Give some examples oft1z53ifilf 36ebb)yi:++pxrp*roc g wg*-mn everyday vibrating objects. Which exhibit SHM, at least approximaf i)c36+w**-+pmobyrgfn1lptxri:5g3 i z betely?

Is the acceleration of a simple harmonic oscillator ever zero? If s-7n.un/5id (cj + snnnogcp6no, where?

Explain why the motions ,p)9hyp1agn of a piston in an automobile engine is approximately simple harmonina p9yg) 1,shpc.

Real springs have mazkfur9c- 0f o5ss. Will the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized f09r o f-zuck5massless spring? Explain.

How could you double the maximum speed of a simh jt2apc/;zl *+ 2bzymple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical sprin.n n,o+ 7s ooej.y;wfxg scale, and then is rel.feyow sn,. 7+o;ox jneased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain gwmm/v/ p8mp4vvwzs n,o:5+k or lose time when taken to high altitude? 8,/pv+skw gmn/ z4pmv wv:mo5 Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). H/t rxws49ia6l ow could you estimate the height of the branch using only a stx6w49 ial s/rtopwatch?

Why can you make water swlboo3(*l *ar5 su;izlosh back and forth in a pan only if you shake the pan at a certain fre*ob *wzoil5 (sl;3ra uquency?

Give several everyday examples of reson ry20 mh6i*crfance.

Is a rattle in a car ever a resonance phenomenoncufi ;zg(z*g;8nx(y u ? Explain.

Is the frequency of a simple periodic wave equal (x7er om qokbj.. ogu ll(dmx 5w)90o0to the frequency of its source?j 0ourl q0 m g.o(5x7ekw o9(x.oldmb) Why or why not?

Explain the difference between the speed of a tra81k*ke4q4870tz:i axwx bd u0 stw sagnsverse wave traveling down a cord andwteg7 8kszq804*atxsud0 i :kb4a w 1x the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes lj 6p45qpq x+gitp87 vaz i:9p,pz n5lon a piano normally have wire wrapped arouvz q 6+l74j p tnxl5 5igp:8a9p,ziqppnd them?

What kind of waves do you think willq1 8il:5z ihye travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally 5qi:8z1elh iy parallel to its length?

Since the density of air dec))x)ol8n qd i,prvvs -reases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would yo8vodp) rx) ilq)-nv,s u expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they zr35q9bb1opne k)a (wtravel away from pkr)b aznb51 9woq(e3the source.

Two linear waves have the same amplitude and speed, and otherwise n7/ iov n4wy v3giq)9e lony21are identical, except one has half the wavelength of the other.g9no3 2w velqin) /n741i oyyv Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two se ps cl6*8hfh+mctions of cord as in Fig. 11–33, the frequency does not change (although the wamf8+ 6 pshh*lcvelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you couldcc*(2bcogu9dky5 zq 2 touch it with a knife blade without 5 9gdycccq22 u k(*zbodisturbing the motion?

When a standing wave exists on a string, the vibrations of incidnu2t 8eho27xp1(mjb vg4 i ox5ent and reflected waves cancel b 482imo1 ogejtnp(5xuh vx72 at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy watk1foynj(* r;b o:ks7s being transmitted from one place to another, how might we determine whether the energy was being carried by particles (material bod1* t:krbo;sn k7o (jfyies) or by waves?

  If a particle undergoes SHM ws4 bmpqqjtp,:jcqz0;qc k-f d82+ a2pith amplitude 0.18 m, what is the total distance it travels in one period?dqqm4+qk0tppc sq-z2c, j 2fab jp;:8    m

  An elastic cord is 65zi h -j*.e3isn 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 “spziijne*- .3 shring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car4qczgo y+d6fmwk50v qg y m;35 compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of +yq03vz5 dm w gy4 qcm;5fo6gkvibrations?$\approx$    Hz

  A fisherman’s scale stretchesk ,j 5 ae3ln ,ltm0a(q9btjl3f 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffnal3mqtl 3t0 jf9a5b( jlk,, eness 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 fhv.d owxa.k 81zn,s1yupb *xl(/fj1c requency 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 from it? axony,/ (vlxj1 *sfw1pc1z.kdu8 .bh    Hz

Construct a Table indicating the position x of the mass inacy vup7( e0a* Fig. 11–2 at times t = 0,t(pveua0a y7 *c = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 m3ad 0q( *jl*r xfmdo+is caught in a spider’s web. The web vibrates predominately with a f0dm*j(3fxd olr m +a*qrequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a fre) xiq-lryi(l( k/lu-7kln k(mquency of 0.88 Hz. When an additl(k lliklmyn--7ui)x((/r k qional 680-g mass 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 spri kyn20j,* -ygvsxfc;65*foam m r dww6ng vibrates 3.0 times per second with an amplitude of 0.13 m. Determing,m;f56vx woj* yc- y 6 ms0f2rk*dwane
(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 equilibr ,p 56ug p/abamv,n 3fd:l*kvoium is the speed of a SHO half the maximum value 5oak3v dp lfub6,:n */,pagvm?$\approx$    A

A mass attached to the end of a sp 3whzjnnu (r)k( )f2qaring 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 spri*8 m-mmjhs0eb y2mth*ng is stretched an additional 0.130 m and released, how long dbej *h 0mym* mhst2m-8oes it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a sprinja f p fxjd**fc(b tf4byfoq-7, )u.*lg with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position*7bt4 xd*pfqfjcuob)ffj a(f*,y -.l , 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 0.200 m to “l/fp4* 4dmub3thl5oufoad” a 0.180-kg ball. With what sp4ofp5lm4*d/3 ftuu hbeed will the ball leave the gun?    m/s

  A mass sitting on a horikfr j81c l 3;6kyaqhu9zontal, frictionless 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 released968fu qhkkl;ry ja31c 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 xp/6b 9bapk 5iu = 0.45cos6.4t where x is in meters and t is in seconds. Deterpp6 b9k i/5uabmine
(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 equilibriumd(onr 9(s6r u573k t/oobcxks is the energy of a SHO half KE and half PE? 37/cr ts9o5kork x( (bou6sdn ±    A

  If one vibration has 7.0 timopvio y2l0s-a 9c5(x kes the energy of a second, but their frequencies and masses are the 9k ca02lxv5-os(io pysame, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from ab z0:,5qcukln vertically hanging light spring once every 0.65 skz ,50b qnu:lc.
(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 identt,x l-wvlf*.w ical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration? ,fwwll* v t.-x

  A 300-g mass vibrates according to the equation x = 0.38sin6., ym(fk o:wv/hr 43yoqb;) lhoo sfr:55t where x is in meters and t is in seconds. Detew3hb f hv/4()olmy5 r,:ro oko ;qsfy: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 SHM, labeled A and B. For eai 0(:qd +yydbm 5di-qgch, 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 ho4re iudn ;z59wrizontal spring (k = 124 N/m) is struck by a hammer, which gives59w rdz4ein ;u 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 stiffness constant 305 N/m vibrates wit*est s7ms*;rg h an amplitude of 28.0 cm whst7e* mgs ;*sren 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 8ns(hrxigv,* to two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a;o6 ytk l:z2d0c-getf fixed horizontal spring whose spring stiffness constant is6tko0 e;yt f-g2ld c:z $ 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 juxmjquf 7 a.pr (sgpv.8(xy* *mmps from a high bridge. After reaching 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 t7q*r.(p8 uv.m j*sx afm gpyx(he 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 in exactly g2hz3f4 lvsszyx5+ psy 3:lw460 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 per qrq d,)48 ca*ykubq 5txwdc+1second? +yc,*qk8d xu41 b5wacr tqdq)(That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on r.ru 5a07va6w lvet0fMars, where the acceleration of gravity is about 0.37 thata7 r5l.tfu0wvva 6e0r on Earth?    s

  What is the period of a simple pendulum (1ob:rio 2 z/fijsos)80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple p*vuit/k6vrjf3 oh g)7endulum is 0.760 m, the pendulum bob has a mass of 365 grams, r367*ijg/)u k hvotfvand it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If nea9 ookt7 (kjr ;4w(zthe clock loses half a minute per day, how should you adjust the lengtkwok a(o4 9 jz(e;trn7h of the pendulum? shortened by    mm.

Derive a formula for the maximum i mu ,jmvh)e.*w)5g:q icly5 cspeed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillatw ;nl2trmtk:9pb ln28 es at a frequency of 2.5 Hz. At it is released from rest starting at tn m82n2p ;lwbrlt 9:kan 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 m k-.k 9p qq9r4v9ccpm:ln sw;his anchored boat every 3.0 s. He measures the distance between two cre99m .9sk 4lw- vnqq: rc;ppmcksts to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz an2.3cr2oux)s l )glftfd travels with a speed of 343 m/s How far uo )r)gfxt3fsc2l.2l apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohen,hzqxn* c fb *ekm0y3 71/gedrtz) and travel with a mcg1d 3fzxeh*7/0 bny*eqn ,kspeed 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 ofwh40 63lql-yjbjgj 1h longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same el1xj(pn 0bgf3 ;kx.taz astic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be k j3gabp1.fz ;xntx0(greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart.8.pl78:y7g shsbcpin3 gf/ mx If the tension in the cord is 150 N, how long will it take a pulse to travel from one su 8fgc.ssi7l7 xyn/ 3p bm:pg8hpport to the other?    s

  A ski gondola is connected to the top q7 :oysvuc 6j5of a hill by a steel cable of length 620 m and diamety 6sq7vo5:cuj er 1.5 cm. As 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 h )ke cz9 od5*n34 dzgiip8pcp8is ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directlyg*p8p4 8d5)d3 i cpzinokzce9 below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from anl*/e36 a 6vxlb9hmgiw earthquake travel at different speeds, and this difference helps in locating the earthquake g9vb/wh*ae6mxl 6li 3“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 wa3s1 .pxd6 sqciii,ro3ve can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of freque3s. qp3,cs6rxod i i1incies), 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 :efo(1 pb yc-s(b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km -cb: 1sop yfe(from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is mr9vp efg(6g4y easured to be 6y9vrgp4ef g( $ 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 a+ 7erz .nx;:s1y;jxxk t9 sj+3hgrog of the same frequency travel through the same portion of the Earth, but onkj+hxe n :7 jsry9. xgtogr1;zxa;s+3 e is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a ss4/libn o8u (:d62;k nzzikva tretched string have the same frequency, but one transportsi: vi(k42 ;kunzonb/a d8zl s6 three times 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 eiev m;6dvef17 -;h-hq9k ny :*ksz9+nxiy iwdown a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s +ivfk ix;:k9eh s*wh -6;e-yiqnd yv97 mnze1maximum KE change?   

The two pulses shown in Fig. 11–52 are moving to3p s6bz kt5v(54e(eqi 6wbf.ib8wmdg (1zpli ward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass eac1m(3z(5w5l8 ( vqe ppdis6ifgb4 btizbw ke6.h other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hzt77e 2gihbhe 2yji9 8x as its fundamental frequency, what are the frequencies of the first four har 9eh8 72e2hiy7gjtbximonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency wl j3 f00z5as.fv-pbhmill it vibrate if it is fingered one-third of the way down from the end? (That is, onl3lm ps-00ah. 5f fvjbzy two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at 62tlthm: 2t *sawe ts8 83yiufle68stysh aml2i2 u83wtft*et: ast three 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 the fre 0k975evd dbj u*ocn,hquency of standing waves is 475 Hz, how far apart areodu *d ,0bk9nehj5c7v two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, wqc-ul nlk8 m.4hat is the frequencnu ck4ll.- 8mqy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance s5bt.9qb4 llkskz-2 a 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 ov5lk2bqtsas- .9zkl4b ertones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured 4 .y2* dycpeauujj ag8c1-o 7yto vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three -jue8yj oya 71yugd2ca4c .*p frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar strik;u k4t /u*yrlk1sbhric(: q*ng is supposed 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 frequb qry ;:*ckkksr41(l*huu/i t ency? decreased by    %

  One end of a horizontal string is attakhzh+g9rxctdk;9up 175rv .gmis5s -ched to a small-amplitude mechanical 60-Hz vibrator. The string’s msiv+7p951m hgx;c-s5k. g ztkr9uh rdass 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)7 96).vqd h gwmrbpxm the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, howqmxgp.)d rb9 wm) h7v6 many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the )z ,h9hvv pbt9right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produp9ht,hzv) v9 bce 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 tun/, 4g.e23a b aeg7x/ omhpxw 4y/kfaraveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle mn74faa /u xgxk.g2ohpewae,/y/3b4 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 unden7y: a1mll ejgt/y9*a rwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests m/e9m*jy7llt:an 1gay ake 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 :ikei)3j f an3hits a layer of cold, dense air. Iff:j3i 3ekani ) the sound wave 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 earthqh,b7gvxuk e ;5 s4ua+g( ,qbibuake wave strikes a boundary between two types of rock at a aek5+,xsgu7b vb i(4,uqhbg ;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 abitg(go 0o7gjyn 1dx-*t)n6edout 0.5 m in diameter. According to the user’s manual, the dish has to be pointed gng) yt6di t* (jg 71d-oxe0noin 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 velocl l/jk0qw,5w gity 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 h/q,w kjlg5 w0lave 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 buq(t5o afp,8* yu4dowgmper has a spring stiffness constant 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 5goyaq wf8o,(*put 4d (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to ab1mtr04t4yh7 4cqekg fire net 18 m below, which stretches the net 1.1 m. Assume that the ne bh mry4g0k41t 7tqce4t 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 freelyv 6jzm r34pg9 .lptmx0ne)+ue hanging spring. The mass then falls 33 cm before it stops and begins vem36e4nm +rx0.pl ut jpg9 )zto rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–dp22itflk ,h2 54), compressing the spring 5.0 m. (a) What is the spring stiffness constant 2lk 2tphifd2,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 justjc5y9+if30k ze9,e s:qw czh g the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the tofgc hkc5se:z9 i0q+ezywj9, 3p (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the centerx. r8c3v mh b6 jr,kj,6vj;bhq of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the;vb m.b8rck 66h j3,x,jqhjrv frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is inkn pf/5v7nh/xt.h p h) meters and t in seconds. Determine vf h/kxp75p)t.h /nnh
(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 osciertju(-8l8/6-lg -gx ublfyy 9 bz 7aillates with frequency f. What is its frequency if it accelerazg/-8ui86yyajxetb l -gru l-bf( l97 tes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats o .gm;rh 0vei6m:bopr8 t+z.non a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps o;m0tm:nz 8ir h.+g .bo vpore6ff, 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 ins6 a7cv7y qb4mttrument are tuned to play at 392 Hz (G) and 440 Hz (6tm774y cba vqA).
(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-paa8e opa3,+-,yq wp*l)nnj hkd rt 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 ligh8o,y),aq p3+*we hjlkn a ndp-ter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each:eq8j lbg48zx prong moves 1.8 mmg:8 ejq z4bl8x 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 oscillatesnsxpm9 ) tabl3g.w *,1jo hi0t with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during then w gl 30*1o.p)hbmaix9tjs,t oscillation?

A string can have a “free” end if that end is attached todq o9watcn 2b3t-7 fhis1+l2kb0ft7 r a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of 7f2i sdrokqln7 ba2+9 wfc1h3tbt0t- such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-wag0h) imf y;71h gqc22maih uo.y swing takes 1m1qyca hg7fi gi m)h.h20;2uo.000 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 20co,fa/j or yc 3u xuu:u cuq)h,9m)bor can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the perio9x)r ym ):uaccu 0u,3hob uo,qfc u2/jd 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 under a tension of 255 h iv 149bj*qqr0oh ajct g2n72N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the tv0jqho9bc r q 2*2a4j nt17ighwo pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with dxxlz nq3c.+1vx* q/q spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations thlzq/ qc *1x .xx+q3vndat 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. Thgdrpcwsg(fqm//6now :; f )9x0tuo f7e steel crane cable is 22 m long and has a diameter 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 (/g:mrptof7n q)6w fo;9 /gc sfwx ud0to Table 9–1.]    s

  A block of jello rests on a plate ;4w0axi0/p 0kf7tekxlw,iae as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulu4i;w 0ikxe, 0/tp7xwk lfaae0 s (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz