Give some examples of everyday vibrating objects. Which exhibit SHM, at least e:,+d. +yjfi/anriol appj+. dly+raone,fi/i: roximately?

Is the acceleration of a simple harmonic oscillatoru2(bhb/ l f9ua ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approxygc6 v))++f ovifg+obimately simpl6cg)off+gb ovv+)y i+e harmonic.

Real springs have mass. Will the true period and frequency be la0,kyln0v/ax0n epxp6rger or smaller than given by the eqlp/ xn avknx,ye60p 00uations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of ae rw/2mgq 53qmrhl6d9 simple harmonic oscillator (SHO)?

A 5.0-kg trout is attach(gz, s7*rqtcfphho7 )8 gfth-ed to the hook of a vertical spring scale, and then is releasedg8h-fzhqf*,trc o7p7) hgst(. Describe the scale reading as a function of time.

If a pendulum clock is accurak7ig hi.yk i2se z-yw4* -0znite at sea level, will it gain or lose time when takhkz-iw*yz i2 i k70s4.n gi-yeen to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48)428s/ uzlu:i *w ihwbzj0eno:. How could you estimat:zo: ueubs i l*zn42h0w8/iwje the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you s6iwr9*/ liax3nb fg9 ehake the pan at a certain frequency?6 i9i9r/xe*f 3 walbng

Give several everyday examples h ,4* ymatyubxw8q0z)of resonance.

Is a rattle in a car ever a rjiiu46y -vh j)34r7 kkni3yl2xa:ea pb x) 6waesonance phenomenon? Explain.

Is the frequency of aeprr1e) ss5 a) simple periodic wave equal to the frequency of its source? Why or why nsa 1r5e)spe )rot?

Explain the difference betweujlt0 s8iar kk70;wc jtvl,22en the speed of a transverse wave traveling down a cord and the speed of a tiny pielwl sj8ik22 k auc;0 j7,tv0rtce of the cord.

Why do the strings used for the lowest-freq:qs qvm.ux5u*uency notes on a piano normally have wire wrapped ar:.q5 uxvsq mu*ound them?

What kind of waves do you think will travel down a horizontal metal rod if yht:- axtk2q) jou strike its end (a) vertically f):ta- kt xh2jqrom above and (b) horizontally parallel to its length?

Since the density of air dr k994j,y2 xyjxfnh0v ecreases with an increase in temperature, but the bulk mnr94kxy20hyjx9 fv j,odulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circularzp vhm69a/1 9iycaf,ws( phb- water waves decrease in amplitude as they travel away from the source9ab-,iay mp6c vhh( fwz1s/9p.

Two linear waves have the)zrz 0w +4h0y (s, bxuavea;te same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Whicbh,z(4+wzsr; ) eva0ta0ue x yh transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in xrbhudzkq e 2 y58i j3t8495fgFig. 11–33, db5yt f zj8xk4 529 i83quehrgthe frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could toc5x0tz1i housv8+ i4kuch it with a kniiv otk0xu8c +51z4is hfe blade without disturbing the motion?

When a standing wave exists on a q) wri ;i;,:0d idr2a ne-ewhlstring, the vibrations of incident and reflected waves cancel at the node-r;:2lwiqw) idd 0hi er,;aens. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to anothe;pn1;553k x xrar *phsll5hr njdt3ia; xre*.r, how might we5ie r xr5xdlnlp.x5rh**sthj1nra;;3p;k 3 a determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, dmr4bd49 cl1 lqjdr++ what is the total distance it trave+44mdl lbr +j1 dcrqd9ls in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs frpy *glrbr59 di51auu )om it but is 85 cm long when a weight of 180 N h biy51 5 duag)r*ru9plangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets in qjvnkh (31 aum2b**mbto the driver’s seat. If the car goes over a bump, what will be the frequency of vibratio b1qvbh*ja2k (mun3*mns?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg y6dcdl p+39jrft, t:w6 9ycfe2xk, ua6 dn.x zfish hangs from it. (a) What is the spring stiffnerdku d,x,nyfj6z6awf clt.9dp c: +xt329y 6 ess 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(gp mmukh41. an7h1ma.0 Hz when a mass of 0.60 kg is hung from it. m1g kuh(.aman h4m p71What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position xt*w m 5d)cmt:e of the mass in Fig. 11–2 at times t = 0,t = e* :mtm)5ctdw$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates aa6(b rdjtg09 e7vn4opredominately with a frequenc ngba4 aet 7(d60rv9joy 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 of1tk31k( nsoqli j**x z a spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added*itx( l q1kkn1oz*sj3 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 vibs4h rmstb9tls5nd+kgp8w4 95rates 3.0 times per second with an amplitude of 0.13 m. Detpg+w9nb4 9sk4t5 5tsdhl ms r8ermine
(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 hapz+3pi 01 w;psoqnc l-b j2.calf the maximum value? a3jplsqc.-c +iwo;p0 1 zbnp2$\approx$    A

A mass attached to the end of a spring is stretched a ditb *n*6zptqg9 sjy+y zm e6 77pv+hs4rstance $x_0$ 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 xxji gfb.f.k*a i-5) o.ja)ib 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does iokj-j* bfi)aa.xii .xb). 5g ft take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with sqf s(i*,sjek5w3swf/pring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium pw5s*ifs,f 3s w(ejk/ qosition, 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 80.0jf ;sq /an:el.gpf.0*-s rasu N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed wil*ar./fn:s.0f-sj e qg asp;lul the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is atta kk l9+5ly:a,exwnw7o ched to one end of a spring; the other end is fixed to a wall. 3.0 J of work is rekl o,l yka57xn9w+:wequired to compress the spring by 0.12 m. If the mass 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 uo9 sr 6oz4d a)b(4-sp bxw rr-a1u8ssx = 0.45cos6.4t where x is in metrbobsx8-s 4p1 aw r)us zor4a-9d6(su ers 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 ener;bc.vu1l9.hndq4 dkf x-, wsj gy of a SHO half KE and half PE?9sd. q4k uhjxfcnvdb;.- ,wl1 ±    A

  If one vibration has 7.0 times the energy of a second, but theiry*,.mw bezr j4 m3xi1p frequencies and masses are the same, what is the ratio of their ampl pie4j b1r,*y zwx.mm3itudes?   

  A 2.00-kg pumpkin oscillates from a wx,qykv6y,f7 vertically hanging light spring once every 0.65 s. v,wqky,6yxf 7
(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 ilxb at62 ov3l-o/1ycparallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrati2 llty/ -o6v3bo1a cxion?

  A 300-g mass vibrates accoknsd7,ioh x 5/hyl9np1ov(l. :g5dddrding to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Deter,(o9pv gld x1d5 s7yk /hnd.idhlo5n:mine
(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 e+ ,0xjc7lqjp0vqg8xvyb j w) 0ach, 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 hor);h c7i0dwzpe.o0bct; sl)cw izontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s De)wto ipw0bc e.;z 0cd);h7scltermine
(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 sprerb 7c/xm p* 5-efn7euing stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0fe5/ume - b7 c7xrepn*.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 springi wr0 mvc rn+e05oy/+ 7qx:vjf 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 tolv;nyci : o jrt1lrod,fi i d ;l(:k:83fky4n* a fixed horizontal spring w8 1n fi4yj rd:(:oid ;lkf n;yltor:vi3cl,*khose 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. Aftezdd p9 vnfr2j9 k98z zamb6a/4r 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 2n dp/zad9 vz2 48j am9fbk9rz65.0 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 in exactly 6 5+eh:8vj txry0 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 p+p s)f i16qlijgvrr +7er second? (That is,+vgq)r r+li61f jpi7s one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is itsi 4g2us* k64(j ipuvla6wn is* period on Mars, where the acceleration of gravity is about 0.37 that on Earth?s(n4 u4u2gvw *ii6kps *aj l6i    s

  What is the period of a simple pend44mr35wr:m z chpdmj 6ulum 80 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 pendulun41/33yubjru rtrl(f6z2 jb nm bob has a mass of 365 grams, and z23rb4lr3 n1jjuu 6brnf/t(yit 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 pendulvk6 *-nyyc/i pmi+ te0um has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shoviiy0-+ t cpm6y*/n kertened by    mm.

Derive a formula for tzi te0ej tng:nr4/o-z) 1vt c.he maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hzce1/ jq utb)i1-yap8 x. At it is released from rest starting at an angle oxtqap8c- ) beu yj1i/1f 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 u.2gwyh(w zvf :k8;0ooeugz zfh0* f2pass the bow of his anchored boat every 3.0 s. He measures the distance between two crest*g0foofekz. 2wfh;y 0g2z:w8vz(u h us to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air ha/qm9vax mv t)9s a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressions)xvtvm /am99)q?    m

  (a) AM radio signals havrkl 8wzwu;))e j))wi) tf,xj q(tmih( e frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed of )(muxit) z ifqww)wke 8jj ;r),()lht$ 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 lfyw wtu74ps ;l..l kw(ongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twi1slty1sf q5s ut7)u0dt9 ol4n ce as dense as the other. In whi)s51l19ut dssq7 tnyluf 0ot4ch rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg 5e 8zucw8n6 r+xsrpy/ is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to trav 56rp8ywzse8xu+n/cr el from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel c1(u5wk x1yhmcable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse 1 m 5yuwhc(x1kalong 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 h531 jscv 3ni *s3ovwohis 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 is the oceanc3*nv5hj3wsvo o1s 3i at this point?    m

  P and S waves from an earthq:mzd l*pic8t /uake travel at different speeds, and this difference helps in locatint/licd8zm* :p g the earthquake “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 approximtuby5 u-mmour r p 519(bu *ub75(iyfoated by 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 t1uui(yy b7uor9rb(-o5 p5mu*u5fb m begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, ac)v)5r 2rvlufnd (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 kv)vl f)urc2 5rm and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wavec+u b00i ydg+xq :eeq- passing through the Earth is measured to be - 0+yex:ciud qb+e0qg$ 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 t; rx y+ n+qw0zkf.9tsrravel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the ampl rwr;k+f n90zq. syxt+itudes of the two waves?   

  Two waves traveling along a stretc.h *tpjay /ca5hed string have the same frequency, but one transports three times the power of thajh.yp/ 5act *e other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed-ioc7:wq zrc d05dv(a to move up and down a total vertical distance of 6.0 cm, from the(o: 0a-wcid7d zrvc5q lowest to the 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 other. (a) Skva0 f /nt-x2sn xxxzpz9:9k(oetch 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 each other, the ao9znzx(x : x/ 0x9-vkfsntp2 string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, w7oqdyxln4c7 i4urss k 99/ z1hhat are the 7hkin194 4s9/r l7 ozdcxusqyfrequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frve0 kiu9 j.2w7qpa 7wfequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a kwqwv f20auije79.7p standing wave.)    Hz

  A particular string resonates in four loops at a freqm ):l: qlxetc:uency of 280 Hz. Name at least three other frequencies alctlm:exq : :)t 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 frequency o*//+1cszoesc rjd .def standing waves is 475 Hz, how far apart are two /dc /roz 1.ed*ss+ecjadjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whr twnymi-:x +b+n:lba 0 :os6uat is the frequency of th::+u yo:mnb6b xarn- +liw 0ste fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. ih-g)k3fvx8 /fzr1au( 7b2hmk k8s d hThe distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the rf3u ka bk/ms1i xhzdf(hhk8g8)7 -v2frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is su(nvguc j(qbso s:q74 .o g)*ifpposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the qsu sj(of) vgoi.bc(q4g 7* :nthree frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to v;c jq 0mkap6o2ibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent j20 c6moq apk;should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attache5i m-lfh * *ss*pxb*-rzl-sbwis ,s;sd to a small-amplitude mechanical 60-Hz vibrator. The s5m- f*bi;i - -sxh*l lr*wszb* ps,ssstring’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may ohz4) d;i -/fk. x3 n0swuscnsbe adjusted by moving the pulley. If 3 s. hx n;-wf ic4u0os/)sdzknthe hanging mass m is fixed at 0.080 kg, how 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 ju mrnn2ru t;uo4;aqn0)st 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 wave in a 65-cm-wide tub a )u;0rnnqourm; t4n2is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wavey9g +iy3xd d/3)ebcol iu8wi7 traveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an in lou y3i7dw)x9db iyieg/c+ 83cident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes froif1j-c ct j8m9m 2.8 m/s to 2.1 m/s If the incident wccjj9-1 8t mifave 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, denstll+pt ,iie: 2e air. If th2telt: ili, +pe 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 earthquake wave strikes a boundary between two types ofit bp:yrf5rc8gz-zw-v .r 0/s v:l7sf rock at a 35plfgvr v t.8:f- wy7:rrss/c0z zi-b8 $^{\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 td5aepu,8g6 *u 5 yuznihe user’s manual, the dish has to be pointed in the direction of the satellit ui ey5*8pda5gnu,u6z e, 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 aiczw2q 5h k473s:d;l9zr.lkfmn 4uqcnd 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 7ns z9hi42 k4ukm lcqfr:; cqz53.dlwhow much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m 2q n0 kd kva.+j9,e1tuhq1rvuFind the maximum compression of the bumper if0,2v1+vk q hqaur d9k1te ujn. the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire nmqe0s gaoxwq1m+ q l p8.,(2poet 18 m below, which stretches the net wq +lpqgq0 a1x82m,o( eo.msp1.1 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 the enq:)t +j335 v mhww 3 ricmy;t1xft;mgcd of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What igm:5 )3i;xhtw1m ;v3rw3yjcmtcqtf+s the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11, r5o /;i6hjrdyhd-tm–54), compressing the spring 5yij- m o,h5tddr;6r h/.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) a/w,2 iuyjfy+3 ;8ecea hxp in(t just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (F( yu;/ 3py8e2 i, cewj+hixfnaig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpmxy sy+-.g a(dw phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emittyad(x.s- ygw +ed?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x j +ump6 gms)jj3doj c7vt9a16is in metersaj71+guov9) 3m spm jjdct66j and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequeng42atbk j7y1r+s sm x+cy f. What is its frequency if it accelerates at 0.50g (a) u4kar+t gxby2s+17 mj spward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands onj)wh5s;ev1 gppriewugv: f; -/v3 .n e the raft, it sinks 4.0 cm wvu/:wpei-j h e)gnp3s 1.rfv;gev5 ;deeper into the water. When he 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 392 Hz (G) and 440 Hz1 irp g99h- oldl68hj6pq3elu:fnau jn:9h + c (:l 8:l93orhqp9npd jnfi-cuh6+e1 gl9 ajh 6uA).
(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 trave 1;( oyaf5t:6bxd+v9cidd xt4 wk/ iecling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of f:kcx5 dc6divw 4+o/y d1;e(abx9it tthe 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 Hz0hx h paj4jo(5l2w oje2kn5j*, and the tip of each prong moves 1.8 mm to aj52 l ojpx(20 o5hjej*kn4wh 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 frceanmo2,v wl8 cu: .m7y.au g /8:neaaequency 1.5 cycles per second. What is the maximum amplitude with which the end of .au ce:cg,a u 8m/a82:ne wm7oayv.nl the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached t,y c p .r4(,qmx oz(rvl el2j,,ws5ijpo a ring that can slide without friction on a vertical pole (Fig. 11–57). 5,i ,4x2opmrewp, rlj,l.cyq( j s (zvDetermine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — ear;s74)vl0pk hyyawqq z3 r3o+ ch one-way swing takes 1.z )+ wq3p7r4qlr;v h3o0yyksa000 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 d(a9gj09oo pm eirection or can swing as a9ap (j9oemg o0 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, 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 tensiep-eew43x(w(8z bhjg .. hzx bon of 255 N. A pulse is generated ahz-.e3xe (wgbxph(je z.84w b t one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sprin -d r n j ;:;mpwx*kq92efcuiqtn423 x+kjhle8g with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top o- +u2qtx3njic d;qjk2 e;w4x n9r8hpm:fek*lf the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane+t r4t4sgfpqk 1s8 3zw/axns+ 5ldsx9 cable is 22 m long and has a diameter of 6.4 mm. 8s9l st45t++xgs3w/f1sk4 rpdanqz x 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 shs;ja 9kk j e/by(5pwcsy 9ie56own in Fig. 11–58 (which also gives the dimensiojce95 ya; 9/y(pk wske5j6ib sns 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 modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz