Give some examples of everyday vibrating objeumn14qnynvm r33 g e)7cts. Which exhibit SHM, at least approxi1ungyn ) mnm7rv43e 3qmately?

Is the acceleration of a :qi ti35hl1jys+ieh +simple harmonic oscillator ever zero? If so, where?

Explain why the motion ohju p(fuq 1d+0/zrk3 of a piston in an automobile engine is approximately simple harmoniphud(jk3/fru0+oz q1 c.

Real springs have mass. Will the true period and frequency b 0my(s; 9dywooe larger or smaller than given by the equatio 9 mys;(wd0yoons for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum cn1be7m nn1wf -9,:hcnnv vu+q9ud r5speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached nt7 ybaa 7mk88vng;m+xzpb+ 3 to the hook of a vertical spring scale, and then is released. Describe the 8+b3g7zyam+7v8; anmbntx p kscale reading as a function of time.

If a pendulum clock is accurate at sea level, wi-3 re ..mby8l,jwpl2gy k(ytull it gain or lose time when tak p3.u8rtljyy bmke2 .,gyw- (len to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48) fdx oy0do0d,7. How could you estimate the height of the branch using onlyof0,o ddd7xy 0 a stopwatch?

Why can you make water slosh back and forth in a pan only ifp bt+w)d0uk1d l6 --rnp2m oxu you shake the pan at a certaix-t6p ub no0kddu2-p mw+) lr1n frequency?

Give several everyday examz ep;y/o756t1ecl ysmples of resonance.

Is a rattle in a car ever a reso 69, hitakrsxfs.5kg 0nance phenomenon? Explain.

Is the frequency of a simple periodic wdq:q*fb(. 2kcp wpkn 1f,xb0 dave equal to the frequency of its source? Why or why noq:1f 2xbnp(bk,0fqd k*.dwc pt?

Explain the difference between the speed ofoagwiz8+b z 2zj,5h)w n+j. cs a transverse wave traveling down a cord and thsb ogji8w +zz+5a2wnjzc.h) , e speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency no1a1yr* rq,qhwjf*2d fglrt. *tes on a piano normally have wirtwh*,2 *qflq gf.r * 11yrrajde wrapped around them?

What kind of waves do you think h5+6viyc stdz82qm,.dw 7mk b will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizonta52tv+ .hw mdqmy c8i,6kd 7zbslly parallel to its length?

Since the density of air decreases with an increase iho6comj 0di: (w;t :cin temperature, but the bulk modulus B is nearly independent of temperature, how o:i :tmdjoicc h ;60(wwould you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water wavesyf0q0q u y)in8k*qnb.d *:pm a decrease in amplitude as they travel awfbn* ya)pnq d .y080*miuqqk:ay from the source.

Two linear waves have the samoij8 ehe:fg/(e amplitude and speed, and otherwise are identical, exce8 oih:f/( jgeept one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the 6mn)mk1bl 0ciuw d:zmb;e/ - uboundary between two sections of cord as in Fig. 11–33, the frequency does not change (althoumm clw-1kz; bb :6i/m)0 uendugh the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places yoab6l xmt (k4qo cb- f(/(zgzm3u could touch it with a kniqlzgmbz6(-(f cx4 tboa (3m/k fe blade without disturbing the motion?

When a standing wave exi*2gzhz/akl.fz ; wn2xsts on a string, the vibrations of incident and reflected waves cancel at the nodes. Doeswnz2/ gxazfzkl .*;h2 this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to asu :k;::csvcz nother, how might uz:kv s:;cs :cwe determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total di, tpv5p9.3ha3 kiybbrpigc2 2stance it travels in onb3b,rhy. kc9ti 2vippg2 5p 3ae period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangsu /flv,wzc7qu1i c ;trfs ku2 /(gt+/h from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constan/ lks,fuwu7quc i/+hg2t(zcr;/ v t1ft k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver ge-cz xwxt4k+ 4ets into the driver’-x4c+4ezkw t xs seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangsy(,tz4hh nb+bf2da ( ,3ubmqd from it. (a) What is the spring stiffnentd mqz,3(fh(,bbbu + hdy4 2ass 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 masd8 lfhz uisdz7vkrg,5o-fq;121 puh ;s of 0.60 kg is hung from it. What is its frequency if only 0.38 kg huqdvs2ugfodhl -71 k;1p 5izzh8rf, ;angs from it?    Hz

Construct a Table indicabu7 ekvqeu7( nw f5p *i4;skr.ting the position x of the mass in Fig. 11–2 at times t = 0,t =k(p v q *s4 7uubniekew5rf7.; $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibrates n7kw fw6p,rc7 predominately with a f,wc nf76kpr7wrequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. Wj;y)*qlfyk (,ak uy 4y8+idpmhen an additional 680-g mass ia 8dy,l+* ukf(4;k i)mqypyyjs added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at th,3mm 9m mo a6:bjcwd*qe end of a spring vibrates 3.0 times per second with an amplitude of 0.13 m9,m *3:omm caqbd6mwj. 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 equilibrigfqr:unn(w u2cn;*;s-62j2 qr+r -rcaf f aqmum is the speed of a SHO half the maximum valurfr; + am;u2 as-c6qcuwq-n(jfq2rf n:n*2gre?$\approx$    A

A mass attached to tct( ,qu7*bovjgoeg +x 4pu48by9y,,qkx4 guxhe end of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a veraglkrd:cn:38 tk1ea 3tical 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 position agag3dra t: 8kela: n1kc3in?    s

  An object with mass 3.0 kg is attachev1g d 6delf. 9lm25hiyd to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic mdhg2 fe6 dly m5i1l.v9otion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popzx1hvrhk.q1- plb/m1wx km fl2a. b)2gun 0.200 m to “load” a 0.180-kg ball. With what spe2am 1ql .xlbk kzb.rv -f/p2mh1 1)xhwed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless ql ;m)bq9y (fd1xvi f9mr/,yosurface 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 masfd1/yv;x9 qm9b )(oyrmfl ,iqs is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equati grwhv2e ra,(i6tb3 qhuz04 ,aon x = 0.45cos6.4t where x is in meters and t is in seconds. Determine e(q2 i,a vw,thhruarz 36 gb40
(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 equilibriup)y gok*5q 5sbm is the energy of a SHO half KE and half PE? o5pg )b 5kyqs*±    A

  If one vibration has 7.0 times the energy of a second, but tm/ +(zoekc)cv wr4nson:1gz) )s5afylo-b/ xheir frequencies and massesa/ mx f: egyn+n)z)()l4vobcrks ozwo/ c1-5 s are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vert -lrppbz, wdv-kay+:4 ically hanging light spring once every 0.65 s. r+ av-p -byd4wkl,:zp
(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 twow l a; gyj/p2i0nrsr,4 identical parallel vertical springs, each with spring stiffness l ;ig,yn /r4jsr apw20constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates acc o8 j+q tggboky+b3c)d pt0fd2 9pol,1ording to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. gtk03 obl+qdpopf,b)2j 1dgy98 +ot cDetermine
(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, vcdmlo45x r29v f7htf/4)vd i 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 at rest on the end of a h h9*zggim (v3r-g 0vnqorizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determineqhm(vz3gg nvgr*-90i
(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 amprdb+r,or 6e6j litude of 28.0 cm when 0.260 kg hangs from it. Thb,rrrjd6+ e6oe mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spri3u.7qb , gcybf/oqkx ;ng 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 afo *p /-ftaidzc u5t8m 0bz/i9 fixed horizontal spring whose spring stiffness ci9-a5*t0uf8 z / topdmi bc/zfonstant 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 f1( fbwr2+z ffitq ;z.grom a high bridge. After reaching his lowest point, he oscillates up and down, hittwgz +q;1f. (ftfbri z2ing 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 h4ip1si n+m0 2aezxv2(xb5 nbin exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to mc9zaq 1s wj2w)ake exactly one swing per second? (That is, one complete vibra2s 1a 9zwcqwj)tion takes exactly 2.0 s.)    m

  A pendulum has a period ofe/kv-k d hwmd5(; kv+o 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on k-w+okh kv5d( d/v;em Earth?    s

  What is the period of a simpler a) gq m4fp6ej).pwb 2xjd/x0 o9tlu0 pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum i. ,epfyc 818m mxojv, )aj3lkas 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12.aaj3, ,km) p.cl881 omfexj vy0 $^{\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. prd:/s*baet 19930 m. If the clock loses half a minute per day, how should you adjust tt*1d:srpb/ea he length of the pendulum? shortened by    mm.

