Give some examples off8j 2ie,jesk-i61ymc everyday vibrating objects. Which exhibit SHM, at least approximately? ee c1i -jyjm2if,k6s8

Is the acceleration of a simpl4i /s1. rabvfbe harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile td95cg yl(pd2 engine is approximately simp2y g9(td d5plcle harmonic.

Real springs have massjpwora4 -ujz4hrrqw. (1v c,2. Will the true period and frequency be larger or smaller than given by the equations for a mass oscillating ( 2pzqrj-ocavr 4,1rjh 4wuw.on the end of an idealized massless spring? Explain.

How could you double the maximum speed of o+gn+ pqxru*( h0.ryra simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached tr-qcg* -wp l6:w9e *6 xknoyleo the hook of a vertical spring scale, and then is releasedeglp:*k lny-e 6rqc*6owx-9 w. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gx -pqsg8nb ;cot3o3-3y5i wtt ain or lose time when taken to h3t3t ngy8tx pbc 5-ois;wq3-oigh altitude? Why?

A tire swing hanging from a branch re v6k ktx/i zcct06lu23aches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatch?/zk06tu citk6l c32x v

Why can you make water slosh back and forth in a pan only if yo/x:t ayjx c,3ys(9wf)qr2g rr u6o:feu shake the pan at a certain frec3:org/(rufs,f q xa:txr6ej) y9 2wyquency?

Give several everyday exampv u(xty1nr 1v(k;1bilk xy)+jles of resonance.

Is a rattle in a car ever a resonance phenomenon? Expz)zw*z1 of 6xplain.

Is the frequency of aty,s /v0zh cma qk5zrt4/i3p6x c6vo1 simple periodic wave equal to the frequency of its source? Whicxt msr6p0htva64k1 qy /zoz3 cv5 /,y or why not?

Explain the difference between the speed t*gq9 n2 ompin-un0r ;of a transverse wave traveling down a cord and nmpr*qnn;g0t - i uo92the speed of a tiny piece of the cord.

Why do the strings used for the2to- :g:rwtli lowest-frequency notes on a piano normally have wire wrapped around theloi:g 2rwt-: tm?

What kind of waves do you think will travel down a horizo7f m9: 9fekypqhw+lv2 ntal metal rod if you strike its end (a) vertickf2le7 p:f9 wqy9+hv mally from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in tempn 79 sqqkyefsh+7by40 4s:wib/ig +deerature, but the bulk modulus B is nearly independent of temperature, how would you expect thqn+y bw4d7+iseg90siq efh/ 7k b:sy4e speed of sound waves in air to vary with temperature?

Give two reasons why cixmissbs6 ;- qbo:p*p0mfg ,/n rcular water waves decrease in amplitude as they travel away from thp /m6,*q g-fb p0msniss bx:;oe source.

Two linear waves have the same amplitude and spmxj8 6qxr rxs8 z9xlmc*u(l7 w v xq8-ol+f/a1eed, and otherwise are identical, except one has half the wavelength of the oth uc8l86+/lr(aq xf ms 7l-mj*v8wox1xz9r qxx er. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in 7/h 0n-c1fncup w3db hFig. 11–33, the frequency does not change (although the wavelength and velohwn / f3d7 p0-hccnb1ucity do change). Explain why.

If a string is vibrating in three segments, are there any places you fvme.*l 1i .mbfw:n(p could touch it with a knife blade without disturbing the motion mi(n1.m wffb:*ev l.p?

When a standing wave exists on a string, the vibrations of incident a 1; k/ksvy)i bqkx-ec1nd reflected waves cancel atb1 ky1s) -ec kq/ikx;v the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another,)qar4;ane/o x how might we determine na 4/x roe;a)qwhether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM b. * ej-*qfygzb:f(nf with amplitude 0.18 m, what is the total distance it fgz-* qebnbf(.f* j :ytravels in one period?    m

  An elastic cord is 65 cm long when a wa0u isly.+wv1 eight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs s la0+viwuy.1 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* fiej.l*fhaf(fi.w9 tr, v8h-kg driver gets into the driver’s seatvfe a*8 j( hitfriwf,* 9..hfl. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches a,rsuv7, upf n4rr r6d/z 62lt3.6 cm when a 2.7-kg fish hangs from it. (a) What is thevfr/ dar6zu476l urr sp, 2n,t 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 fr+ z/g cqwg.,5 q-ndn .n+piutvequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from ituzq+v pc5ng/+tqdn.w- g.ni, ?    Hz

Construct a Table indicating the position x of the 2h7ctnhq,/6* ihh:l kqq.kgn mass in Fig. 11–2 at times t = 0,7n. i6 gk2,ht*ql/ :hhqknhqct = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vib d s3w392 ucnhzc:s/ h/vjsq4orates predominately with a frequency of 4.0 Hsvshjucs9:wo3h /dq/3 4z 2 ncz.
(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 sm 7a5h: 6mw5atwn:z urpring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is w57:t :r haawum6znm50.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a s mn d; r0 .yn0+vnk8g.d )cdkyj/hr:kdpring vibrates 3.0 times per second with an amplitude of 0.13 m. Determine)k8cdmdd 0;+ry nh y .jn0/rgn.dk:vk
(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 o9ns8s l ejzs:cb6.)x u5 jwz)bf a SHO half the maximum valuecn s xz8)bwzljeus65j.s :)9b?$\approx$    A

A mass attached to the end of a spring is st(bzhjz,t6bm) y3v bb1gor,ak*;.ntd retched 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 stretch t7frn)q8fd1 p:j,akno*uwu6es a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium positior k7jq1fnf*ao,tw u n):8pdu6 n again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnes54lc ;r 3tcsquyd2:g7su ay)rs constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.:rssg 4 )yqdc r3l;2yc ut5u7a020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy p46 tr z/ohy;cp7+aes w ym66qbopgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball l6wpb4amy ; sze y/o6 q67rcth+eave the gun?    m/s

  A mass sitting on a horizontal, frictionzvv- zwx*sp);l 4iq:x less 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. If the mass is released from rest with the spring compressed, the mass expew-l*;v4 pqzxxzvs :i)riences 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 accorj jy+2eld2e1s4ehw h:b po+f2ding to the equation x = 0.45cos6.4t where x is in meters a1wyes4b+ f deejo2hlh2 :p +j2nd t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement (rv;1anq u6wujwh1hvq ;4z -g from equilibrium is the energy of a SHO half KE and half PErav g qh11nj;6q(-vw4u w u;hz? ±    A

  If one vibration has 7.0 times the energy of vem/cds snvw*s+w6 *9 a second, but their frequencies and masses are the same, what is the ratio of their amp*9 * sd/swcw +vvmse6nlitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hang2 mjt 4;49qxet0atwsiing light spring once every 0.69xqe t iw4j ;tstma4025 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 suppwpy5n :-g/i,tt4t jw korted by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49w-wti ,tp /g5 tn4:kyj). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x =uz9r f8 +tb,jfwqk+0hjja1p9 0.38sin6.5t where x is in meters anh+ ,j9arjftwu qbk10+8 fp zj9d t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled rz7/50e dg( *z;kvy5p xvsqxvA and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) -9 umy,b8sw o:zsxr tpz 4qk8si ,/a)zis struck by a hammer, which gi)w,-qzt xmkzbr98i sus,a: /4oy8zspves 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 vibratesdldu mn) o z(*:poun7b*o:nbfgz ,08i with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibriu8o,* :lu) bgunoz(opn7zi:bdf m0* n dm 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 spf6avtjnlf8 7d9 gm m*5v .-hwqrings, 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 horizontal s0zkr oi)h;fdvo1m;s, krs95n pring whose spring stiffness constant ii01sr; o rh) 5,szfd9vkn;o mks $ 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 frofail s19 wcj3:cq.6rhm 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 to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee q.ac: ji 3f6whslrc91cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations ink3u*n)gq 8d jz7pxzf.h9i asaz ;/ :oh exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if i k v0tcnorvw;u3 5xf8z-3e7rp t is to make exactly one swing per second? (That is, one complete vibration takes exactlyv3kwv;rr- 30nt8 f x7czu5poe 2.0 s.)    m

  A pendulum has a period of 0.80 s o iwppyxb-ca(a e+c6 97n Earth. What is its period on Mars, where the acceleration of graec+picby(9 -a pa76w xvity is about 0.37 that on Earth?    s

  What is the period of a simple o4x f;a7-j-n f) izl6 rr6vezdpendulum 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 0z 4/k 97lnyh u9vrser,qwv7 umass of 365 gr7l/ k0vvw4esq79yhurun z ,9 rams, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.94-if2 iulln *u930 m. If the clock loses half a minute per day, how should you adjust the lengt *uli4 iuf-nl2h of the pendulum? shortened by    mm.

Derive a formula for thczie2uu j 690ue 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 oscillateyag /b,2kafis;ui7w * s at a frequency of 2.5 Hz. At it is released from rest startingi/iyk aswaf;7 *b,u2g at 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 tgn*p(yxr eyed a-4 38o6t)f. nyr9knv he bow of his anchored boat every 3.0 s. He measures the yndn *e p(x6or. ne489y3 vg-ft)rayk distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 8u gdgdgtfuaj*).(n+javb/) 343 m/s How far g/vd +jtd)u.ba)fgn8 (j u *gaapart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (mv4b+o*i/b; *izw uxx0ssa7okilohertz) and tra*7 wo4v+ szx;0ub*/m b sxaiiovel 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 longitudin3tv)e7dbs5 aidi*b m ;al waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus,m1+ g;3o jx-aiyim(md but one is twice as dense as the other. In which rod will the sp mi i1-mo;g(a+y jmx3deed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betwe8e w,.9 o5oxj 48smohxu r5zlfen two supports 28 m apart. If the tensz oeho lwxu89m4 5.ofjx 8r5,sion in the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hillz w3agb84fe.y7w1xk t 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 cablxgw78bwat3 y1f4.kz e e. 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+.fa- w-bo ;+ody dnyzd i 2j/dqx4lw1 of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at bq jzwxyf2-d++wlnoo.- y/1 i dad4;dthis point?    m

  P and S waves from an earthquake travel at diff*a7*h r2 bndrl+sv p4gt 9aa:terent speeds, and this difference helps in locating the earthquake “epicenter” (wher 7*4a+v9tt :2dasl nhagbpr*re 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 ap 95.tb;jc lxojproximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which xl j9b5tojc;. actually include a mixture 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) tyyj6u 6lf1 8gmhe intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)g f6uylj6y 8m1    (b)   

  The intensity of an earthquake wave passingg+x+rllqk:/ .i imu+w through the Earth is measured to be lx :q/iw.+u+ilr+ kmg$ 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 frequeg8 67v(i u9zm.gh;s: qihcbo b:wid7;s8d pijncy travel through the same portion of the Earth, but one is carrying twice the energy. Wh. o6 hcdbu8gd(qjvp9g::i7bsiz mhsii7w8;; at is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretch0w1- ssi )g6 *bysoelmed string have the same frequency, but one transports besy *1g0)sm-sl io6wthree times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total vertical ,l .q9*g y0gmcw(cvqbdistance 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 factor does the bu (w0y,cgqg m*9l.bvcq g’s maximum KE change?   

The two pulses shown in Fig. 11–52 are m +en7,dfopkn 8oving 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 moment the pulses pass each other, the string is straight ekn+dnfo7,p8. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, o h*f/ bw*s.zxqdz1 55 exvxav3d-: auwhat are the frequencies of the first four harmonics?av xxfze-xv1d bs53 z :da*q./*huow5$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfind4n gw, qq9 d:x3lkuj/gered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates ask d93wl qn/g xqu4,d:j a standing wave.)    Hz

  A particular string resonates in four loops at a fr:ec ldu;wis6yof 5*28 *pzkz iequency of 280 Hz. Name at lea lsz wce*pi8 2 5id:yo;zf*u6kst three 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 is 92m/s gb,vf5a )rud0If the frequency of standing waves is 475 Hz, how dvg5ar), 0ufb far apart are two adjacent nodes?   m

  If two successive oveh hl.1q7r:u+ u ob j)vxor+z 3af8ze3srtones of a vibrating string are 280 Hz and 350 Hz, what is the freqe zxoh71 lr3uroh)+ jbv 3+q8.sufa:zuency of the fundamental?    Hz

  A guitar string is 90 cm long 17j 07aypqfpy r(kje8 and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is und pjyr(y7qpfa08kj 7e1er a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed t3wc /51mx)saru5y r ybo 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 them /cbyyx r 15wua)53rs 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 mew)b *hd evy+77-i snzzpvyx5 w+ +ei:gasured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the-zi+:pv7*vb7x)e iywdz+ e +ghs5n wy frequency? decreased by    %

