Give some examples of everyday vibrating objects. Which exhibit SHM, at lclr r-0oz-(. laoju9y east approximatur -oazo-0jl c9(l.yrely?

Is the acceleration of a simple harmonic oscillator ever zero? 5-i vzlbc1k; zIf so, where?

Explain why the motion of a piston in an au2)wt x07wyf notomobile engine is approximately simple harmoo) ynwxt0w7 2fnic.

Real springs have mass. Will the true period pdwa+p.xba0 / and frequency be larger or smaller than givea/d+.pap0 b wxn by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of*s*uqodhiq ,q a a3ok/f07,nv a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached4:dr /qr /9d,w egjacd to the hook of a vertical spring scale, and then is released. Describe the scale reading as a function of tidq:w 4/,j9 cge/adr drme.

If a pendulum clock is accurate at sea levt;ylt +hvn l*p mpkov8fc)98 5el, will it gain or lose time when taken toykh5 c+p)omt llfvv;*98t8n p high altitude? Why?

A tire swing hanging from 4s:afgl3 ptul01my 7b a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch u1a f7m s tyl3u:g04blpsing only a stopwatch?

Why can you make water slosh back and fortob6yn0yqbw 0.opt5rh l -3bodgt;o30h in a pan only if you shake the pan at a certainbq3pn;g3h0t5ow0y6l0 y - .o dbbroot frequency?

Give several everyday examples of resoxw96 p5-5ldp*x .*te ew lbdqunance.

Is a rattle in a car ever a reson/bz589w; j*fu2tc vzg6j kggpance phenomenon? Explain.

Is the frequency of a simple periodic wavpy 06cm v/amd,bc:*k59qabq s e equal to the frequency of its source? Why or why not?m :a,kp0q yq9v6 c/db *a5csbm

Explain the difference between the speed of a transverse wave try+vik)nzgg*sl +/v/qf i 4d4paveling down a cord and the speed of a tinyl4kp+ggi4vfs/ dqv+n i) / *zy piece of the cord.

Why do the strings used f 2 tjj ofgaa692.;esusor the lowest-frequency notes on a piano normally have wire wrapped 92jf6u g;j.saa2s teo around them?

What kind of waves do you think will travel down a horizontal metal rod if yo95)1kovb8 tu5i*b3xcro6mlin; en lyu strike its end (a) vertim u5vo5x8y9lr );6cn tl3eb o*1iinkb cally from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increaun/dr* j-e )yp(h+:yeyivd 4qse in temperature, but the bulk modulus B is+4hpeud(:) yj -re *dyinvy/q nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they trave4(2rgl ree3iv l away from the s(4re 3vl2rgieource.

Two linear waves have the same amplitude and speed, and otheoa uboxt 4)qe: 824gthrwise are identical, except one has half the wavelength of the o4 : u8ottx4be2g q)hoather. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betwe i-+oba yc:6qew.3tw*s nregrby )-q7en two sections of cord as in Fig. 11–33, the fre wb + tsee)-nr.q3r-:cwiqo7 *yyag6bquency 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 touch i+n37 l1v q6nh-hy2;xpklz vs ix+- 1l3 2kn ils;h67qz vhypnvt with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations tc2ozf0o -eh+wi 0b.fof incident and reflected waves cancel atcifh0 2ozo b-et 0w+f. the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, h)hcsvy3qi. g e(bxmr1u .zor/-y9 2ogow might we determine whether the energy was being carried by particles (material bodies) or by waveb1.m ysq.o-ho/ i9gz (cy g3xrve)ru 2s?

  If a particle undergoes a vg;o81wye 8aSHM with amplitude 0.18 m, what is the total distance it tragevawya8;18o vels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it l8 dnk6mju+orb7yt6xx3q :e;but is 85 cm long when a weight of 180 N hangs fjuynbq7mk 8t 6r:x lox 6e3;d+rom 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 fp6v2 8a):1qgjnhwju its 68-kg driver gets into the driver’s seatq v)2p: juwnfha8 jg16. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale st,4zo+nt ht1gsrv 5.jom5alz :retches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stif rnvol 1h ,at .5+oj5z:zg4smtfness 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 wuh, kc43 6xyhnhn x431nii: vr e48pcwhen a mass of 0.60 kg is hung from it. What is its f6yh4rnh34 ihuv ,iwk1 8cnx3:ec pxn4requency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of t uj su0qy(0.mohe mass in Fig. 11–2 at times t = 0,t.0 0qjou y(msu = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 5dhd vuf:i 9+q0qc */8eykxiy’s web. The web vibrates predominately witvqyfk/ ixey8+hd d 9 5:qui*0ch a frequency 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 freqnuiyvob /xr6y/9f rn9*ab/ 2 quency of 0.88 Hz. When an additional 680-g mass is added to m, the frequenc9ybrqb2ni/ *u v/6 ryo/n fxa9y is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second wi *h17x6nac wgeth an amplitude of 0.13 m. Determine na ch6wx1eg*7
(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 speeih9-jr0 d(d hnk ocw75cgp f;1pdv;y -d of a SHO half the maximum value?pd7j9dc n5f v0og1pk r(d-w;i- hy;ch$\approx$    A

A mass attached to the end of a sp(+v( p)y .rvm, nzvhwnring 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 0.31es5gr doq1 lo( m64ud/.mmq9k5 m. If the spring is stretched an additional 0.136 m9 d1o/5e smul(qmr.doq4gk0 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness c ooe9:4u+tw ea:(pm l:gzmb:ionstant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/ g m:o9z:ei:lau (otemb:+pw 4s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m to “lohrta u:yn7t u0t1 nl-f bu 3z.c-2i5aoad” a 0.180-kg ball. Withuu7.c tzl3ba:n-1ohnuy t -ati0r25f what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfaztx ghj1e: x(9ce is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest withxtg (xz9 je:1h the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45co2ge 5 2+wmf qw14o tvpzrj3r8os6.4t where x is in meters and t is in seconds. Determi5+e wgzf3mowjrovp4q 1t8 22r ne
(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 //vub v.zcje. from equilibrium is the energy of a SHO half KE and half PE? ± b.uv//z ev.jc    A

  If one vibration has .o/bb7 trzuzr* ll2nj sc-h 8+7.0 times the energy of a second, but their frequencies and masses are therrl .h+8/*-c 72bnots zbljuz same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a verticall6m81yd66 ntwaj /xf jxy hanging light spring once every 06an6 yt/f8jm6 xwdj x1.65 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 paralrglr gs *5xi6,3c )cik0wl)hclel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of il c rcrk0g5g swl*h 6,)3i)xcvibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t w/3lcvzb aax s5zn9:a9here x is in meters and t is in seconds. Deter3 ac lb9z:naxazv/s 95mine
(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 SHM7gt6i t n89ixq, labeled 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 at67 :dmdwly-x s rest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an inidd sy7ml6:-xw tial 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 amh:vzhe) f36 ngplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes throughe h3zhg:fn) 6v 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 twonf-h )3 nwnmzl0 noo35 springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed hori(vg/,kyp 1fekzontal spring whose spring stiffness consta f /vk1k(pge,ynt 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 jum4nj*qx u0a5nvof ;b 3yps from a high bridge. After reaching his lowest point, he oscillatefv5ybu;an04 * x3jqno s up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations bra(wdq bn0)m2itl63 in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exa8s rq7dg2vuu-ctly one swing per second? (That is,u dv uq8rs7-g2 one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a per/1 0tecbm5j tort /sa*iod of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0/smot* jt50t1r ecb /a.37 that on Earth?    s

  What is the period of a simple pendulbhnhb;nty b- 0a6 im-,um 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760d 1j((2see mdj m, the pendulum bob has a mass of 365 grams, and it is released atds1(( eedmjj2 an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If thk- 6qm2)yow r am+wp+qe clock loses half a minute per day, how should yoq+-qmr26yw p)komaw+u adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximib+.e3z epzv1 frw (4bum 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 Hzeu9175 kk b,os agr)mtkx(o5f. At it is released from rest starting at an angle o5kebo9sm f5at(7, xkgru)ko1 f 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 u lnpl(zj+ jq./o9 -kgthat wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two l/ +onjup 9-jgq .z(lkcrests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a fred4l pvbwi 1id4-.-: o8gfe )f :wphkvlquency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crestv e4)kgfp .lhwpli-dvf:b w:o8 i-1d4s (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 16.qvce 6tiu*s .00 kHz (kilohertz) and travel with a speed v.iec. u*qst6 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 ofnc 47vx3n) atmk,rhlz8e2 o3 p longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have t *z0,ptel)ksj he same elastic modulus, but one is twice as dense as the other. In which rod will the speed of lonk*ej0zlsp ) t,gitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supportu,z-e/pzm4/p qz c u/bs 28 m apart. If the tension in the cord is 150 N, how lozpz zmc -4/b/q /e,puung 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 by a steel cax lo9gk(o 7)kumd-g ;p: tjie5ble 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 cable. It is observed that okgdet)-og5l(xjk;p :79u mi 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 sf hbn tmj7iae42 v2 6,rhg2x6mhip just below the surface of the sea. He hears the echo of thhi26 agevf t xhm,7j6mn4br22e 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 travel at differ 4ok9 :)iewwbzx1wn4m ent speeds, and this difference helps in locat 1m9)wxo4:kwwi zb4 neing 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 approximatedyzpihhb qw. 47nw*g 88ria)2u by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixtugwb.uhah8y74w 2ipn )zq8i r*re of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of m2s39fwiop1b /zp)20xb ni9q ww(u in an earthquake P wave passing through the Earth and detectef mzu93b12bniiw2) sp(w p /9ix nwoq0d at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the uo9/fz7(5ttl h / p l1*u5h5sfyorowpEarth is measured to be lhf o tp 5py5zhuu1l5sot/9o7(f /wr*$ 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 frequendxfilpp-- p6 afg7(7o8k ua 0hcy travel through the same portion of the Earth a6lio gff p70p -dxa8hk-p(u7, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same 5tahfdz 9n,9wfmvnlk ro 3u4 hme5(. 5frequency, but one transports three times the power of the other. What is the ratio ln hw ( 4o5t9uf v3nfm.rd5kz5h,9maeof the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to movefi cfbzd:4) 8 bpu7ema3qq8l 0 up and down a total vertical distance of 6.0 cm, from the lowest to theq8le 3ubziqfcb7 4)pm8: f0da 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 otmaio:) +c6: h e-mlbaxher. (a) Sketch the shape of:oh6xm: lbm-aac) i+e 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 string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fucs:a7t n(2tae ndamental frequency, what are the frequencies of the first four harmonicat 2s:n7tec(as?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when u7wlg .qj knc,;nfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-jq;7kl.g ncw, thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates inj) 7gbezf68v b ,r4(q2 quenmn four loops at a frequency of 280 Hz. Name at least three otheegunqv2 r(jzq,fnebb 4786)m r frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the freque a5q:cw53d btaei2;w2p h 5xgbncy of standing waves is 475 Hzwwb2 3 ;b: 2 dqiap5xt55geach, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and .ela9y hj)b r wr9+th7350 Hz, what is the frequen 7bah 9wh)rl9etyrj+.cy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The di*)6tb ik7ohslnlh 9 y(stance from the bridl6 9*nh)b 7 iyhlts(okge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suppo3wo-v2hqax ax(a, x. ised 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 h-q ,a3(via2 xxawox. the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is mu/ xj0i mu1.b fdt mljer5g8 *4h3gt3beasured to vibrate at 205 Hz. By what percent should the tension in. m*4b f uu8m i lr/dxjg31e50bgjtth3 the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanicattcz-io i f5)6l 60-Hz vibrator. Tf 5z)t6i ito-che 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 lengt evej.mxbc8n 3pzq5yth a62s (hf 5.y,l(zxl1 h of the string may be adjusted by moving the pulley. If the hanginm zqjx3n yblf268 (ysl,5.cveh51hx(zeta.pg 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 just the rigi7r4weq qjkl9 m0q 9n0ht frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency toi40q9l w9re kqjn7mq0 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 km/s strikes a boue +ct3sblzk.ldxoubs-. j: 1 +ndary within the Earth betwb:sllo-3++d kj. utec.1zxbs een two kinds of material. If 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 sr iay+p hrik+:6wibprn31 6/ the velocity changes from 2.8 m/s to 2.1 m/s If /bi6i 1:p6wahkpi 3y++r ns rrthe 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 aiejjeq m,lws8* /ona* x8bl( )zr. If the sound wave hits the cold ail8e( me/* jbos,8n*wzajl )xqr 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 earthquakeczd5s7ducp w+0ok (e+ wave strikes a boundary between two types of rock at a 380d+kz5 ou7ecwpd c(s+ $^{\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 dia* hkp7+sb7/rkdyocbkl 6xg1 (meter. According to the user’s manual, the dish has to be pointed in the direction of the satellite,6 7 /ygkbl7kr d(opkhb1+sc *x 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 travels across the P)i) j)c g.edr)c dut)iacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately hoi)d c))c .tdijugr)e) w 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 consc0b-mr; fs/hetant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a w0fb ch-rme ;/sall 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 firvj 3m9xi 6mci9e net 18 m below, which stretches the net 1.1 m. Assume t9c ii6 3m9vmjxhat 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 end of a freely hangc t+wrbdfs* 60ing spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency o0*+f wctd6rbs f the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speeds5zwgw4, dgaj 6jc28h of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spring? sc w6d5ghwjg8 2,4zj a   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 y m 6fj/ zr y5(zm+rt3q*8chqplv4.u yof coffee (diameter 8 cm) at 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 (Fiz3y c4.f6q (lytqj/p8v+h u 5*m rzrymg. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 6efn0ud *k+ e9nwwg)ixm s,/ icm from the center of a 33-rpm phonograph record have a wavelength o9is6/xiw,e0 gdw feun)n km +*f 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7:i:7bzc ui2weqtcm) 1.40t where x is in meters and t in seconmui:iewc:)tbc 72z q1ds. 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 frequency irr2rzp--x ht p1);ae nf it accelerates -2 zan)rp -hr1xtp;reat 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats od+t. lk2r-v3.qbffd d9;u3;cesujpln 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 vibrates fdu2ftuk+jfb -ql3 9 e p3cd dr;l;vs..or 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 plgi6umbbo/,s * 0+qcryay at 392 Hz (G) and 440 Hz (A). c os rbq *my+i/,06ubg
(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 st+n3uv9 u a ezwsz,od((retched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in (,uonv w+e u3s (dza9zthe 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 the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each p jibo0u5f: 6qirong moves 1.8 mm to either sideqo i6bju5 :0if 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 2s+a2o rsvm v/e;gcc5 with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibratee ss2om;c+c2v v /a5gr 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 tya7ag/ 5qc 6avnazu2 4hat end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths o q z a752ca/gnyu4aav6f the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.00cl1+jlv);j ;dsvns.z 0 s — each one-way swing takes 1.000 v jvn+ llsz;js;.d c)1s.
(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 d4.b tk fetumt2: g4piay6 1i)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 what amount? [p:a 4yt )4fe.2tmg1 kidtubi6Hint: 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 2 tckjkxu1o;ja4cn)(1qfqm ) ,55 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opp)km1f jjxc u(4,coq qa); n1ktosite end. Where will the two pulses first meet?    m

A block of mass M is suspended from aw-ixct 1zy 7w1 ceiling by a spring with spring stiffness constant k. A pwixy 11c zw-7tenny 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 of the block? (Assume $m \ll M$)

  A crane has hoisted ay*bi5rax+u : t 1200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starrt yu:x+ab5i *ts 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 showl;i3*hd;m qx(np2s ms,qh3l an in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you ;qmslx q hha ;(slm n*,32d3pilet 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