Derive a formula for the maximum c(;r:4hfr wn,l fc +vlspeed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at aa( l-febnuxpyuj2g*1nk((xt b1 + 5fg frequency of 2.5 Hz. At it is released from rest stat(y 1p5fu1 nebk l+fx(b2(*j gugaxn-rting 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 passu:s-mlhx r97au b3tl( the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves ttrhl( 3xmbs-a:9 ul7uraveling?    m/s

  A sound wave in air has a frequency of 2z.ds)a)dp1 eikmuvj 4li( 6w /62 Hz and travels with a speed of 343 m/s How far apart are the wave crdp )w1v./jl6mii(4a d )kz seuests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kpsvv 6v 5q)tm+ +i),lyocpz6oilohertz) and travel with + 6vilv+ty mvc)5,z 6oopp sq)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 longitudinal wavesv5) mz9 y9w:*rqy ow(6thltby in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, bu;ph/doodqb bga *p w/wl .79r-yf 3w+e0rdxq(t one is twice as dense as the other. In which rod will the speed ooq9*g/ dqr +.bhye0xol /(f 3b wpd7drwa-pw ;f longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If thbxdzzv 8ezu9i i*002re tension in th9vzu0zibi r08ez 2*dxe 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 hill by a stea.9 yxu45keejy:(e )ofg3 5wmzvdi c 6b,5my nel 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 puen.634 (v,yo:5medxb5w5 fzjcyge uk mia9) ylse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the sudydm.h rrq u1e:g4 4,qrface of the sea. He hears the echo of the wave reflected from the ocean floor1:qu.gd,re4ymr4 dhq directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthqu-zdv xl w hk-w9v+xn:mo5 s30iake travel at different speeds, and this difference helps in locating the earthquake “epicenter” ws x-+xid : lnvk5z90mwho -3v(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 surfa4t:q :4 kh3xp5wv qxmf*a,jelce 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 contact with the ground? [Hint: Seajqw5l,4:v p3:efx k tqmx4*h t the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earthqub vtd0bb *1 9)njhq.wxake P wave passing through the Earth and q*hwv19 .b0xtj db)nbdetected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through t5uysjho.6 *tgm hnthba4ng1 9f 9t9 3she Earth is measured to be 95jf9s*6g os9thb4htag h un .my31nt$ 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 throughf5veuvcu mx 23ac)m26ba5 j ;nw9(mjr the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudu35 wmmv ;2cje j(vu 9)2 cxba6a5nmrfes of the two waves?   

  Two waves traveling along a stretched stb aep;7r5vtf /b wub)*.z (qeuring have the same frequency, but one transports three times the power of the other. What is the ratio of the amplira* b(zu.p;btq5vfb/7uw ee )tudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a tx;nnc obua s4*je)g7 ,otal 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 factor does the bug’s m bac 7n*4g xo,sjuen);aximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each oa9rui9 9kgr5 ether. (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 mo9guri9 arek59 ment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency,udr 5u),scq -r what are the frequencies of the ,5qs )r-cdurufirst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates aq,l ;.l;hrwb8y:ue4 y+b yi edt 294 Hz when unfingered. At what frequency will it vibrateq wy. i;e ulh,dyy4b8 eb;l:+r if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name atpzuars .v,p7b,9e q/g least three otherp sb gzq9r7v, u,./eap 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 frequency oft zr.hty td+f2 d7k.m+n)gp :dm8 .j0 viq4ufv standing waves is 475 Hz, how far apart are two adjacent nodes?)dp.dd .yvjtit htz4rk+8vfunfq7. :2+g0m m   m

  If two successive overtones of a vibrating string are 280 Hz and 350 snb dz9 938jthHz, what is the frequency of the fundamental?n3bj9sd89 hz t    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distafayah 5iaz, 86dge3tesq ;4il y/t9+ance from the bridge to the support post is L = 62cm andai5glz e4sht 3ai +9a,6/ate f y8;yqd 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 supposed to vibra,hx d,pbixmi c0z8 3r7te 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 the frequency?So thexr78b0i3h xd,cp i,m z three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed afba+3qtj(+:qi2qoz) 4 jnequj 6 tga 5ra* q)to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what pee*bf q ():o)gj tja5raun63a+j aqzq4q+2iq trcent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to avrk qc;q+ x3i.7hba c1 small-amplitude mechanical 60-Hz vibrator. The strivc axkq7.13bh; +crq ing’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjustedfw)ciq7w7tgw 7jq2k6qvi7 psr /d64 a by moving the pulley. If the hanging mass m is fixed 4 sq t7wpk62i67wi)a/dc7gwfvjq7 qr 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 right frequenc -36cs/yxxt,jl; a vbfy, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. ys c;/jafltx v-x 63,bWhat is the speed of the water wave?    m/s

  An earthquake P wave travelinz:v:pv 2 cn po- q+l a4 f6nghpve)2jstp4d16kg at k.0 km/s strikes a boundary within the Earth between two kinds of manp oqdvnp6fa-sv: 4l :jk4c+2 e2 pz gvpt)h16terial. 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 the velocity chh..i luj9dx2 danges from 2.8 m/s to 2.1 m/s If the incident wave crests make hj9 d2lid.x .ua 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 lj2c,fpsq3)vzi 1- ppd ayer of cold, dense air. If the sound wave ) s3p-2d pcvpf1qz,ji hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between tmk/4xxr11os -f-a9 auf+s30ikpqsr l wo types of rock at axrosms3+-/auka- 1qr0 pfi9 4ls1kf x 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s macdsp9 /n;7 cbanual, the dish has to be pointed in the direction of the satellite, but an error ;bac7sdnp/c9 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 trv2idkpw1s. 8hs(p .tiavels across the Pacific Ocean. As it approaches Hawaiis.2i vhkp (pit8s.wd1 , people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stm2 n)mrtolu+n0/d )udx1t sf /iffness constant of 550 kN/m Find the maximum compression of the bumper if xftr) /odt/ m d+s1nu2)u nm0lthe car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a wind8psznap*2ut yn6, /kyow to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple springu,/n* yyp z6skn28tap, 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 p--, 0;writzqn c6 zh)hguvek5laced on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise uwkz5nc)h6reviz;- 0h - tg,q. 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 ;bkkg4cbpqo(p6w a;g64h9 nmompressing the sba;oh;944pg mkc wn gq6bp(6kpring 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cunn, j x lxq7r4) 488lukbnpv+mdlz6j* p of 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 v+j, p unl8n)z*nlx64qlmrxdj87k b 4(Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of aytb1ya5xk(aqo acvp7) 6a4 . d 33-rpm phonograph record have a wavk7 yto)v. cayqxa5461a( ba pdelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t wher9: 6e,g kbfrb; vboy.me x is in meters and t in sec ;ov.,mey b:kbbf6gr9 onds. 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. Wha orh gw1m(67fht is its frequency if it acceler hhwgr6o(f m71ates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man st j494.pi g8oeh rc nip8:n2jbqands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for e .b48gpq4nnphij :rjc82o 9ia 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 in6r tfql;w3y 1.f kf zj3fo*-brstrument are tuned to play at 392 Hz (G) and 440 Hz (A). 3;folzf-w r *jkftr31ybq.f6
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 11–ecs)e2 1 oeir-33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, -ie esroce)21 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 2 :6vm2 +vyambdvd 69 x1t;00xxwvdm sv64 Hz, and the tip of each prong moves 1.8 mm to either 0 xwmv6b1v v6 dmvt+s2 y0v;:maxd9dx 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 ofhgdni3 dhs0u7 /5ixy.jz2 1l,8bxleml5f zk) frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebdni g,hzxf y7 md.sei51582zxl0ku)hbl lj/ 3ble 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 ri/lscg6 l2j hg0ng that can slide withs/h2lgcjl 0g 6out 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 other free.

  A “seconds” pendulum has a period of exactly 2.000 s — e: e5j3mil.xj hach one-way swing takes 1i.h5xjj :3 lme.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 lk4d f31,h+b dr lw3nqin 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:qdh+lfn3k rb d,1w3 4l 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 masi/nxjve8-(.f.) v bvjltosg, s 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at thitgb v, lsenf .v/)-jx8vo.(j e opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling paoxk ahw7k :46u., elby a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of a4kk, l:.paxuoe 67 whthe block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cranepkq2bk,/ 5n7o d7jkxe cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bp5o7 bnk7,x2 dq/ek jkouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives the dn y5o2 mv2hwrt5)x1 guimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this r22m5tvn) 5uwh yg 1oxvibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz