Give some examples of everyday vibrating objects. Whit4op/3i 29r8aydj rwo3p, 6 ryqrh c/gch exhibit SHM, at least appr 2tr/poa4/yghycprroq8ri dw, 6 3j93oximately?

Is the acceleration of a simple harmonic oscillator ever zer zxfh7oc)7,o fo? If so, where?

Explain why the motion of a piston in an automobile engine is approximately,:jugj i 0h: 9wowa8xx simple hariwux,0wja :jo9x8 g: hmonic.

Real springs have mass. Will the true period1aar- shep ztk*bn(k5(sc7o- and frequency be larger or smaller thb-*st1z c7kh(sn-era(p 5oa k an given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the fv y4v-, xd qa5o.y5wkmaximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached taj1nah))up- ojy:+c u4 )-ux; glapy ko the hook of a vertical spring scale, and then is released. Describe the scale rey ; gp:)au l1 u-pjxynhacku))+a -j4oading as a function of time.

If a pendulum clock is accurate at sea level, will i6abb9hetx :7yqmcd 86 t gain or lose time when taken to high altitude? Whhc7mt9 :abex6 8dy b6qy?

A tire swing hanging fromqn9irtgo 7l2; a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only ;onrglt7 92qi a stopwatch?

Why can you make water slosh back and forth in a pan only if you she0b7tx9c/e h fre;pl 5ake the pan at 5 tlh;cfpee x/rb0e97 a certain frequency?

Give several everyday examym l++h5:gbwtples of resonance.

Is a rattle in a car ever a resonance phenomenon? sz)3akb zokhysoc,. r:7 py4+ Explain.

Is the frequency of a simp 5sy7 l, /ng9nqkik*bsle periodic wave equal to the frequency of its source? Why or 9l sbqg7s5/,k*nikny why not?

Explain the difference between t7gvinhpx5s1ra -i;wdufc a,j2j8(0 the speed of a transverse wave traveling down a cord and the speed of a tiny piece of th 7djxi58pwjc0fa u1-; r igahvs(2,nt e cord.

Why do the strings used for the lowest-g(pnwbo8/v . h0 ik7tqfrequency notes on a piano normally have wire wrapped ar/khv8ti7pob 0.qng( wound them?

What kind of waves do you think will travel down a horizontal metal rod if you qcr748:5u ymatjo 7tostrike its end (a) vertically from above and (b) horizonta ouc 7trymq5a 74j:8tolly parallel to its length?

Since the density of air decreases with an increase in temper oqkn yq (tmpde42d6)h:hr.p,ature, but the bulk modulus B is nearly independent of temp :.q ympep ) 4khhno62(,rddqterature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitu.;/bp y *j+fvpjo7xny de as they travel away/ j.y onp*bj+;7yfvp x from the source.

Two linear waves have the same amplitude and speed, and otherwise are identical*7lg dke : zvz9zmaw32, except onzk:w zd z2l9a3mgv* e7e has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundaavevxd0y(,. hpt4 hnz* 6wx(v ry between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocvnx (tpa6 ,ew0hh vv4z(yx*.dity do change). Explain why.

If a string is vibrating in threbeu.4 4vfb(y 1xkj)+ yx.m lwue segments, are there any places you could touch it with aubyk41) 4+x wlme.xj(f v by.u knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflectpl;.z r w*wch+ed waves cancel at the nodes. Does this mean that pw*.cw+h ;lrz energy was destroyed? Explain.

If we knew that energy; ow f7qy9vmy/ was being transmitted from one place to another, how might we determine whether the energy was being carried by partyo 97;/qvfmwyicles (material bodies) or by waves?

  If a particle undergoes SHM wittibq :pe,0mu+1s f xb6 xao9l(h amplitude 0.18 m, what is the total distance it travels in one uqfb 9xit,ospm :+ 6 1xe(0balperiod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 g7 g+ ,uh)ac/qu+yq vjcm long when a weight of 180chqgu, )a+ugy/+ vj7q N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compres1xds5fl,d2okjc :j-p s 5.0 mm when its 68-kg driver gets into the driver’s seat.k:d- sp, j5fcj2odxl 1 If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2snd,jk wizsdy*,,53x.7-kg fish hangs from it. (a) What is the spring stiffness constant ,z,dd 3ss,5 wi kynj*x$\approx$    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 3yd c/y11s mkx5y7z:8* xdkoyb.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 5yx/171k :y o zcmxy d8skydb*0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at tez(+a bao jrdg 1kv )tw7py-191o+w ghimes t = 0,tw (yjg-p 1oea 1bowg 7v+ka9 dt1)z+hr = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibratevmb)f *j :q/uc/zxf.d 3sy ,yks predominately with a frequency of 4/,svj3f*bk qycyz.x:d ) /umf .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 vibrateqe0iapfb 3)q/5 yn5 r qh:*myes with a frequency of 0.88 Hz. When an additional 680-g mass is adder fq:mq 0 3h/iqy*e5anbe y)5pd to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the2 5v; +9rahhu+0d.w+ mit s yj:zxhxdm end of a spring vibrates 3.0 times per second with an amplitude of 0.jm+2a.v wmxx: ;du0thzyshi59+r d+ h13 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 fromgl 1d fjk6m7xh8 x:hd0 equilibrium is the speed of a SHO half the maximum value?:xh08dh 61x d7m kgljf$\approx$    A

A mass attached to the end ;p05p hg ;fby;zm zk+ qp3rfg5of 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 0.2*u 5k/bmch1a7ow worqm;ni8 315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (ne7owkn;wa*/ 5 rmmu 21ioqbch 8w) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness 0 *2qt6fih lpzjnt3 v,w3c*oqconstant k = 280 N/m and is executing simple harmonic motion. When the objeczf6t*2 * ,q vtc3lhn0owj3q ipt is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy poyb6z *s6xhrn x1fwxa6b-2(ruf xn u 11bvz r2)pgun 0.200 m to “load” a 0.180-kg ball. With what speed will the a1uuxbz1*f262 n1) zvy rx whbs x-6brr(x6fnball leave the gun?    m/s

  A mass sitting on a hotbkr i(fb 44253ptpvb rizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J oft344prb (b5iv2fpktb 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 aceojc0gn;8cxph5knp 0 li6kv i90 z /8xcording to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Deter8g8oz/65;pkc x n9nh ixk 0cpie0vj 0lmine
(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 f bygb628 l3wqand half PE? ± fgyw3bl 8q b26   A

  If one vibration has 7.0 times the energy of a sec+ us8gtc9hd (wond, but their frequencies and masses aret+c hsw(u9g d8 the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates fro gv1*sg hz,. /dye.cnwm a vertically hanging light spring once every 0.61h edvg, y./ ngzcs*.w5 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 i9 4x+ lkhg-qt lqs9/pv9ijc,wdentical parallel vertical springs, each wit hqq9lpi/wgx+4s t,9 c l9-kvjh spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accordingusmv/l* e ac927d:gub to the equation x = 0.38sin6.5t where x is in meters andv7 d*aus l/:2ug9e mcb t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For mao9; ym*puz-6 wtyd4 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 osthc, bi2t7 w/n the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives tt7b s/hc2i t,whe mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates y: xw1z/hogi 5ca7 -egwith an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (xgc5hxzi gaow/e -1 :y7=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 conrra3f(jo3ory )e+2f)gni 0ohstants $k_1$ 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 .c9-niw g9yuvgy z2 2xhorizontal spring whose spring stiffness g gz-cw292yv x.y9uniconstant 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 ucc yr v3kn qzh;+(i/.a high bridge. After reaching his lowest point, he oscill ckinyruq(;v+z. h3c/ates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in02jmcm za*o1 s pl+9zm exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to makop:(jmvlx (+a2j 8tb-g;twhde exactly one swing per second? 8l- (tpg(a2jd xjbw:+omvht ;(That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, whe s;( j/n,hal).p5u**-o fl gtbesjwn pre the acceleration of gravity is about 0.37 that onsptg5bh sl na j ejl-;f.(wnop*/u, )* Earth?    s

  What is the period of a simple pendulum 80 6b w5u0umz1te ubtr1rf yj-j n;g)w8, 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 pendi:f b+a 9+u2fpyyns g.ulum bob has a mass of 365 grams, and it is releas+yn92s gb :ffypia +.ued 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. Iw a2*zp m ziq;xdi*+tn2r v.3wf the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened awmqz*+n *vwi.3dp; 2xi2 rtzby    mm.

Derive a formula for the maximum speed)7+j *q(m l3mv0p na6fqxeexg $v_{max}$ 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 frequency of 2.5 Hz. At ilece6ta3 1 jhznzk 2xc)(bw.3t is released from rest starting at an angle ofx31. 3(atnk2wc) h l jeec6zzb 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 cn-v- x :-wvzcwave crests pass the bow of his anchored boat every 3.0 s. He measures the distance betx-c vcv:nz --wween two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of20po+jnui4 v w fa-/xu 343 m/s How far apart are the wave cr n2 ju0x w4v+pifou/a-ests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz;q 6bbb18b epjo*lxs5 and 1600 kHz (kilohertz) and travel wibje xb6sp;olb*q b815th a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in s95lhz :q.e aqb-, mmk
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastih,s ryrl9dzw;lsh6+ 3c modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be gr d6rsl h +rlw93yhzs,;eater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the l-x 0a 3k2epcsjk/ks )tension in the cord is 150 skea2sk-)px3j lk 0 /cN, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620(txedz9a+w0 c m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.+z9w c(e0dxta
(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 theh gk;*4 bd8jwnn2qs)ms3it /f side of his ship just below the surface of the sea. He hears the echo of the wave reflected f;s m) wnh28ik4nd qg/ tsjfb3*rom the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this differenk,n .y pqdr-hgn17 r2hce helps in locating the earthg . rqpd1hk-72,ynnrhquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave ca dnmu,e ao-i13c1j62qoln+s qn be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of eao jndm+l6 1o-,qc3ua12q sneirthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, oj.qh gllv;7 0and (b) the amplitudes, of an earthquake P wave passing through the Earth ljh; q.o70gvland detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing tqtag:2 1vn,idsc a2 slq3y75 through the Earth is measured to be cq 3g:1t5 s tdina v7q,2ya2sl$ 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 same portiom kk4r2 t :yq04hg8pgzl*s1bl n of the Earth, but one is carrying twice the energy. What is the ratio o 1 lr4y0b 2lsg:k4 mq*hzkg8tpf the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the saml0a8n p0 w)6leuigx;z e frequency, but one transports three timesz8iw 0 06a); lgxpunel the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed jm /c7pv5 r(sr9ey5ws to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passew ycmvjrp9ers 575( s/s. 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 each other.5x: hh7zq0u5j6 v ;swx7kc oyj4leod* (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 this mome 5d0 4: ejxw;jx o7hl*6yk5ou7szvhqcnt?

  If a violin string vibrates at 440 Hz as its fundamental frequp krk)4b v,o1k qdo57cency, what are the frequencies of the fick ko1okqrvpb, 47 5d)rst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At wha:3lurq6 r(fv ;oxcb( yt frequency will it vibrate i(q;v ulr fo3:y(xr6bc f it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a freq 16s,h fn (+ps/hockb9 sux(spuency of 280 Hz. Name at least th hs1oskp(f6, c+phuns (s/x9b ree 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 waves is 71 f+ls,eksbv 475 Hz, how far apart are teklb+ s,7sf1 vwo adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what i2 /qg ues,kv*((ir6k vrgs, ets the frequency of the fundamental*(s(/ik r2 s,grkvtev6gequ ,?    Hz

  A guitar string is 90 cm long . 1wv jxff.xqns/vh*d+q4; ahand has a mass of 3.6 g. The distance from the bridgewqsqxf. dx1;+n/h 4ajf.h v*v to the support post is 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 strindf:h(iz k*p i;g is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what perce h k:ip;*idf(znt 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 string is supposed to vibrate at 200 Hz, but it is measurek81 dtlt3-gvw s66ubr d to vibrate at 205 Hz. By what percent should the tensirgwd 6tlvsk6u 183-bt on in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a sx5mz mh4+ 9qfv,tj0dmmall-amplitude mechanical 60-Hz vibrator. The mqxmvd j4 5t9+ f0mh,zstring’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 adjustedr j5*gfj *:;jmi7yc (z- ks3 il+xdmpm by moving the pulley. If the hanging mass m i:mk;ljd5i3+j **sxf pzy (r7-mjic mgs fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequebmmb:o+ .y2ya m4thz2ncy, the water alternately 4 ob m mb.:myz2+tay2hrises 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 wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Eakc n9aag0/4o drth between twa 0kn4o9/a gcdo kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity chan4 sjfhrut f/x-rt+8v, ges from 2.8 m/s to 2.1 m/s u- r fsh /tf8,vjrx4+tIf 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:qulj94a ;s7lo f b/re hits a layer of cold, dense air. If the soundqul: /4e; 79alfsojrb 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 t de f4ahywyc(h2usi08aww05 +wo types of rock at a 38y82c+4sww e0hhd0u i f(aaw5y $^{\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 use6*ritkgfp)4;h cecj 8q o uh/l5so42 f-ij*ylr’s manual, the dish has to b osrhk6*yjc*5q fp) th4gile- 4c/jui; l28f oe 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 velocity 750 km/h tr xbs+ h/9bg ea,b;qqel, r(3kjf. .ygmavels 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 knbqb. ,,9l+eqg hrmk a/;bsg(3.f jeyxowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 55 wr*)ui7i/i ybk,9e bi0 kN/m Find the maximum compression of the bumper if the ca) byi97wk /bi,r*ueiir, 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 stret ;t0e*zlxws8 j4me m2jches the net 1.1 m. Assuzjt 4;0 xl2 semmj*ew8me that 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 placedffyu,1dh zw 3* .6yxsu on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the wf xf,uzu* h sy631y.doscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (r8ds o h*ilbx85gz -c4Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the springgo-c5h*r i8l 8s4 zdxb?    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 a+ /pce7rxe ib .nw24kq/qfay8 sk52ycm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventu8 eic +kyxa2yrq /a7f.b/swn 2 e5qp4kally 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 center of a 33-ee3.os tw7l4 4bu6nqkrpm phonograph record have a wavelength of 1.70 mm eb4ets.6q3nk4lou w7. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equ* bj,2g: u,sr2v ieiokation x=0.650cos7.40t where x is in meters and t *2oi svg 2 ,euki:,brjin 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 ihc70hojy *)ne(v oxuyn: ,fb-v arf9-f it accelerates at 0.50g (a) upward, y*-o(erf:, )9nujv 7 yhx0of cbhvan-   f
(b) downward?    f

  A 220-kg wooden raft floats on a/;se,o 2hx do/qj n3an lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while/x3n/2oo ,qde;j sha n.
(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 mus-h b15zy bm5iero9gj(yu-d s4ical instrument are tuned to play at 392 Hz (G) and 440 Hz (A). m5 iu(9ys- 5 y-og he1brbjzd4
(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 twox8 d8vj9jpcgr9):e 09tbdnz r-part 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 orzjddrn9 :88jc p9tveb) g90 xr the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong mov-fq 4;etgfgz hcuq (32x *tc5 d.hp2hkes 1.8 mm to either side octugqhht.fh4 cp*d xg5f -z(k 223eq;f 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 moqu pf+jce+grf5 s bt530l9x,jtion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of thes5l3cf5pr f9 b,+jqxueg+0tj 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” e.4 ndm5z3q/txw5hvu pnd if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Det q45 t5vmzhux.nd3wp /ermine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a perioq(bwo8;5em 2ugr xc f(jjc:2od of exactly 2.000 s — each one-way swing takes 1.0:rg2qc b owjm(xe(2;f uco85j00 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 o.dey t zr29* gv2mx7vgw:il4 spring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Wo2vw 49le. zg2r7gi*v:dxym t hich one is longer, the 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 tension of :o+jd 5ur 2dlwb1d+o t255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite e52o1:bwdurd+ t oj+ dlnd. Where will the two pulses first meet?    m

A block of mass M is suspended fr,lj -i 0qczij;om 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, 0ijcz;-qjil oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1bog 22. nk:f,zp pu5oa200-kg car at the junkyard. 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. Whatap2.fk,b o5 go2z: npu 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 alsp;wew k-ptb-o; . 6q z,boax+ho 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. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that th zat6;ob pkw -ebox+pq-,.wh;e shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz