Give some examples of everyday vibrating objects. Which exhi.dhypp+ rbr:4-t. fc(pepwv;/fb z ,3e bmm b1bit SHM, at least approxpb;-df t.b repv .hzpp ce3 b:wr1bf(+mmy,4 /imately?

Is the acceleration of a simple harmonic oscicgdh2o4-yjo k 4t3u z.llator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is appp,vl6ba a: 2b9a9q rlqroximately simple 62avr,q9alp l9qba: bharmonic.

Real springs have mass. Will the true period and frequency be large: r,lhb-v2rvewl) et(r or smaller than given by the equath2)rtwlrv,- el ve: (bions for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic osci( ffugf rhs4. 8rr;v h/) 8i.jmrrnsh-pcoa29 llator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical sp gos33.i(d apqbij: c2i: dlf4ring scale, and then is rel i:2db p3(lsq3.id:4i cof jageased. Describe the scale reading as a function of time.

If a pendulum clock is accurae f.: f wob,tgpv 9ql(9)ats/ite at sea level, will it gain or lose time when taken to high altitude? Whqpv) al t,w t.9ibso9/(: fegfy?

A tire swing hanging from a branch reaches*bni yw67,3vhxfsi 6i nearly to the ground (Fig. 11–48). How could i*in6f v6ihx3s,wy 7byou estimate the height of the branch using only a stopwatch?

Why can you make water slos l y,rcf20-,k3 iuiz:g 8kvydfh back and forth in a pan only if you shake the pan at a ceryg, lc2f83yui-ikfk rd,:v0ztain frequency?

Give several everyday exampletm:+p3 us *sy: )nuojns of resonance.

Is a rattle in a car ever a resonance phenomenon? Eas)km tg6((ycn+cv x 9xplain.

Is the frequency of a simple periodic wave equal to the frequencm /3cgxg1ebixw j::/ o*kws*q5i u+pcy of its source? Why or why n /mwxi**w qi31g 5ks xocgebucj p+/::ot?

Explain the difference between the speed of a transverse wave o* c)1+dhit fe0.hpc3 :3*xhjxfpz yw traveling down a cord and the speed of a tinyfhh1 e+ fi*3 :)3px.cojzpctd xh*y0w piece of the cord.

Why do the strings used for the lowest-fu1j,ybrg:i fg--fh 1 kip5/jerequency notes on a piano normally have wire w1fu-/b jh grik 5g1p-,fyej:i rapped around them?

What kind of waves do you think will travel down a horizontal metal rod iff/yhfuto+.q bon98io (/tyb6 you strike iu6o8qh(fyn/ob/+ otit9. fybts end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of h4q)pwm:ed.al0i+lk h ei 5d( air decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you exp. : +(lhlp40khdq ie wi)ad5meect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitus3n41r8bq:mk,m no;-bicjf8 a/aa nude as they travel airma1 n3 84nkuc/, j nomas:qb8;bfa-way from the source.

Two linear waves have the same amplitude and speeen :(rpe,gmk) d, and otherwise are identical, except one has h)eg( :em,krpnalf the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wavlf39 *qmcl fi3 (hc9wwe crosses the boundary between two sections of cord as in Fig. 11–33, th l9l 9h3cf(*miq3cf wwe frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in tp.x osc s4) cewu/h1(jhree segments, are there any places you could touch it with a knife blade without dw1)( xepcscujo4 s.h/ isturbing the motion?

When a standing wave exists on a string, the vibrationsqaor8pc) j)t3 of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Eqr)jaot)38 pc xplain.

If we knew that energy ) 76rxh*nqqi awas being transmitted from one place to another, how might we )n 6ixh7rq*aqdetermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is t2yr4iiq0 hkw )he total distance it travki yh2)rwq0i4 els in one period?    m

  An elastic cord is 65 cm long when a weight of1g iyff-76sot 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from ty-g 6ffi7 1osit. 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 d+0e(t 5h9zlqm7 po tffriver gets into the driver’s seat. If the car goes overl z9e7+mt(of0h 5qfp t a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Whp- gf3;ip mm i5akynj0,g(tw (at is the p np-am53gjwk( i,i;fm0t ( ygspring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz wlnpe+4, o2l.7 h0znql2y pbwwhen a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 w p 2+,neqlz.pn 0boh2l74 ywlkg hangs from it?    Hz

Construct a Table indicating the position x of thej8ggvn,l)*fkzm)( d+omz m 7v mass in Fig. 11–2 at times t = 0,t =zf oklmmmn8g)d)g( *j vz7+,v $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 caugh.z3n ujxtd/3*x e/f fa 4cz6swt in a spider’s web. The web vibrates predominately with a fre6.ft* z/3 dnxfxs /e uc3aw4zjquency 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 frequency of 0.88 Hz. Whehyt (ngjw 1x*0n an additional 680-g mass is added to m, the frequency th(gxwy * 10njis 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the envf4: 9omcd ;,unfrk5pd of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Detkc 4po,mf n:; 9u5rvdfermine
(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 equm5tmu.2r0bcf+ hv v2/zajyv .ilibrium is the speed of a SHO half the maximum value?/z jyvmc2ma2u hv05.tv rfb.+$\approx$    A

A mass attached to tp x1hbxmo.)q 2he 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 vertical spring 0.315 m. If the spring is str: hi5;butz fb/etched an additional 0.130 m and released, how long does it take to reach the (new) equi5u i/zh;fbt :blibrium position again?    s

  An object with mass 3.0 kg is attached to a spring 7e9nh+mvx2vk9v9tm (t m0jq .)ojbktwith spring stiffness constant k = mot be 9mtx79hvjj2n+v k0.t mkvq)(9280 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 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 0.20ol;n;fiy1 kt 4wik k:;0 m to “load” a 0.180-kg ball. With what speed will the ball leave kk iilw;;;4 tfn:1oy kthe gun?    m/s

  A mass sitting on a horizontal, frictionless surface is iu nv*ic vba/gb38)+z attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the sprb+vicz3i/b)v a8n* u ging 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 equal z77ms epf/pdkn h*zvpu v;n71+a )0ytion x = 0.45cos6.4t where x is in me 7smy0*k+u7p1np e)z7 h;dlvpan/vz fters 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 h.,zu ;3d (lcvmwq:tathe energy of a SHO half KE and half PE? ± qtcdh3 (,.;vwl azu:m   A

  If one vibration has 7.0 times the energy of a second, but their frequencies aop:6g z2ozt+j( q v9aznd majo z+q o(zg2ptav z6:9sses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hang ,yx9vu2vz1txg8l,3 t +4eb)muqswvh ing light spring once every 0.65 s. hu gym)vlsv,1e8vwb2u, t4xt9+3 x qz
(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 springss g ecu(rxwswi 6 0hd3d;5x.4j, each with spring stiffness constant k (Fig. 11–49). What will be thed ;x6 .5ircssh 4uxdewwjg0 3( frequency of vibration?

  A 300-g mass vibrates accgy.9wi )k5wkk ording to the equation x = 0.38sin6.5t where x is in mekkw.)g 5 ky9iwters and t is 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, 6vo,s0 biqyv8labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring m/hrdor3j(ky4fut7 2) ypn3 a (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed ofhd 3)2jo/3 rp4amnky uryt( f7 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 vibrates3e6 6l reiivmk*6j6mm with an amplitude of 28.0 cm when 0.260 kim6 ejkl6*6 m3e v6rimg 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 spe( tbiya-. n+urings, 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 fi3in- 9soa .xjnn3r:5hy.c zy oxed horizontal spring whose spring stiffnesshn5j3z. s-9ncxi.o yy:3o ar n 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 reachiz4f4o moaz2ssn*o; 1x ufjzrd1,on;+ng his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the *oo44noo fd2jxsau;m 1 szn+r;z, zf1bungee 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 p), r :8cayssiexactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be 69u5 misccjj3 if it is to make exactly one swing per second? (That is, o6 3u ci5jmjc9sne complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0ts0icwb (z +b zkd.2u,.80 s on Earth. What is its period on Mars, where the accelerc.+d2tu i( bswzz k,0bation of gravity is about 0.37 that on Earth?    s

  What is the period of a simple penduljha 7 y,u,f,l*bwf 90k: pk2rlbo ntf3um 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 pendulum bob has a mass of 32 a:vgfkw),ut65 grams, and it is released at an angle of 12at) gfvw:2u,k .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. Ie:ueh3i p6o*w f the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened by p*ieh o:e6 wu3   mm.

Derive a formula for the maxc08rcd ia4lhq k9r k g/2.qebk8hmzd 4((ese*imum 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 68 a*q(gpg cr1m d-yui2.5 Hz. At it is released from rest starting at an ai*d8rg-(ga1 6 uqymp cngle 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 boat ha84kf 3tav-iapue r +.5jy.ievery 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?hi ukj aa3-4r.8vy+pef5 i. at    m/s

  A sound wave in air has a frequency of 262 Hz and travels/ f-e(fjaom 3) yo9osq with a speed of 343 m/s How far apart are the wave crests (compressions)-o f qyf/jo(9oesma )3?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz ( 9t23 prya:ogfy4 z0ktkilohertz) and travel wyf o9tz 20rtpk4ay:g3ith 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 of1:*f6bs e6k5ns h fuhx longitudinal 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 tu ivb abm3g/;.wice as dense as the other. In which rod will the speed of longituabg.m/ 3vb;i udinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If f6+e d-g9nrns the tension in the cord is 150 N, how longns9e 6gf +-drn will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill jw9j q9fw/z)okl9xd( by a steel cable 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 along theljwqw)/99xz9(ojk df 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 jqfcj8jteme d9u4h1 -0ust below the surface of the sea. He hears tce0 9hj-demt8 4j1fu qhe echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake trpz+pmois pq /,7y-b3o avel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance tzm73p,q y oi-sppb /o+ook 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( -ugjgw-ei 1v+ -nw8v xhbc-z be approximated 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 begin to leave contact with the gw1- gg u(h+-xnvi8ebczw j- -vround? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b)4gvfjri d fve+*os- 5e 3b2k-l the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from i* f2 v5j-3d+revolebf-k4gs the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Em g5t :k,dbi2m ecn71idg+3 grarth is measured to be nt+irc g1e5,i3d b k2:mmdg7g$ 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 trac( d1)-oq zh6ig 2yugkvel through the same portion of the Earth, but one iski )hgu6-(cy dgq2o 1z carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string hwe3*zfwcr2; ba b. pi)ave the same frequency, but one transports three times the power o arw2.wpi zfb;be*3c)f the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a tot42a */aszdjegzz)l3c; i 7 x ia1zref,al vertical distance of 6.0 cm, from the lowest to the highest point, as a wave ;r,)fd23l1 g izxaczesae4z /iz j*7apasses. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. xqf)sogr 1 p3s /wyy)s/.ju, a11–52 are moving 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 moments later. (c) In Fig. 11–f/.s3 oag)sy1yr/qxw,ps j )u36a, 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 frequency, what are0ngyjsgkx7/(0o d zk - the frequencies of the first four harmonicszngg7-/ys d( 0jo xk0k?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequenu+umrq/b13 ued)(ku kcy will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrd )3urk+ub kem/uu1(q ates as a standing wave.)    Hz

  A particular string resonat)9wse1fmfvhd8o* uf*on 6s u*1sfnd7es in four loops at a frequency of 280 Hz. Name at least three other frequencies at whic 8hs m*1osef6n7n*f1)*sfvwfdoudu9h it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92,imt6p;b(ao1qtwa p*- (szi t0miy 6gm/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent ni,(a(aqs g;t- ty bzwto 6ipmm0ip*61odes?   m

  If two successive overtones of a vibrating string are 280 Hz an*-r egzm38o7heym.mf ai b(,v d 350 Hz, what is t.m*m ayfirehvz3(8g7o , -mebhe frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fr0 v 1l,pukbb,ltj vo3pqd-x3/om the bridge to the support post is L = 62cm and 0,b tb1x3u /v , 3vkqp-lljpodthe string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hm zc:c5ra t(j/z, 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 three frequencies ar /amcc (zjt5:re,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar streuq3 fy-o3a 9 r-ize z:ot22ysing is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shoulsy2t o a: rzf-9y3e2i3e-quozd the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-ampz*6cq jv 2:hxulitude mechanical 60-Hz vibrator. Th*v2uc qxjhz: 6e string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length 3 zl+vrv 9g-fy/0 gyam7b6 qpyof 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 achieved9g -abvym60+ qgpvy 7rz /yfl3 by varying L between 10 cm and 1.5 m?   

  When you slosh the water b5vtb(;d4. d5.1 incuxmq9druzcf 1mn ack and forth in a tub at 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 wave in a 65-cm-wide tub is 0.85 Hz. What is the s5fd 1( .4z9.1v5dncq idrxct;um nmubpeed of the water wave?    m/s

  An earthquake P wave traveling at ezzwtb6 7trz+2mi.ged0f (c(who :c 0k.0 km/s strikes a boundary within the Earth between two kinds of material. I(t:r0(wcc+.d bo6i2wg t0ze7 zzmef h f it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velochxhw- +,m- sgj2duj6 nity changes from 2.8 m/s to 2.1 m/s If the inci-jhh+6gn-sx dwm j,2 udent wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveli+i-4i1q toc bmjxzw o,g) 5:nxng in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at a + bj)cw-tq4ngm i:5ixxooz,1n 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 boune;km)f7smd ; ydary between two types of rock at a )7 dym;sekm; f38 $^{\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 diameej.4 3w )ohrn9;pl ly5 iaere/ter. According to the user’s manual, the dish has to be poinlnoew 5 jla43 ri9/;eph.)eyrted 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 veld*: nlompr2 7, mntwz0ocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea:0 m mwpdlz2,o7tnn r* 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 constant of 550 kN/m Findpbjtq f+q.i e; 3om.zxh 0:f0t the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/+;ih0fq f30pb. :tq.metzoxjs (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 192 ude:s/gpk g8 m below, which stretches the net 1.1 m. Assume that the ne9ge2 :pk/gdus t 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 xf6j.mcmzh /7hbe9a gf.3*a pthen falls 33 cm before it stops and begins to ri.amp9.c 3zjhm*/ag x6ffhe7b se. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compress2k+h qo94a kdfing the spring 5.0 m. (a) hq49kdko +2afWhat 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) at just tyz( u6jcg3pe+l im +3df uv./ahe right pace of about 1 step per a3vc m/egu3if6(p yd.+j+ zu lsecond, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograph pwqnu;k t7ob 911gw omil 7g,/record have a wavelength of 1.70 mm. What will be thnip9 w;wbq7l 7m kg,t1oou1/ ge frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is vk/ ou (g+bb-lebhk-aa; sld)0d ++ldin meters and t in suvald )/dgd-ok0bl ;(ka +blh-b+e s+econds. 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 wm:+ gosse .(fo pbe/q/f d ss-qse.a,8ith frequency f. What is its frequency if it accelerates -e .s/ (os/qs.+,pe fs bmga8f:qosde at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floahs((3z jesbw68sv(ol6 rc 3eyts on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vib6vszh e 3e8 (cjy l(sw(bos6r3rates 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 t +ywdhm a1 t6rvzbpv;8:1gn1vo play at 392 Hz (G) and 440 Hz (A)vm6van1tdhywrv ;zbp +18 1:g.
(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 of Fig. 11–33.lpf*arc-nxh v.ks) + l2y+uy4c q+xe , 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 in both sections. Why?) (c) Is the waveleng )* xl fy 2av+ku,.ch-q4l+yn+rpxecsth greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 2utp i--p33l;y),mgw8q loy bl 64 Hz, and the tip of each prong moves 1bqgpi 3l)-y3u wp,l;ym -o8tl.8 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motionp 30y9f6 z9k yjnhfro( of frequency 1.5 cycles per second. What is the maximum amplitude with which the en9 6 0(93kfyjn ryofhzpd 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 atj,m1o6ab 7b uy1ub;1pb 6-qcv qxl/jrtached to a ring that can slide without friction on a vertical po qm; pb6b j- /rcx1qlb1yuuo a6v17bj,le (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 hass ridze,7 wvaz2 3p1k lxdx9*3 a period of exactly 2.000 s — each one-way swing takes 1.01*9xe2 pwzv, s 3 3dkdrzlai7x00 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 spr 0zx,ne v5 ,yyaca6f0yj9/ggming can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by wy y 0,my zna/cg5egj9v6f0 ,xahat 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 255dn6xfqu87 cq) N. A pulse is generated at one end, and 20.0 ms later a seco68 xdcu)qqn f7nd pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring withs y4y.n(i rq;r 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 ju .s r;(yqiryn4st stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel rh-f g/,cub*oy6(3x bn m4o0s :nex+qcn vp 9icrane 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 to Tabl*(r nsoy pigmbxq-n 3/n b4h:ouev0x+c 69 c,fe 9–1.]    s

  A block of jello rests on xj)2fyya5s.c8uu 6y9l6btpaa plate 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 modulus (Section 9–5) of jello is 5pb.ayyf8 6tyuj 9slx c5 )62ua20 $N/m^2$ and its density is 1300 $kg/m^3$    Hz