  One end of a horizontal stri1eogv1/objd/gq 1pu;,md s q*ng is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length is b/ p1od d,*q1veg/gm soqj1u;$3.9 \times10^{ -4}$ 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 s-,9d zf,h5g 0erh pm*egm0gkgtring may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be acp0, grmf09 zm5h,gedg *hek-ghieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and y n 9*(9ik 4liknii/xhforth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a stand*n9/x( 4kl ihnki9 iiying 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 8;/s .eem7u1u imnkve km/s strikes a boundary within the Earth between two kinds of material. If it approachesse ieuk;u e8m7 .n1m/v the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the veloc :r* x*ht7nux9la8kurity changes from 2.8 m/s to 2.1 m/s If 8rxxal*u7nr 9*hkt: u 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 airu+mww x os7ru;qigb3,dy95 4 q when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of rm d ,yxgw74 qw;s3uq +i5u9ob25$^{\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 re6p d4j :zw7tpock at a wd :z7tpej6 4p38 $^{\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 dtjjso/5)t6+fhp/ h-mk0i iht iameter. According to the user’s manual, the dish has to be pointed in the direction of t/0tt-56msohj )/jph fht ik i+he 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 veloci /lcw*1d1zzk tty 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do th *dt/l1wz 1kzcey have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m,dt qn-nwz;8 47g k5ht-hws+wal baq2 Find tatq, -n5 lhb+ datwn 8-2ghkw7s4z;qwhe maximum compression of the bumper 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 oxab .eng. tx-qc);9rfrom a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple sprct9e gq.b-x;ao.n) xring, 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 mas-*ijm ;r.1t8 yt:pej h gklu0my d3hn5s then falls 33 cm beforeey tl 0h3;h mtnm.gu 1djr8:pky 5i*-j it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at.ch*0-rl jnvyik 7xi 2 a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constantl*i-y.rh k7 vc 2xijn0 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 ojq7baz;r 3kse-i9e s1f 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 (Fig. 11–55). Estimate the speed of waves in b;a3ssq i1zrk e97ej-the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from thl n y2j90 ,wzwar0cg/ee center of a 33-rpm phonograph record hav c,ae/0 rjw9nzwlg20ye a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the eqq pvn3v:m0- vjuation x=0.650cos7.40t where x is in meters and t in seconds. v0j :qv pv-3mnDetermine
(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 oscillats9zh7(gs+em ensq 8. w6svpun70k3s yes with frequency f. What is its frequency if it accelerates at 0.50g v+wges m u9h8.76npynssq3e(ss 0 z7k(a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lkxv( ai9.:lp/3bevjjpukb n9 * .fet,ake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the wa3np,(9kv.. kuep*jbi j/v a et9fbx:lter. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G)ja 8 y, ;hu5pyx+j4wrr and 440 Hz (ja+y4upyrjhx5w; 8r , A).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 116z:uzc .bpy/5st-x3vcv o 1kn 87ma tu–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that i nvt 1cu aox7ckz 8bvs6t5z-m.u3/:pyn 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,cy enb(p( h37qto/rv-ir 77zl and the tip of each prong moves 1.8 mm to either r-((777y lve/brz3qhit p nocside 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 oscillateid774tu (s i 4*jznpte2 vlasp.;)/o gbrqc5ys with simple harmonic motion of frequency 1.5 cycles per 2aq y4 .ucds* 4los7ezi)ig;btrjppt (v7 5/nsecond. 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 contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that canz+ : ,i vxmsxq c4ibw/uypk*:8 slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the rx8,*m kp vzw:u:x 4ciis/bq+y esonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has az:8esr1oqduji8 * j(nso o80h (h/vto period of exactly 2.000 s — each one-way swing takes 1.000use 0q*njs/to j8zhv doo((r 8 oi81:h 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 oscillazd q1bi6 2:glb.+oezate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let q.bl2 azg:oez db +1i6$l_0$ 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 strete23yha j)yp1 sis2i, :n p/vozched under a tension of 255 N. A pulse is generati y,ppz n3s21 v2e h/ajs)i:oyed at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffnessfko;950 yj; /fv zdyix constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny tfkx9o 0fzvy/;i; yd5jo just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyardwk1- 6zujq.:jzx6pig 8 8aw er. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is thej x8wuj zai6kqrg6e.p:8 1zw- period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. ecsj6lk:s9+p* mj x8i11–58 (which also gives the dimensions of the block). You push it sideways as showk*e6l s:x8spjjmi +c9n, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz