Give some examples of everyday vibrating objects. Which exhibit SHM, at le+5x)cigg k0(c08kx a cr abit/ast approximatelykg+i 5rcbc 0k t8ica/)(axgx0?

Is the acceleration of a s j-b .f/esr59-3tgq(77cuze vudr u6 ls3v gayimple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an dyabi,c 9*1h5aat idce(m/ 9yautomobile engine is approximately simple ha,dyt/c9 daya5m*hc ii1(9 bearmonic.

Real springs have mass. Will the true period and frequency be larger ogr1 qiyxzi3/1+nq z45lauc4i r smaller thanqzu izl xgcn431 a+rqi/1i45y 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 simple harm(3u 0+edsd 6rr khuhd/onic oscillator (SHO)?

A 5.0-kg trout is attached to the hook olm86ikf-s j1kf a vertical spring scale, and then is released. Descrisl-k jm16kf8i be the scale reading as a function of time.

If a pendulum clock is ac2zojexx u20.m curate at sea level, will it gain or lose time when taken to high altitude? W u z2x.exoj2m0hy?

A tire swing hanging from a branch reachwqhe1ty8,5m l::mxiope )d2 mes nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwaxe: eyml8,) 5pwqd1omh2m ti: tch?

Why can you make water slosh back and fot3 5h pqefdd:/rth in a pan only if you shake the pan at hed/d qp: 3t5fa certain frequency?

Give several everyday erx +boxf0 ,rt0z md1m)ygpz+ +xamples of resonance.

Is a rattle in a car ever a resonam 6p;z)t *kf2aswk p32h pbip/mtu8d) nce phenomenon? Explain.

Is the frequency of a simple periodic wave3r1dxik8yxsv :v ) kw2 equal to the frequency of its source? Why or rvvx8si2 3xwkd):1k ywhy not?

Explain the difference between the speed of a transverse wave traveling,f8-x f7* ,wvfgpc gffebbt3 1 down a cord and the speed of a tiny piece of tp tf1fxg,,3f *bv g7 cebff-w8he cord.

Why do the strings used for the low jr:8kb; x2; v5ksmgpbest-frequency notes on a piano normally have wire wrapped around them g5 ;x;:pbrv2kjk8m bs?

What kind of waves do you think,cegiv : m3tb+ will travel down a horizontal metal rod if you strike its end (a) verticall 3:v gebti,mc+y from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in rs(rg) 6 ie-fetemperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of gr-e f (eis)6rsound waves in air to vary with temperature?

Give two reasons why circular watet,izn: w4icc2 r waves decrease in amplitude as they travel away from the source.4n,:tc wizic 2

Two linear waves have /ukf 1* 54h7apapy mfjthe same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Whf4*1yf7 m/5khajp upa ich transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of i 3+t7sux 6p2ndlv l+3 g*fxuycord as in Fig. 11–33, the frequency does not change (although the wavelength ax32gi+nv+s tu3xp l fldy u7*6nd velocity do change). Explain why.

If a string is vibrating in three segments, are there an*xk d.pa)z aibk/ji. oszi 1)2y places you could touch it with a knife blk o .j2xa )dbpzz/)a*ii1ik. sade without disturbing the motion?

When a standing wave exists 82s o+vgizi/g on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean thaiv+o iz2/sgg8t energy was destroyed? Explain.

If we knew that energy was being transmitted from hu kg9+;y :x k*;ckxt;jiq/oj one place to another, how might we determine whether the energy was being carried by particles (materia k:;+;qu;yx/jtjhx9* kc k goil bodies) or by waves?

  If a particle undergoes SHM wlq+jjv yjcnw2st q.y9ryk g.q:(.2 p.ith amplitude 0.18 m, what is the total distance it travels in oneqrkn (vqq.y92. wtyj+.ljy js:pg c.2 period?    m

  An elastic cord is 65 hrzi/lu1yir./kk3q1 cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this eyr31r u /kizhk1. /ilqlastic cord?    N/m

  The springs of a 1500-kg bqpi 1h vt8erf0dy-)7 car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bu0bt) 1 rvf8dphy-i7q emp, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm w ofy+(qth7 bl 7,p;tmxhen a 2.7-kg fish hangs from it. (a) What is t7 y h;,lmqtpt7f+o(bxhe 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 a frequency of 3.0 Hz whe*hr dy14x sy1qn a mass of 0.60 kg is hung from it. What ix 4yh1drsyq1 *s its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating (aki 0 6fj5rm*otf,rtthe position x of the mass in Fig. 11–2 at times t = 0,t t*jai(m fktrr65f o,0= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 0.25khxo+ w2egu7u/ ex4l. g is caught in a spider’s web. The web vibrates predominately wi+uwg huk7lex/4.xo2 eth 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 a05de7 wy t5bnz frequency of 0.88 Hz. When an additional 680-g me 5t5n 7yw0bdzass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with i6do0r-y/jzwg*q p q 8an amplitiqwy /z0pgjd-o8q6 *rude 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 fro yk)c* mjd/pn)m equilibrium is the speed of a SHO half the maximum val pk) dyj)mn*c/ue?$\approx$    A

A mass attached to the end of a spring is stret5 x bvsb:e8vtw*;(hkl n,cq1uched 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 0.3ugw8.+,wr6 u td/mwe +j mmc,3hg )egc15 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (nhc eme,jguw/c6wt .w+m+m,g )3r 8gud ew) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness constannawb1n8 q3h pf.u3 5jv1sx/hst k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium positioxw 5/p 3j8anh3qfbvhn.sus1 1n, 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 0a 0f9. 6 pnqgpa8ku3ar.200 m to “load” a 0.180-kg ball. With what speed wik8 rang6u.p093 aqa pfll the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one en2p48io. zcyn/ eyehw .20ygs8md8 z zud 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 experiences a maximum accelerati w 8 ye.my2 ediz4oyczz 8hn/02sug8p.on 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 equation x = 0.45cos6.4t wherf / d28d9m0y oadom6uoe x is in medom 689ao d/2muodyf0ters 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 half KE and hal;1k q txd8 0ij*or 2qsq(yrwfk:i/( pkf PE? ± w 1qiq(i8trk(do ;q2*/xjpr k0fk:s y    A

  If one vibration has 7.0 times the energy of a second, but the:h n4euajrj9td ;t a66ir frequencies and masses ar4 :at ujt;69hj6endare the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once everofclirruh:w m+ );v :8y 08m+)orc wviu: hr;fl:.65 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 par-qzx nzl ad:l 98w41slallel vertical springs, each with sprinzx wnl-8lql1a49:d sz g stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.3nrcz j9afz -gx+a *.x5r, gk0u8sin6.5t where x is in meters and t is in seconds. Determij n + kgfr,0z.u g9ar-5xzx*cane
(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 SHM, labeled A and )a biexndh,l +ujv 0 +est80n,.zsct8 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 sprin1d 7ghgk03sa 7*kl nweg (k = 124 N/m) is struck by a hammer, which gives the mass an ini7k03 had gewkl1 n7sg*tial 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 vibragqo; nse u2g:h) zsnomnknc(l2w7/u7 /6q9fhtes with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrio7khzeh;/nu fcq2 7nn qg2glo:nwsusm(9)/6um 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,p9uqip h hsf z:b0g,6. 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 spqs )v 71zof; *ojts/,6hbui.600-kg block attached to a fixed horizontal spring whosoit7s,;u6 )1p v/f oqs zsb*hje spring stiffness constant 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 reaching* v6:kxng5c;n/vafd) se nw-/f m 3pck his lowest 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 u)vm*s/: pe-k; angnwfckc 5x3d/vnf6 nstretched 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 vibrations in exactly 60 s,6kp or vnll73 to.-kq. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum beza.pp5(* lqb d0chb o9l2h;6aw*hkpc if it is to make exactly one swing per second? (That is, one comzapl* bb*a659dw hphcp 2h(c.qo k0l; plete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its pevpb8sk 52er8f s)hgh2riod on Mars, where the acceleration o25gr8vfhkhes8)s b 2 pf gravity is about 0.37 that on Earth?    s

  What is the period of a simple pentend12omc 33qdulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 03)u efivaiyqm 8/ 9l0s.760 m, the pendulum bob has a mass of 365 grams, and it is releasvls3u9e0yq /8ii )famed 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’t,x blt:: s7kjs pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulumst bxtjk,:7l :? shortened by    mm.

Derive a formula for the maximuff g yt,w;)gzzq8k/s ;m 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 a frequency of 2.5 Hz. At j8ew 0c4y lkf* it is released from rest starting at8*kcwe4 j0fyl 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 wave crests pass the bow ofzr bre9e-t3z+ his anchored boat every 3.0 s. He measures the distance between two crests to be 6-te+z9r be3r z.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency +d+yg*xz)8 xan9zwrh 3s)fsxof 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compr) x)g+w9z3*az+s r8hxsdfny xessions)?    m

  (a) AM radio signals have frequencies between 550 kHzb 9r3 h1kwbeskbr/8vq8,jp 0 u and 1600 kHz (kilohertz) andbesp 1b brqk9ujh3k rw,v88/0 travel 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 waves in znvz*,9a a; yx
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twis(wngpxs+t 9lv t r04:akdg qh/ ,j4b.ce as dense as the other. In which rod will thedp(:jkg94 vxqtsgwr4+0ha s n ., lbt/ speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two so n4dw, 1fd - yij+ocz 5aqeg,irz35e3upports 28 m apart. If the tension in the cord is 150 N, how long will it take an1oo g35riz5 - ide,c+w3qjfay ,z e4d pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel ca)1f5twrd(5sx )vva pmble of length 620 m and diameter 1.5 cm. As the gond))x1(pwsv5 t 5amvf rdola 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)cv(x+n2crkbd p4r,q ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep 2kcp(rqxr+b)c4 n,dv is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this diffef:; 9c8m*dvzpa6rmn5 9 qj6ln axj*m nrence helps in locating the earthquake “epicenter” (where the disturbance took plnl*;qc8pn*m j6amz x9 95jfvrmad:6nace).
(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 wave can be approximated by *i9m 9+9wk qlf drw.*exap1xowm/ 4cd a sinusoidal transverse wave. Assuming a frequency 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? [Hinexrofim.q/k1x apc9l**9d w9 w +4wdmt: Set the acceleration a>g]    m

  What is the ratio of (a) the intensiti /sua.2df,bzk es, and (b) the amplitudes, of an earthquake P wave passing through the ad.2 ,sz kf/buEarth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave :42-isfba mkbm 1js s8passing through the Earth is measured to be 1b:m mfs 824ssb -ikaj$ 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 trcy i,9lw )kyq)avel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the yiwql,y c )9)ktwo waves?   

  Two waves traveling along a stretched string have the same7 t71st., p5cx stbmns frequency, but one transports three tim x,ts.p t51smct7s7b nes the power of the other. 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 down a tot)uy1 jbab-q .e:.1nnny)tdz p al vertical distance of 6.0 cm, from the lowest to n:1 z..bqyu1dn) e- y) tnapjbthe highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each othe+sccv)6 jf z,br. (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 mo+,s6)jcf zvb cment the pulses 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 its fundamental frequency, wv or9v7i)zi6fhat are the frequencies of th96fv 7zrvi i)oe 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 wy6y ojyal(( ;b7 *lpyehat frequency will it vibrate if it is fingered one-third of the way down from the end? (j ly7aop6y ;(e*ybly (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequeo vi(3dt6rh10z; mimency of 280 Hz. Name at least threrm(id1 ;tzv6mhio 0e3e other frequencies at which it 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 the94 a78ln ygbbg frequency of standing waves is 475 Hz, ho9b7gbyaln 84 gw far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string ark h xhz2 -uh+mgk7k/z4l/3vg de 280 Hz and 350 Hz, what is the 4 mk-zzh+dhu/g/kh 7v gk2l3x frequency of the fundamental?    Hz

  A guitar string is 90 cm long v7l,v83u b7sf;tdrzm and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and, s;8fmudv 7lzb3v7t r the string 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 vibjzp6 8 .ae+sscrate at 200 Hz, but it is measured to va6. zesj +c8psibrate 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 supposed to vibrate at 200 Hz, bu/ofcb5l : ep7n4amh-q t it is measured to vibrate atmq alp-:he n/45c7 fob 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a 84iw7 , suuxy0/qxkq lsmall-amplitude mechanical 60-Hz viu0/ul4, x8 xqw7iks qybrator. The 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 st jmcw(0g 2n*x,y/y psnring may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L bet(myyspn *c, gwn0/jx2 ween 10 cm and 1.5 m?   

  When you slosh the water back and forwlvkx2 2n5ptna:b8 6yth in a tub at just the right frequency, the water alternav xa :ktl8py22wbn65ntely 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 bou6phu)g n,fnl/ ndary within the Earth between two kinds of material. If it approaches the boundary at an incident ang,lfh/p n)u6ngle 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 underwate9s y 3wps+j,qzr “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If t j9wpys,s+3zqhe incident wave crests 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 hozq)(i zl,5-j d5hyrof cold, dense air. If the sound wave hits the cold air interface at an angleoyjd)5h iz,lzq -h5 (r 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 earthqua +m s-+ uw;4jpv i/h*zgrs/iupke wave strikes a boundary between two types of rock at a 38+p-ripuvgs z+mu s4ih jw;*// $^{\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 user’s manual,whd (zam)o2)ig +*jf f the dish has to be pointed in the dirahw f(2jid+)m)f*zo gection 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 wavelen86 agagf3d(eu gth 250 km and 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 safee(u d6gaga83f ty? (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 spw)x,uk ke8nt .*wlqg 5i.vdp3 ring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, cowt3)*k8i ..kngqdpx , eluwv 5llides 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 to a fire net 18 m .tf zq b;c8v5nbelow, which stretches the net 1.1vt fc.8;qb5zn m. Assume that the net behaves 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 t f1g6qdkgmls llc+p bd4/9pvonk+hph )u+ ,63he end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscikm/6 h b++ln14gq)pfpud dls pkhl9, 3vco 6g+llation?    Hz

  A 950-kg car strikes a huge e- riepr m8*22 tql-wmspring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spqel rrw82* m- emt-i2pring?    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 (diamei b4fh2e:ni ;y:mya k:z3qy- 8raru6l ter 8 cm) at just the right pace of about 1 step per second, the coffz 2yef3rn-:urm:a hky8iiqylb4:6;a ee sloshes more and more until eventually 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 from the cen8b q1tm c(t0p/ ulm0gmter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the qb umt 08gm ctm(/l0p1frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equategb8t1 7 2gv( rhyv87uq69pd .l fkuf)uba3blion x=0.650cos7.40t where x is in meters and t inf7bv8b 6yr1b8d f .g q97uu ep2l)k3 (hlgutav 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 oscillaz;8)d-uxexb +qjez8mxc ,l 5jtes with frequency f. What is its frequency if it accelerates at 0.50g (a) upward, 8+m ex;8 l xd)b -zjuexjq,5cz    f
(b) downward?    f

  A 220-kg wooden raft flokozj .5 l6xfg 5ud w77a9r*nbr75 fcnsats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off,5 57j76u*.og rn7cn r9xkdz5fb fwl as 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 instrumentr8fgl2l+nc( yf8 1zr xe3ah2l are tuned to play at 392 Hz (G) and 440 Hz (A).lg8fa(c2hezy lrlxn1 8+ f32 r
(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 stretche u0i7/jh/i mrk7( utgad two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave ig7(kuu/m/ ra7tjhi0 in the heavy section versus that 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 q*a7r .bb()p3gvfqk -+ te8yg e2 rrnufrequency of 264 Hz, and the tip of each prong moves 1.8 mb *r8(pfvb-tg keeg2r)a+.3qyn7 r uq m to either 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 harmonic motion of freque ey5fp:clkb/,ncy 1.5 cycles per second. What is the 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 :kb5,p l/ efycoscillation?

A string can have a “free” end if that end is attached to a ring that c;u0 ; h,wghi4ozbur- gan slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a o4 ,hu h ru;0iw;gbzg-string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactlyrxx*2, 9eu a;i:ry+meqkfc d4 2.000 s — each one-way swing takes 1.00c;,rqeye4 xdr2+:iu9fx m ak*0 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 oscillate in the vertical direction or caw3* no /x)8a9r(fz bapo9vig ey;3wuzn swing as a pendulum of small amplitude, buvx9eoa*3zu zwnf )a brg 8;o3 /p(yiw9t not both at the same time. Which one is longer, the period 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 123 g is stretched krgb7 i.,zaio p h,x27under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulszr7i2ahb,p xok gi.7 ,e is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling bcc,1m d-mp r z2tr(3 pbh4wfw;y a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. br z4wtmhpd (;1m,3rcwf -2pcWhat 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 1 w6wo4tw g4xmot ffa/j+:/ch(200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter:tg ocj w4+6faw/w/ (4xfotm h 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 plate as shown in Fig. 11–58 (which alswh)az8 2qnqdx -a7l8 uo 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 on a spw -8q)zxah2ln q7ud a8ring, 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