Give some examples of everyday vibrating objects. Which exhibit SHM, at lel:+ hp zp)b(xoast approximately?z(+h:xplb)o p

Is the acceleration of a simple harmoni3sl 7n ocr9:1 iso 2i/wf3cwpac oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximatelyjd1y q5a6r+j ejy/ihc/ 8xac) simpl+/cda ej8i6y 1/hy jjcr5q)axe harmonic.

Real springs have mass. Will the true period and frequen0tbfnwne p y3blb dx 6so3aj d/56/w/7cy be larger or smaller than given by the equations for a mass oscillating on the end of an idealized madw/lbn6xowt6/ ydbb j 753/p fnase 03ssless spring? Explain.

How could you double the maximum speed of a simple hac7+pihpu( pdy, tpi:k32poz 9t vs5/v rmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook ofp f 7bo8psfdxkyu *6 :t5b0a2c a vertical spring scale, and then is released. Describe the scale reading as a function ofxob8c b 7uf6s5a ft0:ppdy 2*k time.

If a pendulum clock is ac4mn7hv4 a 7ae3v7mn (jolgs -lcurate at sea level, will it gain or lose time when taken to(3a4 vlj n o7gnh7 4vae7-mlms high altitude? Why?

A tire swing hanging from a branch reaches nearly txlu25 .q+9.7cc8i+5n r lah fg azccylo the ground (Fig. 11–48). How could you estimatif758ca.+luc zn .2lqcc+ 9larh5gyxe the height of the branch using only a stopwatch?

Why can you make water slosh back andu-g:l :u4yvva forth in a pan only if you shake the pan at a cgvuav 4u- l:y:ertain frequency?

Give several everyday examples of resonahn6d v fa7qn)4u6 h -ke0apifa(i5a3cnce.

Is a rattle in a car ever a resonance phenomen ilqqg,1iun*l 9zz2adbo3f3)y*ce4g on? Explain.

Is the frequency of a simple periodic wave equal to the )i-,m nwgc kn0.uiv;tfrequency of its source? Why or why n,i)wv-.kgu;i mnc0 nt ot?

Explain the difference between thez r*+p7avo/ avi*vz 7y speed of a transverse wave traveling down a cord and the speed ov*pyaiov z z vr+a7/7*f a tiny piece of the cord.

Why do the strings used for the lowest-frequency ne2 s7eu to*g;motes on a piano normally have wire wrapped around the7o2es*t;g m uem?

What kind of waves do you think will travel down a horizontal metal rod if you fzgh1 2is561jg kwn.h strike its end (anszfjh h1 w62i1g.5kg) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an incrle28 pcs* 3x6kpn c0csease in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in ail *02ckx68esp spc 3cnr to vary with temperature?

Give two reasons why circul 0g :hbm)2tcyti5**b7zysiz)3pbxqu ar water waves decrease in amplitude as they travel awa)3:*)ght i5*b2tsbuczmib0 ypzx 7q yy from the source.

Two linear waves have the same amplitude and speed, and otherwise are idexxqrrb fn3;0j*ky9 ;lu5t o9d ntical, except one has0d;jkryx5ubtrf *3q x 9;o9ln half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary bet an,e*.-io zg 4 )ri 0sbcfwhowm512tcween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Expca - c ,ow) bzgf0 wit245n*eosm1irh.lain why.

If a string is vibrating in three segments, are there a, 6ab b61eobepny places you could touch it with a knife blade without disturbing th1oabbpb,6ee 6 e motion?

When a standing wave exists on a string, the vibrations of incident and red:kjhj9,*;3 il6qax jjv,;t 2rtx vznflected waves cancel arx*;,q j2tt k9;hnav 3zlj:i,6j dxjvt the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was bei k,ei2ypedon)3 bg-m4 zx;v)r ng transmitted from one place to another, how might we dete)vegmpyex-o i3), d;nbk42rz rmine 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 the94tlmcq ciy:+ez6mx; total distance it travels in one c xzyi6:elt4m cm+9q;period?    m

  An elastic cord is 65 cm long when 0va yx7/ ,d9i-ehloiqxhs k1; wfcg; )a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant g;f;w9scl/q e,xihoa0 -khxdy1 vi)7 k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets iuor( .a*r -ozcnto the driver’s seat. If the car goes over a bump, what w oc*o(-rzu. arill be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What w9aq wssh45mu0m v31bis the spring stiffness constanwv03 usq b591mw4hams t $\approx$    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 wito+uyos0) qo5bw)oth2pj 73g h ,mrka)h a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs fmhg 3uw ) 50s2jap)7okh tq+boo,yo) rrom it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at (4(a pqo2ho ootimes t = 0,t o 4oaq(ph(2o o= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 sp1lnj h-m5unk. ider’s web. The web vibrates predominately with a frequency of 4.0h5 mlku.n-nj1 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 sprix4 cxw;zq1/lp ng vibrates with a frequency of 0.88 Hz. When an additional ;/4l1 xwxzq pc680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a sprg4p95 . gyucyning vibrates 3.0 times per second with an amplitude of 0.13 m. Dgu5g4pyn9. cy etermine
(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 frcp.htw*krs6 i*1k* viom equilibrium is the speed of a SHO half the maximum valu i*hk k*p t6c1wris*v.e?$\approx$    A

A mass attached to the end of a spring is stretched aym6g8 idwez1- o zx p*2(wf7fo 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. I3: m419fqlmwq ipthtb1t0ez+ f the spring is stretched an additional 0.130 m and released, how long does it take to reach the (ne0t:l t+1tbfp4w1qqhzei9m m3 w) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness cw-;)xn+fxxhjrw3pyn1tlsc9 ,( j 6aronstant k = 280 N/m and is executing simple ha )9hl-j(n3rc;w1sxa+ fr xpwtjx yn6,rmonic 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 spring of tg8:qwmxy a ki00l3(la toy popgun 0.200 m to “load” a 0.180-kg ball.tagl8i(3 q0k0yw ml x: With what speed will the ball leave the gun?    m/s

  A mass sitting on a h;wz +za vdn;u(s+t gj/orizontal, frictionless surface is attached to one end of a spring; the other end is fi+;a(/d uvwg;sztn+jz xed 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 according to the equation x = 0.45cos6.c +s;6ssaixd g4r*e:k 4t where x is in meters and t is in seconds. D 4;csxs:6 srki eg*d+aetermine
(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 KEzw q,- )jlj/9saalfc6su q81z and half PEs 8qlaz61ljz juscw 9,fq)-/a? ±    A

  If one vibration has 7.0 times the me5f9uc(x 1h,k 6 bmhdmu3f;d fmqvo:+ z/ug :energy of a second, but their frequencies and masses are thqmf+fmh dv,mcd6u(hg:1kb eofu/ 3m;x9 5 z:ue same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging ligh-j mw -9z nongjm8,f-st spring once every 0.65 s.jfjmnms - 9w-og,8nz-
(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-rdlv 2d/emf6(3c si x two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrationsd36 2cd-( lxmvf/ei r?

  A 300-g mass vibrates according topb 9sn1g0q65av/zpmp the equation x = 0.38sin6.5t where x is in meters and t b5/ppgv9qm1naz6 0sp is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A a:ixsymdo 50 6l0o5a8zv/ise k nd 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 elo8hk )j*v1 f4ogbam*nd of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives hbj)a 81ko*g *ml4 fovthe mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffnr;7 ihle 1pw9 gajo)0ness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes)oew nip;h1g j ar907l 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, wzzj9a7lfn, )nith 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 strikeooo2hg(4e+n fkg qfnr7-2 ld6s a 0.600-kg block attached to a fixed horizontal spring whosk+-fdqron4o 2l2oh6g f7( gnee spring stiffness 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 reachmx 7* dp*vvx3iing 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. dx**m vxi73 pvCalculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in ms1a o+ ,adn m+lqa;03y/ cbhbexactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be ifw d. uk5t-s,3kk o/ot8tifm;o it is to make exactly one swing per second? (That is, one complete vibration takes exactltdt8oksowo,t.m;53/ fi ku-k y 2.0 s.)    m

  A pendulum has a periw49sewx8+3p 1r+tr mypz x5xvod of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity 8rypeps35 4xm tx 9wvxr1+w +zis about 0.37 that on Earth?    s

  What is the period of a simple penrwh:z4+kqd i y8/0tn g3pm: a .tkc4obdulum 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. vdio. f,(uc;ne2zp6 jmlx,e0760 m, the pendulum bob has a mass of 365 gramsno.( ,exldv,upe z6f; jcmi02 , and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a leb 6 h 0/wcd.o;yi*oiqingth of 0.9930 m. If the clock loses half a minute per day, how should you adjust the leng/wyq ;bdc 06ohiiio* .th of the pendulum? shortened by    mm.

Derive a formula for the maximum 46r *b )qvsn9qk7oef(bd yb)cspeed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequec7t g;-kyr0avs r/kg ;ncy of 2.5 Hz. At it is released from rest starting at an angle of;;/ryv -g7tarsc0 k kg 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 his anchoclnn0 :ll-e:zuu/ xsa kg:3 3ored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are u3:0-x ne3z/akgcu:slnl:lo the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed 3ff1 /d5uwjuo ef7w,iof 343 m/s How far apart are the wave crests (cofw3 u ,oduff ij7ew/15mpressions)?    m

  (a) AM radio signals have freque9d dx-+fn* t/yixwraj;/qf x. ncies between 550 kHz and 1600 kHz (kilohertz) and travel wx/9wdf/ nyjx;rdi qftxa* .+-ith 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 longdb6clvyr 7o 4l(9/- d dck*n(dzv n2abitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the sakwy+ylrjpe lj zz;*ha(u1 .9 .me elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal lylwhz1ka .+ej ;*prjy .(z 9uwaves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betwe haf7am hyhrt. +i76(u,f1s pnen two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the om. sia y7ht fhr6ufph7(+an,1ther?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620 qjn6 .p-l ptp uiyc1-;m and diameter 1.5 cm. As the go1iltju--pq .pnc ;y 6pndola comes to the end of its run, it bumps into the 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 surface of tzrtks,p8p sb p8oz-21he sea. He hears the echo of the wave reflected8-r k1sppp zso2,tz 8b from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an eartkf * a-rv6gd e)ni:q,aoo4 m u)on-/pshquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance toodvonimns6qro:/kg -4)fe ) pa*, - uaok place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal trandhx bn +hk;f7:(m wgm3sverse 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 lea mk(3fh;h:7d xmgb+n wve contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the a:y d,o7ephd2 ;1ln wkzmplitudes, of an earthquake P wave passing through the Earth and dph oyned1d2k :z ,w7l;etected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing throug m pz -bh9.4d b6t-jmsjbt3zh:h the Earth is measured to be tz bmbm69bpt j jd -h-s.3hz4:$ 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 u5*3un n k4 -;4qvqgknlrp5 g+tvc f1gsame frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ra3qufn;4+p k vc g5nvngqrk5ut14*g l-tio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the sahsa .y-*gi sb3me frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the ysba-hig .s*3two waves?   

  A bug on the surface of a pond is observed to move up and ds sd;n:s+ah6mzn0ra9 --bkn oown a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples rk z md:as9-h-a6nsb0+n son;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 each other. ( mbd((cgt+ gu9a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the (g+ dbm(tu 9gcstring 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 this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequenc.ovo,ku 9r +;j bm+heey, what are the frequencijemke, o+our+vb.;9h es of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at xm+knpzu1ue + u2mw c9; w:z9k294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down fromk +9w9zkxe2 m c;p: uwmu1un+z the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at aogk i ncasfr-695 7 od(z3cwy) frequency of 280 Hz. Name at least three other frequencies at which itf nyg)6 woazcs3cd7-9irk5(o will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string iayn-s*cwc5 fcv;4dz 1s 92m/s If the frequency of standing waves is 475 szd wnv5c*-cc4;y fa1Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what:0cv,or jcwkqta x 8).cma58 i is the frequency of the )a:. q80ovjxwtc 58 ,ckc raimfundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance)f bwbq varp karvw/2 22qj-.2 from the bridge to the support post is L = 62cm and the string is ub /q2ajra2pwvv22) kwqf.br -nder 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 it is measured (nwglq35 v qg )g;g68gglh. tjto vibrate at 205 Hz. By what percent should the tension in the string be changed to correch3glq gg;j6)v 5(ng8qg.tw lgt 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 fv2yf;8;4djs4 g,wyu em a ig-measured to vibrate at 205 Hz. By what percent should the tension4 wfg ;m4a ysyge2iu-f8jv,d; in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal sts2jr+q1 dts:o,7k svoring is attached to a small-amplitude mechanical 60-Hz vibrator. Th7jqo s o2sv,+dt:skr 1e string’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 pulle8t 0it2c6 r(cvwxhj5w y. If the hanging mass m is fixed atwi2htwt cjv6c08 5(rx 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 righyz5g/l(u ,e vqt frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequencyzq vue(y5/,lg to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s ooz wms0ad9ih b0h3b,,pd::wb1yi j* strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 47 zbysibja dow0 hd,wom3*bhp0,19:i : $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater.4ht*ox;- 1ablv q;a-pzbp bp “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wav* av -pqo-xl b.h1atzpp4; ;bbe 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.:,/z 9clf mscfph rk;0f s1y4tyq(ww. If th.sty c shww9(f1l crpq0 ,k4f/y:z;fme sound 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 2g )x(,c6mibwt7xhgo53 gqt p wave strikes a boundary between two types of rock at a 387 o3htmw6)x2pxc iggt5g(,qb $^{\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 u dp8 jrk3(.ytho8suv0,8nrpeh0 bj6q ser’s manual, the(8eq8j0b8d hu ppvto3kh.rjn0 6r,sy dish 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( 1 p3agwxtucdw(x) y bu0)gi3 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warnw1d0b3) xapggwtciu 3()(x yuing, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kNu6b7 2hs )czx9v0 cvem/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2cbs)vex v7h zm62c0u9 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a f+ouixeu m sr1.wj6mm 4,kan9-ire net 18 m below, which stretches the net 1.1 m. Assume that the net bu 1jnr6m4imkao m 9-+e. uxs,wehaves 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 hanga2ckd/4e lfe 7ing spring. The mass then faf 2e 7k/c4eadllls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spx,xta 0s0k pa2 o83ruyring at a speed of 22 m/s (Fig. 11–54), compressing the sprxr 3k yuop2stx0,a80 aing 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 cup (nn-ub noel2;8pef ygc;t0 (t 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 pf nt (og;2;ne0(nbeu8t-lcy 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 center of a 33-rpm phono0l934t7ylm a ar1 vekdgraph record have a wavelength of 1.70 mm. Whatlk9e4 30r adt1lay7vm will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates acco k0(ff:vlfoj2 rding to the equation x=0.650cos7.40t where x is in meters :olfkff v( 2j0and 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 os ,peqfuig:4 / e: t8/rcppf(owcillates with frequency f. What is its frequency if it accelerates at 0.50g (a)fre4 p / e:fo,pcqiug8t/wp:( upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands 7; :nfp yins(lon the raft, it sinks 4.0 cm deeper into the water. When he steps off, the n(fs n:;7 ypliraft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 4c:h3qmf h+ ljav7zjj k2om22740 Hz (A). h3v z2hj7kajl2cq2+o7j: mmf
(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-p p :(*)odge+j+h hciqtart cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighterecto + gqi:*dh+() hpj?

  A tuning fork vibrates at a frequency of 264 Hz, and e obqir (.f0 l:,02tbjtv1tpfthe tip of each prong moves q 0f1b jbtto2tfrvi .(:,lp0 e1.8 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harma5tw ;can5d5 ponic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillatia;a dp5t5wcn5on?

A string can have a “free” end if that end is attached to a ring that c ; uhrvo9uaofef; kz4;9h 2:uvan slide without friction on a vertical pole (Fig. 11–57). Determine th9vuu;f2 oh :ve fouk4z9;;r ahe wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a per xlrb +yfg ,2sy9vehohsaa lqq ;6(i1;+t, :lyiod of exactly 2.000 s — each one-way swing takes 1.000r1h 6yvis;9ellxg +q: st lao yf;ba+,h,q(y2 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 direction-he.lcoru) 5c or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vel-reoh c5)u.c rtical 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 tension of 255 N1th;mc0p7x c. ip.itz. 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 pulse1ppt ii.tch0; cmz x.7s first meet?    m

A block of mass M is suspended from,w, a-+ xu; u .*x,lqhgdttczr a ceiling by 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 staytgx+,r.cu h u*al;d,-twqz , x on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junku qn4h 5i2cu,myard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. Wh hinc5um,q2u 4at is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests or-i33 gl/qd0uhm tfzd+w*sr4 n a plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and r4husi3tw d gq m-3*+r0df lz/then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz