Give some examples of everyday viope11f3 9xsm86ox(u xn h 9eznoi7nb6brating objects. Which exhibit SHM, at least appr 6 h1( n1o6smeu xefpz3nonxbix79o 98oximately?

Is the acceleration of a simple harmoniy x(qjm(la0e 2c oscillator ever zero? If so, where?

Explain why the motion of a pq* ,u5.6 6deiw5s:jimzhd jpjiston in an automobile engine is approximately simpled6,6*j5:.pj w m e dsiujih5qz harmonic.

Real springs have mass. Will th91taltcf8iekd p4:x9i 9 3dh te true period and frequency be larger or smaller than given by the equations for a mass x94:9tplfdc8dei91it t 3ah koscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic osl*w64sigbjz , hk 6lb/cillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scf-1vck6l/e skzth8v ) ale, and then is released. Describe the scale reading as a functi6thf)sv zl8ce1-vk/ kon of time.

If a pendulum clock is accurate at sea level, will it gain or lose time wry,q0 7wlrps;. qdgreq +f6;y hen taken to high q0;f sypr,y7+qegdq rlw .6r;altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). H v g1v*0i7; caldfabm-ow could you estimate the height of the bra;c*av-lafv0b1m7 g id nch using only a stopwatch?

Why can you make water slosh back and forgu0o3q0lhvjnb8hob 1; 6 f3 ho,tv kj4th in a pan only if you shake the pan at a certain frequencynthj1gb8k,vlu3o vhb;q3 f 0oh 0oj 64?

Give several everyday example*at*ob9fsj 46 9vgoffg 4oe+*w e7i it o4br0ns of resonance.

Is a rattle in a car ever a real +wqgoch-xkhbgj-(7t n452ti(, eosonance phenomenon? Explain.

Is the frequency of a simple periodic wave equam-rf6f /hoh n :/-frunl to the frequency of its source? Why or why not/r:-fhn-nfr6h/ uof m?

Explain the difference between the speed of a transverse wave traveling do f+3*f (/-dgm cr3e osivfrlt(wn a cord and the s-r o3 etd3mi/*v(rf(glf s f+cpeed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano n t3+ghw qwp,)kormally have wire wwk h+p 3)qg,twrapped around them?

What kind of waves do yo q,f2p9az:dbau think will travel down a horizontal metal rod if you strike its end (a ,azbdpaf :9q2) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the b ur 4,xp7h rgtom1j tz:l:m53wulk modulus B is nearly independent of temperature, how would you expect the speed of sound waug1ow r3:p5h4tmm:,7ljtzx rves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they s1hd j7;owyrmf.k q; 0travel away frw0dqrsy 7k ;omf1hj.;om the source.

Two linear waves have the same amplitude and speed, a-bta9tgd k-,g nd otherwise are identical, except one has half the wavelength of the oth,b g9gta-- ktder. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the . /he.nb 3lemzq1ain.w,ql2 aboundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity d/lw2b z q,e.. .ihaq13nnealmo change). Explain why.

If a string is vibrating in three segments, are there yf ic0/)6vsrs.- ddmz any places you could touch it with a knife blade w/-z)dv 60iyfsds .mcrithout disturbing the motion?

When a standing wave exis gp++u/ jsvr49yro1jz;w +vb sts on a string, the vibrations of incident and reflected waves cancel at the nodby+rs9+4u1pjoj+vr vw gz s ;/es. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mi- xidnwl84i1q ghtxlini48d -w q1 we determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total 4;,qoj:2vf izp jwaw+ distance it travels in one pzpjo2:;w+,qvi f a4 wjeriod?    m

  An elastic cord is 65 cm long when a weight of 75 N hanp)jotse*vn 4.4 7snsigs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic jp*s7osi t n4)n s4.evcord?    N/m

  The springs of a 1500-kg carbg7:cm w; :) +.ywhake4svubv compress 5.0 mm when its 68-kg driver gets into the driverw.;s bvhm7)ue:c a4k:yvw b+g’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale sg2m+fkre- pq8ci u)y w:gl1l5tretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is )l 1eyig p8 +m:u-g2rcq5fkw lthe 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 9*a, oly gvo0tu) rv1c3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kv c0o * vyatol19,urg)g hangs from it?    Hz

Construct a Table indicafcx z)lpttn/5f 2ha37 a g8y:jting the position x of the mass in Fig. 11–2 at times t = 0,lc 3panzj y: 2xftt/fa5)h7 g8t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibqd+3ys-xm4nfq gwl(, rates predominately w,+dq4(m f 3ny lsxqg-with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. Wheep,2 i1g tt*q.o1socqxz0p bi9/o k/gn an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the v /z. go tk*e/1 s02qx1i,qigotpcop9b alue of m?    kg

  A 0.60-kg mass at the end of a springwp., 6vlc0 uz; f(eqgu-/e21btdwffx vibrates 3.0 times per second with an amplitude of 0.13 m. Determincp1qvtu.-l wgd6f0ex, 2 ;/ef(ufz w be
(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 equi :zbt(89sqmqx3/avt3r:m z: 6acifm ylibrium is the speed of a SHO half the maximum val:v6(/fz 33cm9: irtqm 8szbaytmq: ax ue?$\approx$    A

A mass attached to the end of a spring is stretched a d3v oara52xwi (l, vm0iistance $x_0$ 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 the spring is a++g e;mg u a db-m s:tv5 zt:2urj1mz7iw*v4tstretched an additional 0.130 m and released, how long does agg i z4dmt+ttz:2u ave5vb1 us +7mw-:*;rmjit take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffn-usxsg40l *kj ess constant k = 280 N/m and is execgsk- s 40*ujxluting 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 compk/r0*3lwk -qw dv,zc xress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will trv *dkqzwwl /,-03k xche ball leave the gun?    m/s

  A mass sitting on a horizontal, frzxhvnqy;+ 2(q ictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spr2nq+;(xvyh qz ing 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 = 0.45cos6.4t where x xa+cmxf ts2/ b oh./5trq,*acis in meters and t is in seconds. Dt//2cx * b ,so ta+af.x5cqmrhetermine
(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 equilibriue-, zf8ueydljt8,gf) m is the energy of a SHO half KE and half PE? ue,j)88 f ygf,l-zdte±    A

  If one vibration has 7.0 times the energy of a second, but their frequencies aahou-s 4:s-mfau ox7 -nd masses are the same, what is the ratio of their amplis- auox4uoa:- -ms7hftudes?   

  A 2.00-kg pumpkin oscillates from c 8wp6ac3a/x t3j .yq,u*waira vertically hanging light spring once every 0.xc/t3way6i8 r* cuwa,.apqj 365 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical pal8r +ea3crz 0lv/q :t,:shf qbrallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What wi bec8 tsh vq0rz,aql3rf/ +::lll be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in mn 9pbei3u/9xm jha 2sak1 9to(cmeh*,ud :vz;eters and t is in seabv j2cxis/mh;m*3n aet, uz uo9:1 9pe 9dh(kconds. 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 SHc1 9tbsptc o91crm9 m:la9nu y9 9gc0iM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of,r,x (ml fsap3 a horizontal spring (k = 124 N/m) is struck by a hamr(als,x,fmp 3mer, which gives the 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 3uq1c wcrhpsf8- zly*b6 k0e8305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium 1 b8pr8 ucqewf *y0 sk3zlh6c-point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness consgkryw+ *hte-f*za4tvhp(t* xyf a l ;d8)/3rmtants $k_1$ 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 strik*0*j ajr;zw ow5h. mhxes a 0.600-kg block attached to a fixed horizontal spring whose spring stm * joz.; *hjh0xwwr5aiffness 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 -2lgqx zb+p pd 2u0s5qmass 65.0 kg 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 bridge. Calculate the spring sti+d 2p 0xu2pgslbq5q-zffness 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 vibrax 1zxb9fog ,md rwq;(3tions 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 exacttelnqt.*t5* uthqae nbq+a 5- 2x.e;j ly one swing per second? (That is, one complete vibratben*tq55atea.+qt. j uq2x;*l-thn eion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its perionx-;: kp5 joeed on Mars, where the acceleratio kj;ox -:5npeen of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendul1mbzpf i)82 )d+gim lwum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the penjlr(xn kr1ft:c 2(3n hdulum bob has a mass of 365 grams, and it is released at an angle 1 tj3(fxk: n chlnr(2rof 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 pendulqywstfin6 7 n1al8.k9um has a length of 0.9930 m. If the clock loses half a minute pe7 qwnaynils91f. 6tk 8r day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spes3mfnb.meq hg. xira:nk 68 5tmqd-u*(z6 )lced $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscidx(pddm3 *afs4u-0n yllates at a frequency of 2.5 Hz. At it is released from rest starting at an an-3*u sn 4y mddxafp(0dgle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his m4m bk,s2c:p:owm tv+ anchored boat every 3.0 s. He measures the dim m4:o,svwbcmk+p2 t: stance between 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 s5pulwc 3og, +p,ko(ykpeed of 343 m/s How far akku c3+p(g, 5pylo,ow part are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies betweez qtsfxp(rx5yv.xj3s *w)-f1 n 550 kHz and 1600 kHz (kilohertz) and tra jxx5.1*ts(x rs) vfzf3qwp -yvel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal22d:u6baacicg; vm 0fas7n u - waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one en jjot2xm29j1 fj2h;2u8w*oi + m i;r;vrcdcis twice as dense as the other. In which ruwo h1;+22v8 m2 r; d*ijoerjcxtjicfn9;2 mjod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the te39)d-niayf+q *s vtn7r xo-52ogfu bbnsion in the cord is 150 N, how long wi9 7a-ixnd yb 2ot)ffr* unb+gvo s5-q3ll 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 stn13m( rtgntzm8gf3 *ajr, d( keel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wav*jmf d((agg 1ntktz8, nr3r3m e pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. He hsabb r0):yr5 wcw4ie8ears the echo of the wave reflected from the ocean floor directly bw54 i8by0e ac)bwrr:selow 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake trav a+qgoi 57e7r .giw)tbel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took plte +.br75 aggiqiow)7ace).
(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 trol.1( r0xfgd sz9p0ubansverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), wzsolg(0. d frbxpu091hat 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 inteni/ohubt2c 9nj*2 )hlwsities, and (b) the amplitudes, of an earthquake P wave passing through thel9h)cbun w2joht/*2i Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Ear2cpb)pc ukyq/oga+ld (,q- l2 th is measured to be 2la c )p-gdq p,qy b(c+ko/l2u$ 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 t g5 6ajelq5 4stlm*ah2he same portion of the Earth, but one is carrying twicmlqg 4j5a 2hlse6t*a5e the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, aqvg n4a28 gg,w2;voobut one transports three times the power of the other. What is the ratio of theav2oaq;og v 428,gw ng amplitudes of the two waves?   

  A bug on the surface of a xesm.5zj jp-9 f6fe d jojj)0-pond is observed to move up and down a total vertical dmj -exf0s9 zf p-jeojd56.jj)istance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are mnzlc +sr 7wzquvt/b* q:s;a +;oving toward each 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 straight. What has happened to the energy at this;bwl*csn:qa u v ;qz+zr7s+ /t moment?

  If a violin string vibrates at 440 Hz as its fundamental frequen/s82)llom ync(6 rgds cy, what are the frequencies of the first f )lsm/6y2dcro(n ls8 gour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At whsq1erw,6+,sb ( ue )i/mjcdnxat frequency will it vibrate if it is fingered one-thir,)6 u+wnmsqde /sxb,je i c1(rd 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 at lexgz3k+/kgwp-sv sn1*kz)wp4ll s81s e+e x. nast threen8ll-+) es gz1*.x3g4 nsskzpv1 e /xw+pkwk s 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 wavesuxi498sidqrpqv 17 5 e .dsf*t is 4dt7qf*5 1x8s dp v.u9re4qsi i75 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibuknp) g* n:b v8+wwmi2rating string are 280 Hz and 350 Hz, what is the frequency of the fundambwwv g)+n n2*m8: kuipental?    Hz

  A guitar string is 90 cm long and has a ma 2kq /a co*9wpf+hj6auss of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamenta2of/qaj *p+69 cw uhkal and first two overtones?    Hz

  A particular guitar string is supposed h;d1n 7 g/ee 5fjiwginv//yf1to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in /fwjneiv/d 7 ni5/1ygeh1 ;fg 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 Hzbc p7vpxd rz7x 8ja10zxkc8bb4/o2 s(, but it is measured to vibrate at 205 Hz. By what percent should the tension in the stringrvpdabzc7 0/oc p1kzb88jx7 sx x4b(2 be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to r+ul og8+zsofwwqdo/.n e q1 8d(*:mwa small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit len8wnwq8 l dmeg*o/.o:rfquo w+( s z+d1gth 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 mh wpo6ws0y+s/v9fe6u ay be adjusted by moving the pulley. If the hanging mass m is fixe0 o/sw6u6f wh eyp+v9sd 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 z/r hp7e8e)bi 6xm6stforth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relativelybs6t)x8p6ie her7 /mz 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 boundarybvn47 rkg em24qs d56x5vvw4 w within the Earth between two kinds of material. If it approaches thee 4245w4 6bn7xsqwvvrvd5 mgk 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 underway4d 78aap0 x znpwk9fed15*lbter “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wpp1 7 nkdx0e ly4bfwaa85*zd9ave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelin54, c0mv sytsog in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air inocs0sv y,mt5 4terface 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 rock at a ic 7z.i--ch 7evz4exq 38 vc 4qe- c 7ei7hzzx-i.$^{\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 use,9i +v4k swnk*weoscp4-sd 7ir’s manual, the dish has to be pointed in the direction of the satellite, but ansck47iv 4,si9 k+ won *d-ewps 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 and8xvl j39:ei4. dsoa wb;fpb9y 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 warning, people have died during tsunamis, some oj.b w8o3y xvabiedsfp49;:l9 f them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing ca; ju-md7sghbzc8 ci44r bumper has a spring stiffness constant of 550 kN/m Find the 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 conserdc4hib sz7u 48-;c gmjvation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretchmr;wf7s czuvi-4eew8;c:ob*n0 h 0q3 d mzi )ies the net 1.1 m. Assume that the net behaves we8emv -zmiir;qi h7 cf:4c0n0 )z3bs *d;woulike 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 onsc*-se:jf7b;u5n- ui gs,cge the end of a freely hanging spring. The mass then falls 33 cm before it stops and beginsue7 en;sj-sig:cs c5bf,*gu - to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed ovs u e-wel /wz+j*nix:-0gf. j-mx77x o2z qbof 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) Wxe7e-g*vz: 0x.jn u2qw f -blwo7mjo/ szx-i+hat 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 of coffee (diameter 8 cm) at just the right pacep;h ehd3nz; :q of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill ove:q ;z;ephh3n dr 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- mv:;zw.gl hb 4h-r2wmrpm phonograph record have a wavelength of 1.70 mm. What will be the freq ;wwrmhmz.g 4v:hbl- 2uency of the sound emitted?    Hz

  A 2.00-kg mass vibrates w 9*ugyw tjm z;(s+1l+xyqn d,according to the equation x=0.650cos7.40t where x is in meters and wx 1y, ql;y d(+uwj*g9s tmn+zt in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. Wbsqq-hjgba9b,w ,67 mhat is its frequency if it accelbm-bgq , 97ws,jqhba6erates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Wvkr3.4ykpd39a/ f-,sx pu n4a*w yeulhen a 75-kg man stands on the raft, it sinks yldkfnwk-s,*u p3eu 3v4x9paa y r./44.0 cm deeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 u0tg;h( o.qksHz (A). qug.(0h kt;so
(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 tr lia8:xrs(2l n ,)(nk fvkd)nhaveling down the stretched two-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 (bk dhf(sl8l)2i,arvk:n xn( )n ) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a z(2l p0u5bm9up; fgxu frequency of 264 Hz, and the tip of each prong moves 1.8 m(;f9m5 l2x uzbuppg0u m 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 harmonic motion of 5qy q*6mt trast.g.f3fd/; uofrequency 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. 1/m5; q*uq srg.f .tft36 oaytd1–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is (hlz-n2ra3f el. /wpu attached to a ring that can slide without friction onlz e(2h-r/f3npla wu. a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-w5-os .ov r)uyuay swing takes 1.00s 5. -uuoo)ryv0 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 or can swin(ij ly)oj 7nwh 4fk5o:g as a pendulum of small amplk l( hf ooiy:54jw7jn)itude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: 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 123hnd 6do65,3opsd voyw: l(7 fr g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two6(y57orn, f3 s hddwvpo6o:dl pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring wituz7,n3nr6x w w nl4n chbjl9.7h spring stiffness consc37lwnlwn,b xn6 .u rjzn497htant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1ojj s8hay ;r2l07+grg 200-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 atrlj8h s 72jro g+a;0yg 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 rsh6/;3jutxgsmaje3 . tz1/ rFig. 11–58 (which also gives the dimensions of the block). You push it sideways as sh /.rxu6g31rm3js tszh a;tj e/own, 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 the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz