Give some examples of everyday vi+.)v oviwylh-isl2 .,6jcth fw-vq7 ibrating objects. Which exhibit SHM, at least approximateli-cl wt hqw+o2y-.sl7 ) ,.f6jvihvivy?

Is the acceleration of a simple harmonic oscillator ever zero? ;dikt :p7bf/eIf so, where?

Explain why the motion of a piston in an automobile engine is gz jm t: q6pl;* r9gsucd -*.zk6jp6cdapproximately simple harmonic6 dpgzgtjl*r6-jsd6*pc:zq .uk ;9 cm.

Real springs have mass. Will t s0wo dm32voj9( 0 pu9ndhe)amhe true period and frequency be larger or smaller than giv()ap2 u0hmeo0 vd9sd oj9n3mwen by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the max (1ryt(emqsg61o w qf073h jmdimum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and thsomd/c wkq-t9z) i+ )den is released. Describe the scale reading as a function of time.wsizod+9) ) d -ct/kmq

If a pendulum clock is accurate at cx1h n1s *mdv0sea level, will it gain or lose time when taken to 1xs0 mdv1h*c nhigh altitude? Why?

A tire swing hanging from a branch reaches nearly tor.8qsd+ 2ve 8b0ygpnm the ground (Fig. 11–48). How could you estiq8s8ryb+0n 2epm.dv g mate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a/d io(6ef z-s) n0( +/pbflkw*j 0+cpmsftjvw pan only if you shake the pan at a certain/ if wsb-+cpv mepd0/w jok(fj+ *6szn(ftl0) frequency?

Give several everyday examples of :s+wqxslcj :-rxajig,pt-d 5 2+0 i ukresonance.

Is a rattle in a car e *yo8,jnmn wb-y(1kcqver a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its soi +dfd.c(yu( furce? Why oid.yfd((+ cfu r why not?

Explain the difference between the spe,xqh9.k n+mroed of a transverse wave traveling down a cord and the speed of a tiny piece of the ,h+nqr9k.m ox cord.

Why do the strings used for the lowest-frequency notes on a piano normally have uiu(f xu8,pbmnu; -o6wire wrapped around themiuu,u b-(fm o86px;n u?

What kind of waves do you think p:2 lykxm2 vizr.. p4iwill travel down a horizontal metal rod if you strike its end (a) vertically frk2iv.z.mrxi4 yl 2: ppom above and (b) horizontally parallel to its length?

Since the density of ai+tppx9bt2r 5h34 lxx9.avs xe/ ywg7rr decreases with an increase in temperature, but the bulk modulus B .ast9pe4x/ xrlr2p5 w7b3g vy xhtx 9+is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves n*tqgitc*lqo5z 3+4 ,k snkq/ decrease in amplitude as they travel away from the soutgk*t 45* n clqksiqn3/+,oqzrce.

Two linear waves have the same amr n( vzmocf4g 2xgu)q*m.3+bp plitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits mor*x3fg4g +qomm)up2z v.r(nbce energy? By what factor?

When a sinusoidal wave crosses the boundary between two sec8i sv vyma4 p2a0vixy0ys;9d (tions of cord as in Fig. 11–33, the frequency does not chyy( s 0idp4vv28 0yimxavsa9;ange (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could to k3lm(hj5hrj- uch it with a knife blade without disturbing the mot5jm (-kj3 lhrhion?

When a standing wave exists on a,uojqom7 0i6 5xvr -yz string, the vibrations of incident and reflected waves cancx5q 0-u7i y ovzojr6,mel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmittednmtwohe0 e5oucb 3bd 1 m(60i: from one place to another, how might we determine whether the energy was being carried by h3t w5( 1ceoo b6b0i0mmeu:dnparticles (material bodies) or by waves?

  If a particle undergoec l v h(dusbv+t0 )dr)f+*1dfos SHM with amplitude 0.18 m, what is the total distance it traveoub+h+)tv d10 fs*l(ddr)f vc ls in one period?    m

  An elastic cord is 65 cm long when a eri6j7xe9 z -4hd;pekv v3-bi weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs frr p-ievzb- ei ;edhv43kx6j 97om 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 f/-ho99swpsu,o as8 r-kg driver gets into the driver’s seat. If the car goes over uwsr 9-8 /o fa,9osphsa bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it./v8 t iq*6wrmq (a) What is thwrmi t v*q8q/6e spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz wh9*,1d*g kuhdzz nqk-aen a mass of 0.60 kg is hung from it. What is its frequency if only 0.38k1 ddz h*nq ,kgz-a*u9 kg hangs from it?    Hz

Construct a Table indicating the position x m /7l)ozrb7xxof the mass in Fig. 11–2 at times t = 0,t = x/r)omx7 7blz$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 predo d:yddo;o c/t2minately with a frequenotd:/ ddy;c o2cy 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 wijpdzfi nt- k x+ 5ur/h2.xn2sq-90cmw th a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency ixidmn2su -.hrfc 9 -qjxk2pz/5wn+0 ts 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0rtlihs)gy4m 7f: 8 y6y times per second with an amplitude of 0.13rlmy 64: gyf)s8i y7ht 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 o +8y)ynrz+/zw9ue yxequilibrium is the speed of a SHO half the maximum valueyo)/y9uzwyxn8e+ r+ z?$\approx$    A

A mass attached to the)ma34,lo p.omt(k 3-d enel el 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 vertical spring 0.315 m. If td2 ei9/s.k:smda. +gwhax p)ihe spring is stretched an aiads kspei.9:/m2d gwxa +h) .dditional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is atvwk zc-da,g,c0d:0x p tached to a spring with spring stiffness constant k k a vc0zd-,xpc,0w:dg= 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/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 springq r8syrn-j qv0h/cw)r4 :*l. )sblzxn of a toy popgun 0.200 m to “load” a 0.180-kg ball.q):lvhl-. snbn rrj8q4rc yx ) sw0/*z With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless8nr7o ix 45c-f vxgv:l surface is attached to one end of a sprinx: n- g7oiv4r5lvf8xcg; 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 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 edg7 uugyp .81according to the equation x = 0.45cos6.4t where x is in meters and t is in sec du.yg e1g7pu8onds. 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* fmsjfo7xq;1 /lrte5 and half PE?/frf; mo t e1qjs57*lx ±    A

  If one vibration has 7.0 times the energy of a second, but their freh7ume(bbu+lo 2 ejv/ ;quencies and masses are the same, what i em/7juh2vl beb(+u; os the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertqkv) qrd,7fi 1.kf um.ically hanging light spring once every 0k7kvf q.)ruq.md1i, f .65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identi 7l )i1:npl5lds k uzg5 0(axywo3le1ecal parallel vertical springs, each with spring stiffness constanl: ng(iew)ul1 37sx05ldy5pzo e lka1t k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.ww tr i9ka 4b9qk.;sl.38sin6.5t where x is in meters and t is inwr k4tq9bsa9i ;wk.l. seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. F,ct.n qz( lfiwa2ol7yu7h, 9d or each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a hiv0o9y zdy( ;m.:ogc morizontal spring (k = 124 N/m) is struck by a hammer, which gives the massoo.y 9 (iczm0y:mgd ;v 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 spring7 at 1-u3wjzpa stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium z-u3j aw1apt7point (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 spring stiffness constantsx 09aobpnr xw39f k0l:zbf ;6z $k_1$ 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 sprinb4i7 pknepjv i 5l)k*ws w(j3,g whose spring stiffness constv7*n)li5kpb j 4ew(wpsk, ij3 ant 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 *7p.1x jajmadz2mwt3 jumps from 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 bridtw 1dpjjmaax.mz732* ge. 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 vtgd c. qbq8d8n j4a1a:ibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per secfrzd8;blpp9 gy(twi 5. .qk3 sond? (T(8t isw ylz b;p.pq5f93 g.drkhat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.v3qe -y3; o8qp*xrxh -wd3uny80 s on Earth. What is its period on Mars, where the wy -3oeq v yx33nx-rdp; h*q8uacceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simpleaa p-g ezqcut3 6yh797 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 zogpgk*3z)y:h y: *:*r qzjgo0.760 m, the pendulum bob has a mass of 365 grams, and iy zp)yh**z jgo::* :o3gzqgrkt 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 0.9930 m. If the lt+(*s3vztqsu m5-vd clock loses half a m-ml+ dsv(t5s3t q*z uvinute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speedfak (7h.tfb8t $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscilx9 9g6w2kik fblates at a frequency of 2.5 Hz. At it is released from rest starting at an angle of 1 xbkif9gw96k 25 $^{\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 his anc elwp)*js24(y aouu x-hored boat every 3.0 s. He measures the distance between two cre a)jo42y ls*xu (wepu-sts 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 travelpyfgkby:,rbj:k1p 3, s with a speed of 343 m/s How f3yfb ::p 1k b,kgypjr,ar apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz jqlbiluuo63 o u3+ 5:cand 1600 kHz (kilohertz) and travel +c 6:5 u3lqij3boul ouwith 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 longitudi m ;/l9oxi mkfyn+hsk3yl )*o3nal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but otd5 c4 ,ojcu60uf,obbne is twice as dense as the other. In which rod will the speed of longitudinal waves be greatjub4ofu 6,oc b50,d cter, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m ,juuq(9d m mg*apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from (m,*judqmg9 u one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620 y9p+i- .t-k2:f+jprmqqr .m y bmdk1cm and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into thrc1 p+ -b q.j q.t+k9rm2k- ifypmydm:e terminal and 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 surfa4(no99kc p4fgq5ahgx ce 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 this po4gh 4(xnp9ofg 9aq5ck int?    m

  P and S waves from azf)(4sy wrw2 v9x)r t+bwux:un earthquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the distur wvy(4)tzwxw:2sx9rbuu)+ f r bance 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 . l1 .z :sjg3fi,khm;qlaw- kk1nlh0c surface 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 f3.lw zh0h-mga1 kkiq :jk.;ll,ns1c to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensitir7pj9q l ae5e(/n1qames, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two a7n59aqp/qel 1j me(rpoints 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to be 4v ip)xnmm-n94mnn9m i)p xv-$ 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 frequenu2ol /l1i 7i0 e5peqsycy travel through the same portion of the Earth, but one is carrying twice the energy 5e1oeq/ i7sylli02up. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string h*zfckd4 crgiwtgvh *5. o920t,3xhtp ave the same frequency, but one transports three times the power of the other. What is the ratio of the amplitd .zvgrpo4xi 5*cg*hw,tf0hk3 ctt92udes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total vertq zrn6v+g 0avi8bekdt-, q01 iical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. iqgz0 ,t+0 1e6qrkdv-vi8a bn If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward )fe,9a:7 essycu21jdh2/z fsf tnk) keach 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 straightys72 2)ekchj s9 )nf/fufd:z1 ,estak. What has happened to the energy at this moment?

  If a violin string vibrates at 41q cxzieo;8( m40 Hz as its fundamental frequency, what are the frequenciesoxzi8(1cmeq ; of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingerdpo1tp*x ,cq6ed. At what frequency will it vibrate if it is fingerexd1pot*,6 p cqd 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;-zz,v bhmr q:voi,2h at le; q2v bm,ihv zrh-oz:,ast 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 If the frequency of standing wa.xuzj0 qyi; su-;kls 6- q)crrves is 475 Hz, q0;cu;rqru6sk. y s- ijl-z)xhow far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 H1jcb +qg uw+n5df4ead--ry*j z and 350 Hz, what is the frequency of the qe*1 g+ard+-j5-4d fbjncwyufundamental?    Hz

  A guitar string is 90 cm long and hatru j,3 jdji)z)9tarit8s /w-s a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension rtdu)t/3)a9irtwjj ,-j8isz 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 H6ymht7g4thd-cwq td3 6i /ic;z, but it is measured to vibrate at 205 Hz. By what percent shoh3 w6th cymgd-tt;d 46i7/qi culd the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measuredbwpjgwc(6m .sv8 hx;6 u9k tzi5s-6 vr t-wj uhm 6wki69xs;pvvgtr zb6s(. 58co vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontaoq2h*yl 4ybqv-o *rf*x xh7r)l string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length h2x yrqh*o y*-x4l*fqbo7) r vis $3.9 \times10^{ -4}$ 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 lb-j7-tl ot*twength of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 t bl*7o-jttw -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 fort pi:/etx kb+xqldt c6e* r;okq*u, z6:tfrv4)h 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 standing wave in a 65-cm-wide tub is 0.85 Hz. What is the spex* rrpicf64bkv6zq* t lo ::/eqtx ,;kt)ed +ued of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Ear7mcu,hh 4yx4ith between two kinds of materia4 c hmxyh4i7,ul. 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 velocitn bnzk3fj8.b.f sc3j .y changes from 2.8 m/s to 2.1 m/s If the incb3c .3jnn.fb8.jf kszident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense air. h0wp cmxd. ct9zm;gp-f0rj38If the sound.p0t0 f8-m;zdc3c 9wjxmrhgp wave 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 two types of rf4i u.2am/y tvnf+)frock at a r /2f vfin).m+ufa4 yt38 $^{\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 suni;qm frtz 24c,c0:9vw n7u manual, the diz 9vsntc7i2; :rmc uwn0f,4 qush has to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and ve;5tjz 0i,ejul;.xgg o.c 4e iblocity 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 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 anc ziige,j ;.. oe 0jb5;x4lgutd boats.)    min

  An energy-absorbing car bumper has a springpw8 ar5 kvf)9 j0bihxoc wn y6bf.3z3, stiffness constant of 550 kN/m Find the)v98rco.b0h nab3ww 3 fz6y5ipxkjf, 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 from a window to a fire net 18 m below, which str(,p),.hmvl f j: i(0a(iye y cxgpwgf6etches the net 1.1 m. Assume that the net :6gfx0,c e (hf((ip)gvj,iylma pw.y behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hangin0kqra)r; mlr)9z n8dwib+id/9 chmc6 g spring. The mass then falls 33 cm before it stops and begins to rnrm )6dczk;wbr /9a q0hmc) 89dli+r iise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge uhj l4 ja(d0erj -aw.;spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness a4 ;j -d(ajle .uh0wjrconstant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just rrxv s:3qh9b7f8m.lg the right pace of about 1 step per second,r87f mxb vq:r.s39hlg the coffee sloshes more 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 cm from the xp9 l0w60 zgjvt7os kt6 wkp:.center of a 33-rpm phonograph record have a 7pk.kv06stw0jpo9z w6:lg tx wavelength 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 where x is i6 yi)0j-4gxta hawgn- qymt(8n meters and t iy6n8agittma(4hy- 0jx- gq w)n 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 accez7f .may5z. x )wmq0lglerates at 0.50g (a) up7 .gwym0q). 5m xfzalzward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the rt h v)dquulqhs 76,,y2aft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates y) h 6stlqu,d ,27quvhfor 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 tunlzxy,74aqd uj/t fl;g6p s 1,yed to play at 392 Hz (G) and 440 Hz (A)/,y lj sy1xad76,pgtu;z4 fql .
(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 ofis.nnyx q /,w1 Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelengthxs1nni .w/ yq, greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the ti -lr 25t:+ oj2c0 jynkcls+vkap of each prong moves 1.8ov jk0s t rjk2l-clyn:+a 2c+5 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmdmy-0 acf 4w1uonic motion of frequency 1.5 cycles per second. What is the maximum amplitfda40cm-y wu1ude 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 cu;k2eqtv0p+ sqf +. uqan slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengthtuufv;2.qqq se0 p k++s of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactlt79zb e1mfpy0y 2.000 s — each one-way swing takes 1.001zt7 ypmfb90e 0 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 vertical d xe5d 2lutik5:irection 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 kd2e5 i:xtlu5swings, 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 123rer+jm2.j8j,4 c;u0 iwkcbvo g is stretched under a tension of 255 N. A pulse is generated at 8cj +4r2cbmv,u; owk0jre.i j 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 stiffn;avq :2rjyij vq/h3*4b hxb9 mess constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will aq/ jrvhh3 9 mvxj4:*bbi 2;ayqllow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted j-fv8gr22plgxfuv, )- gr5l ia 1200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mml g)prfvx8gfujg2- 2,vi r5- l. 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 algrr6 ;lt5w8a.3z ciksh m05xfso gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate.ilfh s; a3mg6x5 ctr0. kzw5r8 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