Give some examples of everyday vibrating obj 8ojp;t16qo-ktx)vu a+n unbz(+ddh 2ects. Which exhibit SHM, at least appr2z+ojq-h(o n8pb;+dut)u1an vk t6xd oximately?

Is the acceleration of a s*.soh /fob v2sagj)1ot d9mw 7imple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston itq:h:bire (ei-;k 2wx 4snzm7n an automobile engine is approximately simple harmon -:w7qmtbi;i e xsenzk4:2(hr ic.

Real springs have mass. Will the tru4, *zfheiuy3 be period and frequency be larger or smaller than given by the equations for a mass oscillating on thyb*zui3h, ef 4e end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmoniczj-8hnln t,*r oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spr+d 0hnri ;z2,dn ggf5pi6iob 0ing scale, and then is released. Descrb;,g0 dzg2+n5i0i fh 6dip onribe the scale reading as a function of time.

If a pendulum clock is ax.v9r1mrln8q4 o3msaja 4 wb7ccurate at sea level, will it gain or lose time when tak .j4rao49s a3xn18brqmlm wv7en to high altitude? Why?

A tire swing hanging from a branch reaches nearly tim lu sf(r/q -gri :k-+q,a/wjo the ground (Fig. 11–48). How could you estimate the height of the branch using onl+k/i,l ui/- qmr(ja sr:-fqgwy a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake+hbsc6 6nlxb . the pan at a certain frequesbnh6 .+ cbx6lncy?

Give several everyday eo6 *q5:e6i bcc,qowx mxamples of resonance.

Is a rattle in a car ever a re wek60y5.no),i zwomtsonance phenomenon? Explain.

Is the frequency of a s:-y -pfbfa) m68wdyg-c x 5tyiimple periodic wave equal to the frequency of its source? Why or whg m-6pbfdy:-xcatfw8 -5) iyyy not?

Explain the difference between the speed of a transverse wave traveliacy6 z2hsf ,4zng down a cord and the speed of a tiny pia 6,zcy2sfh z4ece of the cord.

Why do the strings used for the lowest-freq:w7di 381qppkelzjsa7 eu+7o uency notes on a piano normally have wire wrapped around thipklew7d7sa1 e puz:37oj+q8 em?

What kind of waves do you think will travel down a horizontal metal rod if y9 ri(a( hx bjfg:cmhda w:q-,.ou strike ica:.ab (d,(hj-h9r xigm :wqfts end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in tempe(by3jm k.qu s9rature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air t 3qyb k9mju.s(o vary with temperature?

Give two reasons why circular water waveai:.nb pss xz*e3(0c yq rv-v7s decrease in amplitude as they travel away from the source:iqxcvsarn- s(*.pvb3e7 yz0.

Two linear waves have the same amplitude and spee :/uuwnat(4/yey jqej6x19lc d, and otherwise are identical, except one has half the waeytq /wua u jx (94:n/1ecy6ljvelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections ofnu)fbqra--ri3ek -y7q pq* 2f cord as in Fig. 11–33, the frequency does not change -e qfa-2fyb-q 3q7 *p ri)urnk(although the wavelength and velocity do change). Explain why.

If a string is vibrating irw 2ckami9:; c;9moft n three segments, are there any places you could touch it with a knife blade without disturbing the motio rk29;t:ac 9 ociwm;mfn?

When a standing wave exists on y ,kv.r8ciq 5oa string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that yqo,rv5 kci 8.energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to anotbsj91v8hr; wr.ia qj5) ovl.m her, how might we determine whether the energy was being carried by particles (material bodies) or b;hqwalm 5.o19 ijbrvjv) s8.ry waves?

  If a particle undergoes SHM with amplitude 0.18 jo5ws c6y0vu)//uq a sm, what is the total distance it travels inwy6j/v qu u5)a/ossc0 one period?    m

  An elastic cord is 65r;8bpy ew*d5 uh 8zscr /t u,r+6glr7x cm long when a weight of 75 N hangs from it but is 85 cm long when a weight oftcl6 rry*gx5u7 zw d,r/8s +bue 8;hrp 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg 0 8zpkr4j7oz 7scx(micar compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency0z7 (jczm7i r kox4sp8 of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm whr)jl (es0kw0y)g9 p nzen a 2.7-kg fish hangs from it. (a) What is the sprinslyrj) p)g0e0(9k w zng 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)xlv )pc;.ffx a mass of 0.60 kg is hung from it. What is its frequency if only 0f.)fvpcxl );x.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the massucor- rwy2 /h22(y6u dg8s pgsskf,/z in Fig. 11–2 at times t = 0,t =h2cyz( r g ps-k2ssrw,fu/o 2yd/g68u $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 axz: w pl6xv-ko .ie:l04/psmx spider’s web. The web vibrates predominately with l6px:l.p-wx0z o/ i 4s:vkxema frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When an ado:abf ) 3t8qkxditional 680-g mass is added to m, the frequency is 0.60 Hz. What is the va8f)obta 3x :qklue of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 a ,n8 hwf65sebtimes per second with an amplitude bna8s6f 5we, hof 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 equilibrium is the speed of a SHO half the maximum valq(1rgeu,w;+7 vt qp0fi lebf 1g+fpbqlwt ee(1 0f7vu q r,;i1ue?$\approx$    A

A mass attached to the end of a spring is stretched z :gbpd;-/ hdra 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 vertuk(,d7yajg vn) 2j l(mbib:m (ical 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) equilibri,bj(:n yv du la(ibm(k7m) jg2um position again?    s

  An object with mass 3.0 kg is attached to a spring with s;wmban, (az2 o3yu6z (c uvb*dpring stiffness constant k = 280 N/m and is executing simple harmonic motion. Whe;ny( bo3cv,*auu6b2w m (zzdan 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 comyvcean27 dqs d+jb f w2lh67.1press the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave t 1v.ahyl2nd27jqs6cb df+ ew7he gun?    m/s

  A mass sitting on a horizontal, frictionllj;+8: dw1po r9s1 oghg*rkreess 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 f hw g8o9:1rl*p eo1+dk ;rgjsrrom 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 accordf:(eeya4-yju qx )pvjdmdd)9ty 7/ j *ing to the equation x = 0.45cos6.4t where x is in meterxdfjd)mey7-*vy j uy9:qdpj(a4 e )/ts and 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 from equilibrium is the energy of a SHO half KE and haldfcc*zgx zn ci*47d7v ,, 6allj/g;yt 4,jlapf PE? ,,n;c 6lyla7cd,t p xjzilagvz/c jg4*7f*d4±    A

  If one vibration has 7.0 times the energyx1) 6xrcp/b*.yct xbn ub*d u- of a second, but their frequencies and masses are the same, what is the ratio xbn6cxyx. u/r1d )t*ub-b* cpof their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once.ijo:7 3us;k0m e wv5)kwvook every 0.5k; o.w ) ve kmv7ouiwk30oj:s65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical sprizb *4wve75: xg.kjsvcngs, each with spring stiffness constant k (Fig. 11–49). sc jke z*.bv 47xg5v:wWhat will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0b 1gu, e*:*zzbj(hx;7qwo;mde6vc j l.38sin6.5t where x is in meters and t is in seconds. Deter;hub(6qe7voezz xmw j* g1 *:cj;,db lmine
(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 examplekgzq8e7fl7is v0cn* -atr 0m *s of SHM, 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 enapsu(3ul4 8mz5ko z2jd of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s De5 apzum3kj2z 8s u(ol4termine
(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 withniphgugvh7y3q2 +/v/ 06 ocd c5jrl 8h an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes thrrli o+ h5ccvu3p6g8ngjh 2v/7h qdy0/ough 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 s ovg6+ bxx -w/ g0(z.g9r0lb 9-x 2zwrrwclksbprings, 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 at)1s3 jej2yex1i:b k(h;07 ga wenzmtitached to a fixed horizontal spring whose spring 0ixatej m( y3e7h2;wik:g1 s b 1zej)nstiffness constant 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. After reach bi;sotb.55 :p ck:iuaing 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 le i:cu.b5s ;ia:bpt5o kngth of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s.08nib9 dimlj) What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one sdc y3)a yoo)wdd9w3 fc:6d 2f dmsk-u7wing per second? (That is, one complete vibration takes aw-7mu:2do yd3)c9fwd d63f)o ckyds exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wher : 1qra*n:m edkpnsk4gj6gp -7e the acceleratiggq-j1ern 4* :n6smda 7kp:p kon of gravity is about 0.37 that on Earth?    s

  What is the period ofq2cw b, ve*2 fce*yaxakk50 b3 a simple pendulum 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 pe ).,r g qpppeaxod08b.ndulum bob has a mass of 365 grams, and it is released at an angle of 0pbaepo., xd8gp).qr 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(y,msfo q gu6s4-ejm3 ck’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day,suy o6 ms(-,je4gm3 qf how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum so(n guvv93t (dpeed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates 2r8mco( lc 5/ecs25z6wqqi zr at a frequency of 2.5 Hz. At it is released from rest starting at an angle ore82lcsro2 cq/ mqzc( 5z w56if 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 pfc(sy:n;j f 3his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast n 3pf(fcs:j;yare the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz anpbf-ygvzzo )9u;6i0ghgv29 h e/a m3nd travels with a speed of 343 m/s How far apart are the wav)uo i69 g z/0eh2mav y9nz;pbgvgf-h 3e crests (compressions)?    m

  (a) AM radio signals have frequenciet-1iexq)dl d6gk3 l:k s between 550 kHz and 1600 kHz (kilohertz) andq1x63l)k- e l:tdg kid 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 longitt40v in+vrw+z udinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but onel(u2pa8 cs+qhym( l*w is twice as dense as the other. In which rod l 2(hu+lsp*m8(y wqacwill the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports8x2nst2. wuzk 5lka,d9k7w h g 28 m apart. If the tension in the cord is 150 N, how long will it hz 89 uw t,kk.2gl75ksdxanw2take a pulse to travel from one support to the other?    s

  A ski gondola is conneu7m:kyhx/ (n)m- bbyicted 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 nh)/mu-7xikmy(b:y b sends a wave pulse 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 surface of the sea. He hear9zf*qhco8 qzvj0)*c8c7oga4qo* v xe s the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the c89vg* c*o)qe zj zq 7 oo8a4xh0*cqvfocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and thisbq70zhak:fk , ;e;wjo difference helps in locating the earthquake “epicenter” (where the disturbance took plac; 0kajq,;owzf kbe7h:e).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinuso7i(u hu dbefoc7 hx*rra+ +b .n544chuidal 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 5474 f xbo7hua*e.(uihnhb+ +dccur r contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of a0 orzpjv29sb ;n earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the r9j0pb2;so zvsource?(a)    (b)   

  The intensity of an earthquake wa:q9 v+qstry 1)kstx;fve passing through the Earth is measured to be xqsv+k rqs91:tyf t) ;$ 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 sam8 m nw)h msjhv-*rkd pir16* xr).f9iqe portion of the Earth, but one is carrying twice the energy. Whar6.vni x 8fsm hip-1) jdq rh)m**rkw9t is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same yyq enao;:5 kt8kbr0ef*oc57frequency, but one transenoqt y8o 7 bka:y;e5k5rf *c0ports three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a po7miwk kqhs o 3y2fcg3 u+px*:)nd is 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 x32pum) f*kisc : gqw+ykoh 37decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each othvj u;)5aj;zh uer. (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. What has happened to the energy at thisav)u j u;zhj;5 moment?

  If a violin string vibrates at 440 Hz as its fundamew)k zo*(2)r y:e gdkfcntal frequency, what are the frequencies of the first four hfrz edo c )(ky)g2k:w*armonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequytw8hl px*-,h 6tz;xd.jl+ ltency 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 a6hl tz+;l*hwjxy8 tx .-,ltpds a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 2f, ivi (q b(zs5-w0kbcc16udj80 Hz. Name at least three other frequencies at which q1 (v- ,k c5cbfb0isdu( izj6wit 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 frequenc)aa/xj:3s tcgq4d0d my of standing waves is 475 Hz, how far apart are two4 3da j:g/qdxs)0t mac adjacent nodes?   m

  If two successive overtones of a vibrp8o(q7j 8wk qmating string are 280 Hz and 350 Hz, what is the frequency of the fqj koq88p7m( wundamental?    Hz

  A guitar string is 90 cm long and has a mass of v()i,2iq fu0y.aa nxl3.6 g. The distance from the bridge to the support post is x2)auniy lq0i, af(v .L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but ktge3n tob8 c31;fh6qit is measured to v1te8h;3c o3k6 tgqfnbibrate at 205 Hz. By 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 str,tb s f:/a+l jn:rqqb*u7u 7jcing is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. B,7q /ja+tj7qf *:l:unrbsu bcy what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small2bud3yoo(xax ,:6 7 jnvte0 +5bv 0r b)wimzag-amplitude mechanical 60-Hz vibrator. The s6 mj0 txa) (oz52,u3wi:eg n bvaobvbyr7+x 0dtring’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 adjusted by moving the pulley. I6 co iy zpw+uje:dc,53 l6w47rx+g ziyf the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1u lic:w jx6o6zdi5+7ycyr,pzewg+ 3 4.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency,4v0jy, wnew. e 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. What is the speed of the water v ww04een,.jy wave?    m/s

  An earthquake P wave traveling at k.0 km/s srh5ur mfy+x 8t7s+dup4hx65wtrikes a boundary within the Earth between two kinds of material. If it approaches the boy7uust6 fx54r wmh +h+ xp5rd8undary 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 amimtn kfp:0+a. --ei,fh cymh. .acr1n underwater “shelf” where the velocity changes from 2.8 m/s tfh+ytn:i-ha01mmmcacfe k . .-ip, r .o 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, rh i.cqb,vu8j4w;x8t dense air. If the sound wave hits the co8i. vxhcqjt,r4w 8b;u ld 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 betweeq hhbx8sz6 k r49g cd5/q:zfj)n two types of rock at a 6qjf :/)rkc458dxbhqz9s hzg38 $^{\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.+9p6fe9nt w ma5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of about nfm969+t wp ea2 $^{\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/ cxmq)vzi8s68h 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 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 strand 8s c)8ixv6mqzed fishes and boats.)    min

  An energy-absorbing qk7 ag2x2vbkv*04lw vcar bumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, co 02v2al*g7vkbvw kqx4 llides 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 windomp/ f i4g,etf2w to a fire net 18 m below, which stretches the net 1.1 m. Assume tm peg42 tf/f,ihat 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 c (xixa/4(hwm 9*l xrnthe end of a freely hanging spring. The mass then falls 33 cm before itx(rlhc w ai*(9xnmx4 / 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. 74jia pj (ujwuep0rp 6y0f2u611–54), compressing the spring 5.0 m. (a) What is the spring st0uewuji2pfrapj04j66u yp ( 7 iffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diametet(ovshq xfa 95j-xpwoa 5o/ :6r 8 cm) at just the right pace of about 1 step per second, the coffee sloshes morexpos fv 59q(:tjx-o wa/o6ha5 and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cmxw6zlukii1 469f lsv . from the center of a 33-rpm phonograph record have a wave.l1 vz fu6l ixs6k94iwlength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accorma+uo8s)d1o f ding to the equation x=0.650cos7.40t where x is in metao8u)+s odf1 mers and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if it meabc2eo/6w0accelerates/we6a20mbe co at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a k776qxij 4plroqd9 w975-kg man stands on the raft, it sinks 4.0 cm67 dr pjl9kiqow7x4 q9 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 to play at 391x;my rwkew2 b*(ayr 5.wgx+j2 Hz (G) and 440 Hz (Aexw.y5j;rk1 +2ywx(gbawm* r ).
(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 streg 3af;.r y.hcv*a2 xrttched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heav2y;f.vax h3.a rtcr*gy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of l7zd e0dkrvw8n-5 ay:5dh q1deach prong moves 1.8 mm to eit kz1l5dn ryh7vwe q5-0a 8d:ddher 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 1.5 cycles y:ub z :mmyy1 faih 1p6p((1ldper second. What is the maxh1 m:y6( u1:a1pm(dy byiplzf imum 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 can sli qp;bsx :e+qz3kef (1lde without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one enkebfe(:1+ lqx ;sp z3qd fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 (j 3.,dook /1kk e vrl i1 2gguzdlofu+.ce:0ds — each one-way swing takes 1.0df2(l kog,11 : cuov3douk.0rd/ geie+l z.jk00 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 csn1+fgx )-s,r7az qb vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, tc nza,+ )sg7bsxf-rq1he period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tensio- wdc-e8faf* hr m7x 22rg/sebgspi), n of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two be*e/ --msg,rrf a2sw27cifx8)pd hgpulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring st byzxp)uh b5g:)+hk/eiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will )/ )hu gk+z:e xypbh5ballow the 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 is 2hff)td/p4,*)skqz b n2 m long and has a diamet*/hq dtp,)zkfsbf 4n)er of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives the3ex( tu2 iye( ghjjl.4 dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. Ie uj34 gei(y 2tj(x.hln 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