Give some examples of everyday vibrating objects. Which exhibit SHM, at lea (uytpmd61hdj/ og((m st approximatel 6tgopd(( mm(udjh/y1 y?

Is the acceleration of a simplea5 z+hqp c(2ry harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an autovwo1uqrb h8gmdt. d+ : uqrt341- oj;zmobile engine is approximately simple h1 :q.td13u qrwzh8b-g4o;ur+mvj ot darmonic.

Real springs have mass. Will the true period an-w9r wcs) nk1l )(zrded frequency be larger or smaller than gi kr-wd)1zw9s)rn e cl(ven by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of agbt 4n zld6402qyrb dnxlw,;4 simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then i m :mal0mi,hx3s released. Describe the scale reading as a functiax,m0m m il3:hon of time.

If a pendulum clock is accurate at sea level, will it gain b qc0ke0xxn y-wb)hyf6; 39 sxor lose time when taken tox-;nbbs 0x96f hex3wk) c yqy0 high altitude? Why?

A tire swing hanging from a branch reaches neo u4erz s,9makvu+)boj,w 6f k(l).xq arly to the ground (Fig. 11–48). How could you estimate the height of the branch using6u k bsoek)jrl x(w),ozq4a v9muf,+. only a stopwatch?

Why can you make water slosh back,8( :0m efrdfoe 1dhcv and forth in a pan only if you shake the pan at a v:e,0mr(decf8hdfo1 certain frequency?

Give several everyday examples of t ukabs) fsd8a 4 /hss,vp(:s+resonance.

Is a rattle in a car ever a resonanc0awf3 l wwxm ppvvte01ab,k6ms5e603e phenomenon? Explain.

Is the frequency of a simple periodic wave equal to gjm,3 muh e.,mthe frequency of its source? mu,3 gmh,em.jWhy or why not?

Explain the difference between the speed of a transverse +epdufwg5qi /* m0i:on l334orbk -aywave traveling down a cord and the speed of a tibodgn0u*:4 pw - 3ar me/+iof3l5qykiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally ha5xz7g p /uj/wyve wire wrapped gup/ w5x/yjz7 around them?

What kind of waves do you think will travel down a horizontal metal rod90shmh hs85bq 5x43y8gl xs)d*i rh st if you strike its end (a) vertically from above and ys0 i 5ssh*mgr95d4hh8xt) blxshq 38 (b) horizontally parallel to its length?

Since the density of air decreases with abn6-ju;p8 9stn1dtqnn increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect thn;-tq6d tb1u8nsnp j9 e speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitudeaf6l )xhexw t1oo em/) ,tq/+s as they travel away from thxo)sx1eh/ m6efq+l,t)/ ot wae source.

Two linear waves hav:tzo7 iy9gzg7 e the same amplitude and speed, and otherwise are identical, except one has half thgzt9ygz io: 77e wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundaryygez 27ado5wh3 jg*) xnh6 f6y between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do c hj hy)3f ygz5x62 w7*eodgan6hange). Explain why.

If a string is vibrating in three segments, are there any places you cou,33v 90:.o gbk sjmlpym*etvbld touch it with a knife blade without disturkom3g0btvjbp : ,*vy9me. s3lbing the motion?

When a standing wave exists on a string, the vibrations of incident an2 8b ijklpgb5lcih, d ng34-;pd reflected waves cancel at the nodes. Does this mean thanb 4j2c,b3k;ld 5iih8p -gg plt energy was destroyed? Explain.

If we knew that energy was beincej (j5cg k+b5g transmitted from one place to another, how might we determine whether the energy was being carriedcjc b k+(e5g5j by particles (material bodies) or by waves?

  If a particle undergoes SHx6 y1)1hx 4cteegxv7 qM with amplitude 0.18 m, what is the total distance it travels 1 x71ctevqe h x6gy4)xin one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cm lwaw5rq 6 /jcc6ong when a weight of 180 N hangs from it. What is the “spring” constanc5cww6a /q r6jt k of this elastic cord?    N/m

  The springs of a 150:dk o8 ;gy6 ;at qgwhefg60kv*0-kg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a k:v qd ;0ggy w*;go 8eahf66ktbump, 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 is1 s sc,ybq/(e w3kl: pr0ts,s/xxg0 qt. (a) What is cqb(x xste 0 p3rssqys k//0g ls,1:,wthe spring 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 when a maxu6(un w0rl *r8gw z 7xa5q)qwss of 0.60 kg is hung from it. What is its frequencw q*w0urnx(rzwlu87q6 g)xa5 y if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the positl5aq2 o 9achv3ion x of the mass in Fig. 11–2 at times t o a3vh925aq lc= 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The ec ,l5*r )xxbhweb vibrates predominately with a frequency of *cer)x,lx5 bh4.0 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 yn9we-pe+ ,cya frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. c,ne+y pye-w9 What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates hl4+zyv p 9al 79lfr+z3.0 times per second with an amplitu9a+l llyf 4r+zv7hz9 pde of 0.13 m. 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 equili( bdk/1)crr hc5yrj nf:gmydx :6p t*0brium is the speed of a SHO half the maximum valued:5kc )p t1*gd0yf:j mrhcny6(r/ xbr ?$\approx$    A

A mass attached to the end of a spring is/rcad j5ie0xjm 4)ff9 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 w5 d43z1pe zzq/9( dqxmv6rjpa vertical spring 0.315 m. If the spring is stretched an add/1 zwdqxz6jme9p5 ( drpzq3v4itional 0.130 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 sto xis 9e(o/6mzhc0x97yk 4drsiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m fh0dsy/94x6m 9(oozeix kr c7srom 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 0.200 m to “lop5l1gr;s59z fv: 9qidqwk h8 uad” a 0.180-kg ball. With what speed:91sqw 5qur z9gik;fp5 8lhdv will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surqd2v aq( uvk.76yt*mr .v.f heface 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 with the spring comprqv(v2 y 6metr da.q v*..fk7huessed, 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 according7 lh8hfcwl 3hw8n h)h( to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determinenlhh ch fw )(7lw38hh8
(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 azo qm7 (4s5fdc9m (wkb SHO half KE and half PE?wqskd7 ((b z foc4m95m ±    A

  If one vibration has 7.0 times the energy of a second, but the 6jbci)7 (lkqz7.:s pr c:d.xklb6a(fz dkd *kir frequencies and masses are thezd6 )kkfqja ( .cdc7xb6 .: rl:(k*pksdb7lzi same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangin(sj 6tpctspdol l91 .9 by5sb4g light spring once every 0.65 s. 51tc bly(dsp ss4lo6p 9.9bjt
(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 para2; c fg/yqrq9 efy:gty4u/dr :llel vertical springs, each with spring stiffness constant k (Fig. 11–49). What gf:qgyuy;r e9 y r 4ct2f//:dqwill be the frequency of vibration?

  A 300-g mass vibrates according to the evv;(x;6:2u rvt0 daar*jfw k iquation x = 0.38sin6.5t where x is in meters and t i;0aj* u6a;rtrw d xkf(vvi2v:s 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, labeled A and B. F k(yjass8,-tq9o).yuj cvgo 4 or 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 yi ru.m;6(tu*uk0p q pon the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96rt p(0u 6yup;i.k*muq m/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 wi-kfa7ag) vs8gxad,z(y w.i d1eo q)0 yth an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equifxv)a gg d0yy(1. 7saed,kqo )z8i-walibrium 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 spri 8fhai,ay v51cng 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 hori1ar + hu3x lbu*,9bppkzontal spring whose spring stiffness const,b*pu 1h 39puk axl+rbant 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. Aft;gc j;/.qumx7o miwmf f8 43jqer reaching his lowest point, he oscillates up and down, hittingmj.mco4ix jgwq8/f u3;m;7q f 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 in exactly + mff2vvb cw 5 .57b9gbqjthf(60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be uair* q 1:u 80y 2gmus*i+bngtif it is to make exactly one swing per second? (That istu2sua:y bgi qgrm *u+n 1*8i0, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 sbew7)nxox*v mxfesa1tt) mb *b8v r2eh72(0i on Earth. What is its period on Mars, where the acceleratx )8oh7e*ft bvvxr*wi0 1 sna2) 27 mxmbteb(eion of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pen(ynpuw51/ 1ea +qllo zuw8 wq05jw 4akdulum 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 365prnqu t ss 4e;.ae:uw;gx) .s z(37npx grams, and it is relr n.sau.: un; s weez3()7 xtqpgs;px4eased at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clo u6j7*g mm*rgjck’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjus jgrm*7u j*6mgt the length of the pendulum? shortened by    mm.

Derive a formula for the i bl .1v/ahxc2maximum 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 Hz. At it is released o;j dq b**efymw8/d 97ou+gcpi1fut9from rest starting at*fwu;+fyou8 p1co 9 qgtb/i9d md7*ej an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of 8i9mybdr .ib 4 /n)dt)u(onuw9eig r.iw:,lb his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 tdb.i)n9l m)8 (e r,od:binyrbuwg./iu w94im. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a spxo(syvk 6/ wxe *g8hq1eed of 343 m/s How far apao1 x6*kwq 8y(sh/exg vrt are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiloherf9 .du1 id1m7f7nrzv 1b) zfc/r3m zjej.ly9ytz) and z y jrbmv7 uieffnz9y1lr7zf1j. /.dm3c)d 91 travel 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 lzv5 u)q4 +0lievyux8 mongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same19esa m).a)wowqk+xso6,a d s zk1qs0 elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater,soxoke ,ad6wsawsq0.z qk + 1m1s)a) 9 and by what factor?   

  A cord of mass 0.65 kg is stretche*tnre l93h2mu,kv /jxd between two supports 28 m apart. If the tension in the cord is 150 N, how lmn2/x3hvjke*lrt u9, ong will it take a pulse to travel from one support to the other?    s

  A ski gondola is connee2ti3tk w41cs cted to the top of a 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 cable. It swt3 c1ei24kt 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 just below the surface of the sea. He hear-herw yzs7(v /s the echo of the wave reflected from the ocean floor direcwr/ hvs-7e(yz tly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this di*ft. f w44xsn)te6qs ifference helps in locating the earthquake “epicenter” (where the disturbanf4 swe xfiq)tn4* 6t.sce 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 surf2,(x nh ahb 5h 3wqktbg6)pz8y(if mn4ace wave can 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 con) nx52zh63f((4,hqygb8mpa knwith btact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amppva96p gb 52s .e1tyhilitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the1 pv6tb9 .ge psay2h5i source?(a)    (b)   

  The intensity of an ear0 hfd /if6opr0thquake wave passing through the Earth is measured to be dfoh6 f0r pi/0$ 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 through the same poo 5y1n -3exrypr7*0.d q gzafkrtion of the Earth, but one is *yx1f0 o5y-epagdrzqn73k . r 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 frr pg. *c,an.vaequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two vg..a,n*pa cr waves?   

  A bug on the surface of a pond i 7:xp,k urwf:)f:b ncrs observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what facrk: rubwxn:7:c )ffp,tor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moxshtx-d*) e6fsah/ u(ving 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. 11–36a, at the m)6 hex h(*ustf/sxd-aoment 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 aze5v * +(ein mhg*ji/zs its fundamental frequency, what are the frequencies of the first four harmonic*5ig/*vmej +zzn(ihe s?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hmzqf*98q0zgkt u)nnxj-d4w5z when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds om0n*u 4nwk)g9j8q- 5qztfz d xf the string vibrates as a standing wave.)    Hz

  A particular string resonates in fourlrjaix: e10 fo n;y sueab8,m+, :aj1g loops at a frequency of 280 Hz. Name at least three other frequencionymx,+aga: 18 f:s, ;ej10l jr bueaies 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 freq9w3cwe +6kq qthj luj8q+j:qchu:+*q uency of standing waves is 475 Hz, how far apart are two ad6qq :+9+u3w uw+kt* :j jqjh elc8hqcqjacent nodes?   m

  If two successive overtones w -z 2+4rnsg1,tyst0r ;:du dkm0rmzjof a vibrating string are 280 Hz and 350 Hz, what is412sugnsr mzdz+,:dk -rmw0r t j ;yt0 the frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mbq btj1)t1ao(9e0 -xow+ji rfass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first w1-t eb9fr ojj+01tai ob(xq )two overtones?    Hz

  A particular guitar string is supposed to suk /oqqk(l3x(v7dk * vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. /(3(qqk kdklu7* xov sBy what 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 i0wo9q0r nml7a i ntd*6s supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the stringan*t om 7qw0 l9i0rn6d be changed to correct the frequency? decreased by    %

  One end of a horizontal yh/+lgu8ub/9ui ha n, string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass n,8ul ub/+iy9 ahgu h/per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjustewr n4 5i5)o ody2d3p4g(hrisy d by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many diffe(y hg o)iryisw55p dro34n4 2drent 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 right frequen2lps87g5jorv s: x(dp cy, the water alterna g(2:7op djvr l58sxsptely 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.00eky29 0fn mln*wgj*z x ikn9, km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident anxwn9njf k0l*y m9,i ze02 gk*ngle 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 underwal :4rygwhui:vy+er/,eho , o( ter “shelf” where the velocity changes from 2.8 m/(:rveo/, 4ohyi:r,ge y+hlw u s to 2.1 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 a( j(1 zhgkt7*bd*9oky0uo w17vdz cxqir. If the sound wave hi(7* kkzx7u91obg(jwy t* 1 qhzo d0vdcts the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rock aq ;m 8ad f91xy(x9taqbt a 38ax ;8y aqm(q19bxdf9t $^{\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 xd h0p7y 7,zqw0.5 m in diameter. According to the user’s manual, the dish has to be point yz xd,h7pqw07ed 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 ffl.okljb:zzm 9d.qrg*: /;b and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximatf/ m:;b:z*zfol.dk .9 blqrj gely 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 sprnnt. ded:k22faog ,i4 ing stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with masiag entdf o2,.2:n4kd s 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, f( pv0u02ki e crwc8f:which stretches the net 1.1 m. Assu(r2u0wc8iek f: cp0 fvme that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The ma .kaq)h* wuib:ss then falls 33*uhk)a:.q wi b cm before it stops and begins 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), c,yex7gusau0m*gzf y957 boo 0ompressing the spring 5.0 m. (a) What is the spring stiffness cef a0mo0xy7*,guz9sy5og7ubonstant 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 the right pfb)8muj 1 foy.ace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the s1.)yb mj8ofufpeed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonogmu3 1gt;u g u66l3eat*9o oefrraph record have a wavelength of 1.70 mm. What o t o93egur6f;6 3mu1u*egla twill be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is inb udkpied,1;5 meters and t in se,pbkdedi ;5 1uconds. 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. Wh6kfd8bj.hopb.rx .q : kc o6b.at is its frequency if it acceleratehrf ..ob.86c djkx:k . bpoqb6s at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75ut;2 dey l tm5t uf/6dje b:f3h0xwex//sf6j;-kg man stands on the raft, it sinks 4.0 cmtee l:0;f266wx djd tbj/xh3/5t;fmyfuuse / deeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned toz1rkbe 8u1cvf ,-.pho play at 392 Hz (G) and 440 Hz (A)e1k ,r f.vpuo bcz1-8h.
(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 trt035lq tv j6sdcsdha2u)dk5 /aveling 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 s dt5sdl/kd h3)c2utvs j0 aq56ections. (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 ohr4v wur34 y/6/oza5chbm3off 264 Hz, and the tip of each prong moves 1/aobor/ zw56ch m43ryf3u4h v.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 frequency .kr 4j90rvly a1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose cont9vr 4l aky.jr0act with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that c- 6 k plf0 vgltddr+5510rkkeaan slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the op1 fllardtrkkd5 -6v+00gke 5ther free.

  A “seconds” pendulum haoe3n;yd1pk- a :ioe 2f 1wd)cfs a period of exactly 2.000 s — each one-way swing takes 1. wdipe-3yc1a;)de:f1 onko2f 000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the s9w 8ysrh f. +bg ;rd j*ehlfw//lc/e)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 swi*eyrsl/;l)fbwhh8+d/f9 /erg . jc s wngs, 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 gh) ug): q6cn adjl0f;h is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later ahcldujf 6) 0)ng;hq:a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring r3oz9h f/;y84e(xz 7fwkk1 twenuu7k 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 xnf ou3ke k ekw/8urh z;(79w7yz1f t4the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable isl8u70 :2 wc)nvchc ayz 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 tuwz:)7y ancv208 c chlhe 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 (whicv+k9epkk hc6d2o) ayu40tm) hh 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 sprin))ckmu 9tae0dy+ph 24k hkv 6og, 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