Give some examples of everyday vibrabgyj3ix: )6cuzk+h r y)jekd0a ( qw;(ting objects. Which exhibit SHM, at least apprq(ydxkh: e 3+c( ;0z6 bru)gwajij ky)oximately?

Is the acceleration of a simple harmonic oscillator ev.* w9:owqtv saer zero? If so, where?

Explain why the motion of a piston in an automobilal-ipq09 br.;ee v, e41z pitham2t-ze engine is approximately simple harmon e2t9;ilvzpaat 1 -heipm. -q4 e,0zrbic.

Real springs have mabb5luy,8d w4 nmqd 8k )ds82h hlkpp(4ss. Will the true period and frequency be larger or smaller than given by the equations for a mass oscillating onknb wllsp8m8 y b)k44(,dp 2qu 8hdh5d the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator k1j-/8ovuyv -(ys mzg (SHO)?

A 5.0-kg trout is attached to the hook g 1r9/y hov-lw2 gilj;r1cq6e of a vertical spring scale, and then is released. De 1o lw-16ygq;i /vcrhg2jr9 lescribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gn5n:7 ;pr+p o: * jqzkzy)hdvbain or lose time when taken to highvkhr5+n: b) ;zoj7p*pyd : nzq altitude? Why?

A tire swing hanging from a branch readedpa)r eourxpcp5p:0(ff6 4 :0p(z cches nearly to the ground (Fig. 11–48). How could you estimate the height cfpra4dppp0:ezc0e :6 rxof(p5)du ( of the branch using only a stopwatch?

Why can you make water slosh back and;a rymavcbzx:g2m +zcnin(6 2 ; :zzh3 forth in a pan only if you shake the pan at a certain frequency?am:h:z2mzvrzg3yn (z 2i+; ccb;xn6a

Give several everyday examples of rjkx(t d gafli p3xlk z:5c1y;l./4yym/ ./ roresonance.

Is a rattle in a car ever a resonancf 3 8q nzir-rgpp30lo(niouts324+ vge phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its source?clnsn1 0 h -pg0-n0hbuwlm)h5 Why or why -51 0c)nlhh0lupbgmnwns0h -not?

Explain the difference between the speed of a tra wbh6nicxff+5/r f7w p52d3h cnsverse wave traveling down a cord apxw +i7bf w56/ffh523nr dchcnd the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes0ga4 rs;z: cxf on a piano normally have wire wrapped around thegzac s4r0;f:xm?

What kind of waves do you think will travel down a horizontalfi( 9inoz vk ;d,pd5p7 metal rod if you s7,d zvod pf p(nii59;ktrike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but;7n( ucyzfot3 the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperatof(;yz n7t3uc ure?

Give two reasons why circular water wav sm 9ee8nm /xgu(-umz7bl6gc3es decrease in amplitude as they travel away from /m nxe67u3m-s 8zlc eg9mbu(g the source.

Two linear waves havel8 j.dbdf6.z hioe5 7p the same amplitude and speed, and otherwise are identical, except one has halfbz5h8.pfl7di6. od je the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectionsg3:8qg-usv:r/e t/unkh01ft*v yc ht of cord as in Fig1u/nycgts/*ghht: :u-kt8ve qrf0v3. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segmoy*0c:wz/ j69ch ox8l xdii0h ents, are there any places you could touch it with a knife bla6h*9wyxz j 0icc/8 hoxo0l:id de without disturbing the motion?

When a standing wave exists on a string, the vibrsoz1bft7p8z3 jscf yu5* 0:q lations of incident and reflected waves cancel at the noz8u*s50oljysq b7 fpt :3fc 1zdes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one/1xgfgy 9jg2b5.(x f)v( fqng rmj t+o place to another, how might we determine whethn v.5qb y( o)1ggfr92g(x fgt+jxfj /mer the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total 6 uq3t8fht xo/distance it travels in h u t/8otxfq63one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hani + x0iz9as)rvgs from it but is 85 cm long when a weight of 180izr9a xv)i+0 s N hangs 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 into tq3qmljnbsv6f x 5 l,.54d31 s -lshearhe driver’s seat. If the car goes over a bump, what will be r l1.x5nbsq-j3el dms3, has6lv5f q4 the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg f(bbuk1 cidnz1+ /by, uish hangs from it. (a) What is the spring z dn,i(/ bybu1c+1 ubkstiffness 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.k 6e74 jg 5y8mj+ -zhg0ry tvnyzij1t,0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0. tnzgyey4ygh6 jr,vm t87j+1- 5j0k zi38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at q(-g*qr/k-pj w2 gddotimes t = 0,t o(d*qg- kp2wq/j -d rg= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 ,/8quouogsq0 c fv 5+ncaught in a spider’s web. The web vibrates predominately with a frequency of/ov+85cnf suoq ,ugq 0 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 rulqr- +8v hed5thk 8.nu 67qga frequency of 0.88 Hz. When an additional 680-g mass is addre7t 56 ku-gl+vn .dhqu8qr8 hed to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end v i9.9 vqtkzplqo :5hb5yd,m+ of a spring vibrates 3.0 times per second with an amplitude of 0.13 m:hpmz9il9kq5y+ 5o.vb q d tv,. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maxe 5clsv)08z hjimum value? s)v8l0chj5ze$\approx$    A

A mass attached to the end of a spring is stretched a distanceh fma)u bkw:5al;q-jjqa1:6(tg 4htu $x_0$ 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 islui f ruv.3mv1 q1p8i* stretched an additional 0.130 m and released, how long does it taku3uvilfvm11p*8qri. e to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring w/nxhkx,)j(tvy0y dv ) ith spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the t)v/0kdjxxny hy)v (,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 8 kof(x t1ef ,9jyxoe ,rjb;2i60.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun? 2,6 xti(r , xb1j;9koyojefef   m/s

  A mass sitting on a horizonta-d df 0u-f 6l 2aaatlhu8p3*bal, 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. 2*tf3fh- p a l-udaa6b l80audIf 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 equatiotvw6t47h akdzi* 1 sjlu4at0+n x = 0.45cos6.4t where x is in meters and t is in seconds. Detertlsv tt ja aw1ikh046+duz47 *mine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SH 1*a/a kfi9q)s 7r h+bdlls7gzO half KE and half PE? ±qz /7lilhs r7 gfkb19s)aa+d*    A

  If one vibration has 7.0 times the energy of a second, but their frequen ; r(52s ew7ahooxxxvv 2h063 lxfe:wtcies and masses are the same, what is thr7th w 2w5eo6vs0a xvfxe 2;x3xlh:o (e ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically .69fg26*cdeahmmcqhd 88b ty hanging light spring once every 0.6f qca6c d9mmg8dy8.h6 tebh* 25 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical paralleej-v8n-x 4;q2vp .eqek.z ib .zkb/ak 3o2af al vertical springs, each with spring stifz3ikk;-z4 b-e p eakn2.bvqe. j /. vofx82aqafness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x b kjch95v,ek,d w*p cx-69ygh is in meters and t is in seconds. Deter,9h xh,*ckkwy9bp-5 6egdvj cmine
(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 ac;9w v0f;.r7d nic gaB. 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 spv* g.:mmx4 8skiuq,lb ring (k = 124 N/m) is struck by a hammer, l vq,b*4i msx .8:ugmkwhich gives 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 with an a.wdmn2icanwdihk u .9y)34v 23 dozu7 mplitude of 28.0 cm when 0.260 kg han dwm3)hycoind9 4..ui23z2dvnu 7awk gs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffnessp;tjcax06b0 vh+dnjdt w/0 2k 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 fig46 3aonkln tq k)q2,ixed horizontal spring whose spring stiffness constant is a,qq)no 6gtkn 3ikl24 $ 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 65.0ms50 ql9 a e;rlr-4emc76kdmy kg jumps 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 tor6ec 5a74m ye0ml; rs9ldqm- k rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s.0gp9uy3ki mg-*bpe 3 *us hjazo*e),c What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simpleve(xj 2lgscuxeq-5( va8/ v--v 1 fgot pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 s.) gx/afg5o 8sv(eltvx1q cej--v u-v (2   m

  A pendulum has a period of 0.80 s on Earth. What is its period on ewu,cj h6w2 t+Mars, where the awjeu6 ,t2ch+w cceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm l nl(r l j :ij,vrbk6b+ck0(ya3ong
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pend)f69m7go 8cnen t ;xerulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12.0 8 xe67nofm9 ;nrte)gc $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clockv/(pgxz9;cjat xj ;5g loses half a mip/j g9;(vcxzxg5t ja;nute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula forna 4aent bj87- the 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 oscil*zr5 1k rlfuk7lates at a frequency of 2.5 Hz. At it is released from rest starting at an angr5 7kf*k 1lruzle 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 hisjw1 z bxig2hk-av3u5. anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves trave gu ih1j-3.xzk5a2wvbling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 m/ d*b yxl--oy zt/ul57hs How fa-lut x b7o5/lyh-d*yzr apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertubbimrkpp5 8i+m7,y,o 7 fw5tz) and travwb,,rimpfpbuk7m8 ty55+i 7oel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudintnn(b)8-b3doc -k avlal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulusi59a8e zlb- rqky w4u., but one is twice as dense as the other. 9.r4bqi uak l we5-8zyIn which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If th5*f)qkgx(nrgw/7i mb48;su hrmj 1ge e tension in the cord is 150 N, how 1k* mmbjg qws5hr/(;f4 8)igr x7geunlong will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of whede(.,f3p78 nw fl8 9wjp yq;g+ ctia hill 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 the cabghd +; w8c83 (efp7ntw 9.wjy pielqf,le. 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 hismlp.kokw vh7x;-x3 (k 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 dehpkx7 lw k-o3v (.mk;xep is the ocean at this point?    m

  P and S waves from an earthquake travel abv7odcv+m*1f h11 6ver jod.n:f aaq 7t different speeds, and this difference helps i1ode da:1.hmn 6vo17b7+ a *qj rffvvcn locating 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 approximated by a sinusoidal tra6a9exk 6*)f ,d xgafgynsverse 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 begi*xay ),ga9xkfefd6 6g n to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudz m 4ouy7req0rn(6n1c es, of an earthquake P wave passing through t(n c64zu17mn0e qrroy he Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to be,czj48iz5in e 26ys+sm 8egac 248 ssci6je,ey ia58z+gm zcn$ 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 travel thrc nxpa)5ir,e8p: ue4xough the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes or)8 pp4iu e5exc,:ax nf the two waves?   

  Two waves traveling along a stretched string have the same frequency, b7ycri f656 b18hot pj6bnkdf +ut one transports three times the power of the other. What is the ratio of the amplituded6icn5b f6jfo 1ytr+8b kh6 7ps of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total verticalp5, mg8b8tpv l distance of 6.0 cm, from the lowest tvgblmtp 8p85 ,o 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.ox( 6fxqk :ws5 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly ovek 6:x5qf(sw oxrlap. (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 string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, w0me)bjvt 0 4cwhat are the frequencies of the first four harmonicb)0v me0wt c4js?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates aca.a6; kjor/ ejr)*)ra *ohk dt 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is,*ojd.6 rka)/;kahre jr )o *ca only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four la * w4nck)* hwalsv4g(oops at a frequency of 280 Hz. Name at least threch4aknw* 4w* sav)g(le 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 ix .iap+ waz5km,z:(c is 92m/s If the frequency of standing waves is 475 Hz, how far apart are t(mwazi5ik.:zaxc p+,wo adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and zy* 81n0zbqmafj9/j1utshv*350 Hz, what is the frequency of th qv/10tbjsz 1m 9z8n*ujayf* he fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance 1wn5ph*n,i1bsfbm u o 7(sb9sfrom the bridge to the support post is L = 62cm and the string is undw sshfo957nb1ibu1pn m* ,s(ber 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 Hz, but it is mef :k3p11 wd(jzqa1ql yasured to vibrate at 205 Hz. By whal1kp1f 3ajzdw:q q(y1 t percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppneru*. i1pa8k osed to vibrate at 200 Hz, but it is measured to vibr8.pken r ai*u1ate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is/ f4gc() kmhff7xbk,u attached to a small-amplitude mechanical 60-Hz vibrator. b7 g/hu(xkfmf4,ck) fThe string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the sa+ 79sc.dnjmttring may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different s79 nc.mda+jtstanding wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the wat:jy;8a+tu:1z-o krm mzvu; uier back and forth in a tub at just the right frequency, the watr:8mj z1:yi; mu+ukt oa;-uvz er 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 speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 kms-ic*kcu6pm +8t ;qqe /s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an in k +;i8*qctcu-m6sepq cident 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 fromud:4k7fdd3b vs. a r/ mi6p)lj 2.8 m/s to kdbd/j3dr ims4).pav: 6l7 uf2.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense air. n4d vp l;u 4 c;t1xap4biqo/)kIf the sou 4nq;ldibx4;au14 ot kpcv)/p nd 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 boua dn*31 4bqo* cdqvggzz 9sd-(j, v-ufndary between two types of rock at a 31-abdcvjg3oq*4u9dz f q,*sv- zg( nd8 $^{\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. qhc+mnh*a ;+sAccording to the user’s manual, the dish has th*aq+sc;mh +no be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h )d* iuudn/2 ;vnkdt*c 5hh- aztravels across the Pacific Ocean. As it approaches Hawaii5-d*ucihuzhd2tk* ) nav/dn; , people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffnren)0 nbr) h:aop 1pv/ess constant of 550 kN/m Find the maximum compression of the bumpe)he nvbn1o0/r parp :)r if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretcboj/g r1gt3u i9jf1 k6)1qs-9 sgoz hkhes the net 1.1 m. Assume that the net behrgk1jhko-of qgzt s 1/93 bu9 16jgs)iaves 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 springh(vtu* 6t*qx zp(cd :t.2j kqn. The mass then falls 33 cm before it stops and begijt. z6q pd ut(*k n:q2tx*(hvcns to 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. 11–54), comp1etkjsy 8o;8ldto9t p hbo+p(; 5-xw pressing the spring 5.0 m. (t t +sbhoe8 l-wt8k1 ;xy;(59ojopppda) 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 5zf b: l( qf 7ska5i+jfgmil1o2rg1)gcoffee (diameter 8 cm) at just the right pace of about 1 step per15qf: ifa+s l)z 2l fr1b7g(gojm ig5k second, 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 ce 6r ,(fwqf/xfq(++s +pxqwhz lnter of a 33-rpm phonograph rezqhff+ qpr(f+lwxx,+(s6 / qw cord have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accofvs*ex ok*gt4m3o2;v 5p0f ur rding to the equation x=0.650cos7.40t where x is in meterse0pgr;*ofk*tv 5x s3o2ufv m4 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 frequency f. What is its fxr +va-n 5ht-g8ax yc:requency if it accelerates at 0.50g (a) upward,a+y grv-h-x:nx8 5tca    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on 1 acy9vdk0z7g the raft, it sinks 4.0 cm deeper into the water. When hk91 zgycdv 07ae 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 Hodz r( 7rn/ain-y-g kl7hz6i.z (G) and 440 Hz (A)r zy -r(k g7n in7ia/.d6h-zol.
(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 travelin r5/ 4o*lk5vsxyz5sbf m h;-qrg 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 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 t5*mr xr 54q-vok;s h /blzy5fshe lighter?

  A tuning fork vibratky7(m +.p papdes at a frequency of 264 Hz, and the tip of each prong moves 17d+( kpa.pm yp.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 motion of f +i5hg8a y xc,:ifgl d1ja)wu(requency 1.5 cycles per second. What is the maximum ampli5ui), agc + (i d:ljgf1waxyh8tude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attachedkc gb; f7x9k:y/ 8tziv+yd /n2r/i jzy to a ring that can slide without frictionfnji7bc y9// ztd2r 8kg;vz+ i/xkyy: on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactlsxns;cc-3l 2 jy 2.000 s — each one-way swing takes 1.000 s. c2xjsls-3nc;
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or ca5 fk2my *qllni4t(7top3 q7m cn 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 t3p7lnl(5y7 mtmqc * q itk42ofhe 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 N. A pulsev7: (hzvav; zf( vf58qxhgo-c is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the 8 ag(vvv-vfh xzz:5 (c7 ohf;qtwo pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring o7n:2x q)h zvf9w (ydcstiffness constant k. A penny of mass m is placehw27vqc o z:(yfd9nx)d on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkya50z8ye+, ep wsemxu(c rd. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts cw y(zesex5 +mu 0,ep8the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also 9.oao zf 9n2qqgives the dimensions of the block). You push it sideways as shown, and thf.o9n oza2q9qen 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