Give some examples of ev jxxfpmj yxj1e3at u (0ge2x);01d5imeryday vibrating objects. Which exhibit SHM, at least apptmf 3 uex0xe j1)j 5j;dm yaxx(2gip01roximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, whvwx9 e;ldnuq4 6 au87were?

Explain why the motion of a piston in an automobile engine is approximately simr*t(sqq34vd; ( :abd +vi hhfbple bi*(tqv : b a qrd+d(hh3;s4fvharmonic.

Real springs have mass. Will the true 7+ x;ye:ackic period and frequency be larger or smaller than given by the equations for a maa +:e7k;icx cyss oscillating on the end of an idealized massless spring? Explain.

How could you double the maxia-zkb1u(s3nl 8q8g 1yxgv . sbmum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to :lt jp-w.omfc0rda9ku u0: j-the hook of a vertical spring scale, and then is released. Describe the scale reading as a function of timtpcdr 9 ju:0lf-o0 -muw.k:jae.

If a pendulum clock is accurate at sea lm+ 56u* tqc btsqb+gq4vb ;+cievel, will it gain or lose time when taken to +v*g5q+ti cqt b+;s c umbq4b6high altitude? Why?

A tire swing hanging from a br l v9 tzz1sum6-lalf x1;0(qxranch reaches nearly to the ground (Fig. 11–48). How could you estimsl 9t 10x(vlfx;6qza -zml1ru ate the height of the branch using only a stopwatch?

Why can you make water slochi- r8ey65ls n +5ajhsh back and forth in a pan only if you shake the pan at a certain frequency+snh ahriljc8 e5y-5 6?

Give several everyday examplesxj(die -ce(p. of resonance.

Is a rattle in a car ever a resonance phenomeno4w*59 pbo-p2o 7lah 1ikr fjhbn? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sourg x,dm;tc/a)gj zjk6, ce? kdc;6z /),,gjamgt jx Why or why not?

Explain the difference between the speed of a w,xv1o fxcf60pyalp92cj :1,xpol e 8 transverse wave traveling down a cord and the speed of a tiny piece olxo6v110 xyelpf,xc, p:a fc 9p o2w8jf the cord.

Why do the strings used for the lowest-frequency notes on a pian4* ikvj br80z)-0dgy8de wwxr o normally have )8 xwkvezi0dw-r 8 *b0drgjy4wire wrapped around them?

What kind of waves do you think will travel down a horizontal metal rooqu :pr+ /l*n+t p y+ky*d3tgj78 apsed if you strike its end (a) vertically frg 8jt+*ksuynrypp++ a*l/tp 7d3 :qeoom above and (b) horizontally parallel to its length?

Since the density of air decreases wiza/kcn 8x),4 ceorehw o0ark4-+u3n tth an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary nk/0 rteahwnx -84ck c4 our)za,eo+ 3with temperature?

Give two reasons why circula gjp-9+z rgoiadwuw ,2d+;s n)r water waves decrease in amplitude as they travel away from ga so) 2iuj+, g-wpr+z 9n;ddwthe source.

Two linear waves have the same amplitude and speed, and otherwise are ideeuj7i:fj pk 38ntical, except one has half the wavelength of the other. Which transmits f7je8uk: jp3i more energy? By what factor?

When a sinusoidal wave crosses the bolu5y/rf;5d r+bvy m6 pundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain w5lp+ rufbvry5 6;d/ymhy.

If a string is vibrating in three segments, are there any places you could tqu51f7 lhl7 auouch it with a knife blade without disturbing thh5uaf1l 7u7qle motion?

When a standing wave exists on a string, the vibrations of incident and rlg na 6,m.-7 uymmtme2eflected waves cancel at the nodes. Does this mean that energy was destroyed? Exemu l ,ga672m m-.ynmtplain.

If we knew that energy was being transmitted fro40:whs d un.b2vb;zyir qs- -om one place to another, how might we determine whet ny0dbo;iq:z sh-- urs4vw.b 2her the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHMbb o02y4q93c i60t;5j t n(u obldbj/xnkvsl( with amplitude 0.18 m, what is the total distance it tra;dvn yun60 x(934lb/(ot5c2btl sbqo jibj0 k vels in one period?    m

  An elastic cord is 65 cm bw 92 j)j*p,4mpwa/b2rqs ythpgo5 3plong 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 of9 )ty agop bj*p52hqp/ ,w4bp2 3jwsrm this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68 1w4-noq5/jdc iqlcxq2c 3snd: v,ts8-kg driver gets into the driver’s seat. If the car goes over a b/ :ci-lqqd1ct3vnjw,xsods2 4q c8 n5ump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 7 -+ zdj1ffmvqwiwt91.i ) rjynt x 3tq3b8q5pcm when a 2.7-kg fish hangs from it. (a) What is the spring 91n.qf+ rftyj5 t jt)qii1v3 bx7p8mqzwd-w 3 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 f.xxxcn/on j13 :5 zpffrequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs nfj xx z5n 3p.xc/f:1ofrom it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times t kky(,y*cti /j xwq0jfsx1 g*5= 0,t f(,w jtyxj0*yq5/kk sc*g1xi = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 sptn bsq/wz:;2c;* .,o 8wduesc (px fdaider’s web. The web vibrates predominately with a frequency of 4.0 Hz. oaxbsduz;, n* /ws2:cdwqe(c8.f ; pt
(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 vibzgjh o+;e vugeiy1* ;c086 kvlrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, th +* g8z vekgoy1h;ul;jve0ic6 e 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 second73 q prtrqfxrccj*7*7 with an amplitude of 0qc*p7 q3rtfc 7r*r7x j.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 the speed of a SHO half the maximum va.;k2u udevf g5lue?ue5 2dv.ufg k;$\approx$    A

A mass attached to thg2suqt 23y hg2e end of a 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 :4x uffeh: un6q*p/prvertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position againp:xhf p6e4/u: u qnfr*?    s

  An object with mass 3.0 kg is attached to a spring with r+1h6qe)vk ezspring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 01zheq+kv er6 ).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 popgunfxo,)d g3kpuibjnwlb48* +o9 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gu gpx,iu bo*d98w4k+bj3 ln f)on?    m/s

  A mass sitting on a horizontal, frictionless sr (vdqv 7+3qh4xm(2 sona.z sjurface 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 h4 xo(+ .qsd2v(zvsan37mrqj is released from rest with the spring 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 vibrates according to the equation x = 0.40oup cm x*i*z v) p5q9))uzgyr5cos6.4t where x is in meters and t isu9 )z5g pv*)m0zq* yr) ipuoxc 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 ,-d r d rvo3jgal(n.h0jib8w*equilibrium is the energy of a SHO half KE and half PE? r3i8jlgbd hr dwnv*j.a, o-0 (±    A

  If one vibration has 7.0 times the energy of a f+h*cv4 beiv8 second, but their frequencies and masses are the same, what 8+ *ihc4vvfebis the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from (p* rospt,i:ha vertically hanging light spring once every 0.65 s.ppit*(,r :h os
(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 vertical springs, eachh/ z9xuynuyd,a):-y u +l 4vun with spring stiffness constant k nuhndy xu9+y4 aly,z v-:u)/u(Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5fw2i: i mqwq3ax7i.c*t where x is in meters and t is q3.fiwamixq2 7c: *iw 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 of SHM, labeled A and B. For each, what is u62kknb,5yulg 1u +yv
(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 ,r)*8go9oslzhbiac 27+i, h; zmwyqk (k = 124 N/m) is struck by a hammer, which gives the mass an initial speeiic ;rs,, q)zhm72 89hzwo+klb* agyod 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 vibrates18t0gx+ 5j gv uowss8 7ad)aej with an amplitude of85ja)8v+xa10es utwsjd g7 og 28.0 cm when 0.260 kg hangs from it. The 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 spring stiffness constants n ebed0 -wp1g5hxu3i 2$k_1$ 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 strikr 4jfe ;*f:smu 0cajw0es a 0.600-kg block attached to a fixed horizontal spring whose spr0fr amc*ej4ujw0s;: f ing 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 reachinjw ,plfn;w 8mvn5i7 0l numpw8tuq,,7g his lowest point, he o ljq wm0m,;p,ufwp 88nlwu5n ,t7n7iv scillates 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 vibrations ir*tg(( x1eb8p u ph .dnppk)8wn 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 swgl6n +vyu(i:vdrcv j 6rlr 0y ju,31z*ing per second? (That is, one complete vibration takes exactly i* +rjgu: ( nvyzv6u 6 13rjl,yvc0dlr2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, we9i;-jyk8 qh bhere the acceleration of gravity is about 0.37 that on - b h;i9qk8eyjEarth?    s

  What is the period of a simple pendulum 805ws, mzd1 m78clkr)tf 3b jza; cm long
(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 365 gz*-q8f : t2clfyajl ;krams, and it is rz 8fkt;q2lly-c*f:jaeleased 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. If the cl vy7te :jkeh*.ock loses half a minute per day, how should you adjust the length of the pendulum? t.:y k*jehe7vshortened by    mm.

Derive a formula for the maximumv-6w m8zkm 3iy 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 frequenc 2-ind ewjcp *d-7w kbrv0,9y 4wvgf+ny of 2.5 Hz. At it is released from rest starting a7vwr4+k* 0 y wjwbf9-cpnevdd -,2nigt 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 of his anchored bj ldo( onq:+l9smvu 1af/io/ fqx3a(4oat every 3.0 s. He measures the distance between two crests to be 6j3afs(o qdo+mi llqou4f/ av nx19/ :(.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels io;sot8gh.om tj+r95 with a speed of 343 m/s How far apart are the wave crests (compressiono.9tt5hr;j8gi+ osom s)?    m

  (a) AM radio signals have frequei3 bx e 3pfqvxy.(4.a(db,hx qncies between 550 kHz and 1600 kHz (kilohertz) and travelyq3 p eaf 3xvbqx.(d(ib.x4h, 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 wavesw 4) yqwu qce3-4hqu,z 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 the*ljzvx/6 ,g tz other. In which rod will the speed of longitudinal waves be greater, and by what facto/g,lvz 6*jt zxr?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the t ebx+ti;rqc n3mqw3.6 a/aks9ension in the cord is 150 N, how long will it take a pulse to travel from one support to the other?r x/6.w mc qa3at3b9 iksn+qe;    s

  A ski gondola is connectedupmdd*vr )*s 2 to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes t)2udpv*sr m*d o 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 r;ddb1yyj*, nthe sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the oceann; *ybjy1rdd, at this point?    m

  P and S waves from an earthquake travel at difiuwxm7bqi 7akl8 rio,,2 kebu8/ 9 qf+ferent speeds, and this difference helps in locating the earthquake ,k 8 / xe 7ifbri2uai8b ol+qwkm97uq,“epicenter” (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 surface wave can be approximated by a sinusoidal trad) (+3 h*rt h:mkqnkyinsverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of dy3kkn(+i )q*r:h tmhfrequencies), 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 an9/vpuz9s1vs 9 igl6p;;be llz earthquake P wave passing through the Earth and detected at two points 10 k9el9vzvu zsp il6 9b;;p/gs1lm and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing tg8fq ct -8qkrf78sk3ao,u bv*hrough the Earth is measured to be 7,*ftr8-agc 8vuk8s3o kbqfq $ 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 frequency5ks hhhm5hop+ f 7a)/oc ,gc m6uddu:3 travel through the same portion of the Earth, but one is carrying twice the energy. What is the rau upo5schh/h: +)35o ,dmdfgmkah6 c7tio of the amplitudes of the two waves?   

  Two waves traveling along a stul82w7xyq0ytujrb6 h t2. yb 7retched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplituttuwr227qbx 8 u y.l7j yhby60des of the two waves?   

  A bug on the surface of a pond is observed to move up and down a t n xi cgw,piaank;;i1zw 9zx/88pu1(notal 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 does the bugz9aiwin8k,;g 1xp;i n8(cuaxwp1z / n’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving6(qle f o5 yj/m*nnpe0 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 momoq0lnj*6npyf 5 e e(/ments later. (c) In Fig. 11–36a, at the moment 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 e ngpy3 ddvt-2s /j7pok +vcv;e m5q):frequency, what are the frequencies of the first four harmod;-t3e+ 7jc5 /sgevoq 2 dkppnvm)y :vnics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 27 a w,; 5hjzi4dnlrx4eg6xut294 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 vibratesx4e;2nj 4l57 ,dr uwaxhigzt6 as a standing wave.)    Hz

  A particular string xybd f 8;.h(uu7h+*lqx u 3nmrresonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at whic.8u um*;h+h3 lxuydq(nr 7f xbh it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of wave v3dln669o; e9rhmm -s 5hiu;vfg.ycws on a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adj;r;5wl6eh9.hvv3ynmcs gdi- m ou6f 9acent nodes?   m

  If two successive overpo r5xo6 m)gy6rm d-1lwtz1u/tones of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamental? om rutx61pd1 low m6g)5/z -yr   Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. tf: uu2,jv7s(fb 5z mil jfpnnh1p,88The 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 f(8,5zj7f8f2, lhsunupm 1n:tbijpvand first two overtones?    Hz

  A particular guitar string is supposed to vibra /i)y/bi-lljs /ikb5 ete at 200 Hz, but it is measured to vibrate at 205 Hz. By what perce jiiy/klb/-bsi )5 /lent 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 Hl: s+7a::hpu cm*rnr zz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? pn:scr +au: 7z*mh:r ldecreased by    %

  One end of a horizontal string is attached to a small-amplitude mechaaegpx(7f*9x+bz ) rjanical 60-Hz vibrator. The string’s mass per uafe r )z97xgxa(pb*+jnit 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 abr 4jdqij0x8 a.uy.2 0v5fbq of the string 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 between 10 cm q.avd bji2ary bj0f4x8u.5q0 and 1.5 m?   

  When you slosh the water back and forth in a tub at y5iy3m zzn.g5yn k :k-just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wavmyyykn-5i 5ng zkz: 3.e 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 strikc+kjcik4/; ckg1 dbvr8 1a 4*vhqa tt,es a boundary within the Earth between two kinds of material. If it approaches the boundary at an 8;c ct/*,ckrg4v 14v k1qhibkjt ada+ 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 8c k4o 0gj*b32mgzuc m“shelf” where the velocity changes from 2.8 m/s to 2.1 m 32c0mck*gmgou4z8 jb/s If the 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 of cold rwxh0x7 zrr1-, dense air. If the sound w7r-xrxw 1zhr0 ave hits the cold air interface 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 boh-dkbg * vb (ky 1m-lwt0i8ah,undary between two types of rock at ah tbbk 0- *g,-wyi 8(hamv1lkd 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 diameter. Accordik vmht4lb8r1.ng to the user’s manual, the dish 1l.tk8 4vh rbmhas to be pointed in the 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 and velocity 75 x4mx-.9 k:nol 3xncjd0 km/h travels across the Pacific Ocean. As it ap3 locdn -jxm:xnx9k4.proaches 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 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 conslj2i wj k1jeo0ozoh*si47o, (tant of 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 conservahk ze0l,7oooi4(oj 2js j*w 1ition of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which4; 4vaplthnk 8 stretches the net 1.1 m. Assume that the n4ntp4; av8lhket 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 the end of a freely hanging spring. The mass then 8a(( /quoyzorfalls 33 cm before it stops and begins to rise. What is the frequency of the oyzur(8( /oaq oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–5f1 7e hzay2a2:pr xqv64), compressing the spring 5.0 m. (a) What is the spring stiffnexy2haaevz2q 7rf: 61pss 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 8 cm) at ju.c g; ,pgx m qdb j72u95u6bidn)5vcnast the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over tb9u .gcup;7dd )mn i52gc6 qa,5nbvxjhe top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certatb7s :;ia 368p*px wqtxvygr7in groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the souray *ip t7xbqt7:w;gsvx86 p3nd emitted?    Hz

  A 2.00-kg mass vibrates according to the qkv)g97+ twhm+ 4p f*ayhbd;, 0niefn equation x=0.650cos7.40t where x is in meters and t ih* ny0en tma ,4v)++ 9gd qwkpffh;ib7n 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 frei.wh,ilao jj- 0lrlp:m3-0vq quency if it accelerates at qi -i0rvl-j.3 a jll0, pm:ohw0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a l ch/wcs5x *yy)ake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he h )wcc5yyxs /*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 at 3q s j5oh.f*a2/ji ;;bqx8zgxve 6 0crb92 Hz (G) and 440 Hz (A*;r/g. 8vbe0bo6 2hq; xaj xf iz5scqj).
(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 ownem8ur,; ,pdo0c 8ap8 t9cy p f.(vhxf 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. (The frequency is the same itvx,.eoac8 h r 8wcmpy0, fdu;8pp(9nn 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 of each pr6gjo+cm 1gk1 nn( c+v qfc870o bjs)kzjn .k.gong moves 1.8 mm to either side of center. Calcu. 6cv+8n (1cg 0n kkob jc1ngg+j).7mkqfsjozlate
(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 frequency 1.5 cyclevrc g0jpj9cz4 yv/)5ws per second. What is the maximum amplitude05)gvz4 rc jy /c9jwpv 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 attf ;dt.5xtpgo(6bs-f .cn( ulb ached to a ring that can slide without friction ot .fxg6p;(t.f( -nblu 5sdbcon a vertical 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 xo(s)t-zwou 2 ovaqay+e:63 v a period of exactly 2.000 s — each one-way swing takes 1.00 uwosxq+o3ev2- )6aavzy :t (o0 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 direc xm0n w qyw5m(p 0nha)rvn5ic8p4 v(o/tion 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 the period of the horizontal swings, andp w cro m )qahn0i54w/xyn8(vvm5n(p0 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.h w-8mtw.onz(o;tso a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will(too. nh8t-w;om wz.s the two pulses first meet?    m

A block of mass M is suspended from a ceilingq r(+1t4f- g*kdud qtc by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the mt f qru +qd(*tdg41-kcaximum 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 1200-kg car at the junkyard.zovp udo4h.fe3 uzs;6t k(s/7egn 2 6q The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at thvz ; g3s6u7dn( ke2oo.s t6zpq/4f uehe 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 (whi+ztrl+)lmc 7/cq9u-g m2r uemch also gives the dimensions of the block). You push it si)+ em q/27ur mzcc-r+mtul9gldeways as shown, and then you let go. The jello springs 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