According to the user7;d27r do+g ct8 hv 0dsola;ud’s manual, the dish has to be pointed in the dir+s8;d7h vdodrl ;7audc t02 goection 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 auw/q0jzj6oc2 nd velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approxij /6z20wjoqcumately how much time do they have to run to safety? (In the absence 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 stiffness constant ju(g knvz73s thp48-wc+mecl -n;2znnn*k- fof 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]8 v * (jc2enzm-lt4-nwhnnfzcku7- gk s;n3+p    m

  A 65-kg person jumps from a window to a fi(kxdqpb0;q4,s*zt uf re net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple s4x ;tsu,0f(bqz* kpdqpring, 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 pl:t.ugod;dpd : aced on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequeto.:gu :d; pddncy of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11*/ai.c cbwznp3+ dt v+–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of th.c zbp+/avn witcd 3+*e 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 8 cm) at just the right pace ofa cmj33zq2zm4co;u n 8j sem84 about 1 step per second, the coffee sloshes more and more until eventualsz4mnc2u;488mcazoe3 qj3 j mly it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm ,bx2c/atx x:rfrom the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequencc,xa /tx: r2bxy of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0;ii7 jgkkw c t9pt40l0.650cos7.40t where x is in meters and t in seconds. Determipj iwtc 0 79kg0tli4;kne
(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 l*2y2 ow( wj) zshwx7(*t uvnifrequency if it accelerates at 0.50g (a)7ws)z(h*vi tnl2 (wu joxw2*y upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 7 /kz(u28biqni ;wpl8ks);n dq5-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he step lnq)u8d;qnsb8/ (2i kkpwzi;s 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 tl* o58 ct :dyslg) h82oxyuvj2mvs0,instrument are tuned to play at 392 Hz (G) and 440 Hz (A).2vh *88dvoyus5mtsxtcl2lgo : yj,0 )
(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-pahj bfy p0df*73rt cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (T yjf7*30pb fdhhe 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 tiplnoik- t9h2wfps+ jsg fk9(968lv oj- of each prong moves 1.8 mm to eitpiswvo9 8 g njlhlf(+9f-ojtk-9 2 6skher 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 oscillates with simple harm;8rhmcrc1hc.hk k/ m.onic motion of frequency 1.5 cycles per second. What is thehk1ccc/.k8rhr mm.h; maximum amplitude with which the end of the board can vibrate in order 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 slidimo n((v:/s s7blcq2qbc1b 1o e without friction on a verticansq(bv 1s :o(qlboc /bi7c m21l pole (Fig. 11–57). Determine the wavelengths 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 7nx yh5)v,cip— each one-way swing takes 1.0 x y7ivph,nc5)00 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 spj+rrv a-/cs ms*3kv f,ue5hx7ring can oscillate 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 period of the vertical oscillations or tkhv+-3vue jf*sm/7rasxr c ,5 he 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 123 g is stretched under a teh9lz uc+eg;+lr-lk 9 lnsion of 255 N. A pulse is generated at one end, and 20.0 zr l9-lc;lg+ke+ u9lh ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring q m,2hwdr9kx 1stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of 9dr 1mx,2qwhkoscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. To( q2z0aslns+ajt*bw mb v 3-3he steel crane cable is 22 m long and has a diameter of 6+ a*a30tbs m jnq(o 2s3bwl-zv.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 x,u3d68k:bh5zi * pl x/lm*s djoln9rplate 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 98,:m *lo*p/xn5zl bxdlsru d6 jhi3 ksprings back and begins to vibrate. In analogy to a mass vibrating 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