Give some examples of everyday vibrating objects. Whicps;p 7* oq/zyqh exhibit SHM, at least approximao/qzp;p*q7s y tely?

Is the acceleration of a simpo a7j02nw83o hrq ai.(zx9 ccnle harmonic oscillator ever zero? If so, where?

Explain why the motion -*q a(jxd tmy1of a piston in an automobile engine is approximately simple hajt-y1qm*x(a drmonic.

Real springs have mass. Will the true period and frequency be larger or smaller rp6x6t z *2znhthan given by the equations for a mass oscillanhz6zr6 *2px tting on the end of an idealized massless spring? Explain.

How could you double the m- ,hdjy n);dny .s 6kpq2wmktkq6n l:4aximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attac10 b x6yjcl3nrgidhg-kw86 8b hed to the hook of a vertical spring scale, and then is released. Describe the scale reaxj rywbck- 66h3d l8i1 ng0g8bding as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose timeis8t uw3mz0o4bha5s:b8: k sa when taken to high altitude? Whytbsms3u 8i h04k5s bo 8aaz::w?

A tire swing hanging from a branch reaches nearly to the ground (Fig. -eogivh+ 7oj +11–48). How could you estimate the heighihe+- 7o jg+vot of the branch using only a stopwatch?

Why can you make watefsh:cbh qxg2 v8p9 2-or slosh back and forth in a pan only if you shake the pan at a certain frequencv q o-2:c9f8 hxpghb2sy?

Give several everyday examplesey gaghtkq.+*s/x ;ne0a*sd3 ,9 mcfo of resonance.

Is a rattle in a car ever a s5 eh o6g sgp8o*44ukoresonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequencx5 l7sh((aee/kq +a iry of its source? Why oxr/lqe7aia (( hk+5se r why not?

Explain the difference betweenq(mjq5 /q.jl s the speed of a transverse wave traveling down a cord and the speed jqmjsl./q(q5 of a tiny piece of the cord.

Why do the strings used for z.cb;rhgrdd548c+ xm the lowest-frequency notes on a piano normally have wire rcr g4m8x d5cb +.h;dzwrapped around them?

What kind of waves do you y+s9a1bk-y mly /v (c4sq*xc othink will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paralvbmy/s + c4kxc(l qy9 yo-s*1alel to its length?

Since the density of air decreases with an increase in tempxg0r(+rla6)nj ont)s erature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in arx))o nr6jtn+s(l g0 air to vary with temperature?

Give two reasons why circular water waves d c;ohce+x(cha1; v96zo* n ruzo *g7uhecrease in amplitude as they travel away from the sourcexcuruo6e 19h;h;*h *( nvo +cagz7ozc.

Two linear waves have the same zqqcwov.j794 / rp1aaamplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which t qrpq 7z oa/9wa41j.cvransmits more energy? By what factor?

When a sinusoidal wak 2f)d 2l1hlaxve crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Ex1d)lk2 hl2fa xplain why.

If a string is vibrating in three segments, are thdv lj0n jt) 5k+k(zlf6 s*gzu0ere any places you could touch it with a knife blade without disturbv) z kzg( nfjs6k*jl 0t+u0d5ling the motion?

When a standing wave exists on a string, the vibrations of incident and reflecte51p*:x rnh2 8iwjdvsdd waves cancel at the nodes. Does this mean t5 vdiwrs:*h82d 1njpx hat energy was destroyed? Explain.

If we knew that energy was being transmitted from o0jm hmd4;wo)k9 :ihsjne place to another, how might we determine whether the energy was being carried by particles (material bodi ;d :4ihos jm)k9wj0mhes) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the tjj-wdbty ni .2o05m *motal distance it travels ijomb d.tnjiw 0-*y5m2n one period?    m

  An elastic cord is 65 cm long when a krrqf-m a.syos/6 * 8mweight of 75 N hangs from it but is 85 cm long when a weight of 1ssqm/-ko rf*.y mr68a 80 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0hun rr;ksu0 ;) mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of 0)s;ruh uk;n rvibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs guvzp k:y1 .uc5(pokn)z /p( pfrom it. (a) What )oupkzk /gpnp(u5c:1 zyv( p.is the 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 wi 6vz,v+,o7r q5pxatv nth a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its f,tpa7ro6,+vxvq 5 nzvrequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 *rip)ozbfex igb747l 6 ep; 0bat times t = 74g6e xfi*bb0eppo;7zrl ib ) 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 ojpa9*x2l9 y7a edan 0web. The web vibrates predominately with a frequency a*aoye2 9pald0 7jn x9of 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 freq8wf -ejthi7gsvsw sk 7v6n)8f*j-wry*u /y 8c uency of 0.88 Hz. When an additional 680-g mass is addedk ny7 s/f*u*ygwrwes h-swjfiv)6c8v87 j-8 t 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 spring vibrates 3.z* mh,4aqr*jo0 times per second with an amplitude of 0zoa,4m**j rh q.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maximum vjz3. l c rig,5w ynbm p7j0ig/(,u0arball /ij0 wc,gyu(z,nrr3i0pbg.7 5j bmaue?$\approx$    A

A mass attached to the end of a spring is stretched a dista3oq aw ,qb p,**(soetlnce $x_0$ 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 w am; lksn2:d9;emj c -f*fek.a vertical spring 0.315 m. If the spring is stretched an additions-neldjm;ka9k:efcm f2. *w ; al 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to acmndv3y j2y4 3 spring with spring stiffness constant k = 280 N/m and is executing simple 4mj dn2vc3 y3yharmonic 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 cok-iu;(r4 abuvg.6 (t 8 xfkmvqmpress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speeduk tm vqf ;x.v84(bira( kug-6 will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionl67 pdl(:ml qwm.aor0 ress surface is attached to one end of a spring; the other end is fixed to a wall0(wol.mq dpr6 :mlr a7. 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 =mwe:ou pm)*- 21pxnkv 0.45cos6.4t where x is in meters and t is vo-p2m*p:n) k w 1exumin seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilib u5/lo6ggrn ;f+rov.g rium is the energy of a SHO half KE and half PE? ± +.rgvofo ;nl6 gug/r 5   A

  If one vibration has 7.0 times the energy nl .i/mq8j+iu oj3iw mvy(gt(k(aw :7of a second, but their frequencies and masses are the same, what is the ratio of their amplitudes?8mw3iv(/in(. tqjol y+gma:7j wk u(i   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once eve 9dxpjw zkea34x1g1o4ry 0.65 s. x9k z jd4wgex43pao 11
(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 kn 2:81ernjm0v;xswh ih bye y5*vwy)s- h0j0 supported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be thyh;0 :vsry-skw*myh je2w nv085)1 hbiex n0je frequency of vibration?

  A 300-g mass vibrateszcu2(.xdl .2xi-( ys echba j5 according to the equation x = 0.38sin6.5t where x is in meters-j si5y l(2 uxh(bec.2da.z xc and 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 ou 9g*er8 jju6B. 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 a horizontal spring (k = 124 N/m) is 2 (yx*ofkkoy7 struck by a ky( 27ykoxo*fhammer, 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 305 N/m vibrato 3kjdtmz;gy 90aanm:g74 1k jes with an amplitu4oktmj:gz0a3yjd91mnk a 7 ; gde of 28.0 cm when 0.260 kg hangs from it. The mass passes 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 spri 7pt)b3ks+3 c.1sz+lg trubfxngs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixedor a av 4rxj50ua b d(akt/tvl9uwj3:a,,4a/i horizontal spring whose :j4boartaa9a403,vua i5rx/ uvj( dk ta/,lw 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 bmenrf8vj-ws+ z5rfvm2 k2nl71c/,v j ridge. After reaching his lowest point, hev8 w l/evmfr svrjcm,n 51j+f72-nz2k oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched 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 exactly 60 s. What is ox 6uklrlw253 its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple penduniz w6 c )l3q(6xsi7ublum be if it is to make exactly one swing per second? (That is, one complete vnuwb36 is)i7x(ql6c z ibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 sr, k9ubr.e 5uq on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 thatuuk qr,9rb 5.e on Earth?    s

  What is the period of a simple pendulum 80 cm long g.aslg(, 5qlbe)gej cpz 0 96q
(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 p/gbd0b) boqlji 8 *sd,endulum bob has a mass of 365 gram g8db,/*sdbo0 blq)ji s, 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 length of 0.9930 m. If the clock lxs9clw aty71j,j+ kn9oses half a minute per day, how should you adjust the length of the pendulum? shortened 7jt l1j,9 ay+9ckw nxsby    mm.

Derive a formula for the maximum acx87ua*3 n c9tv v)qm.ljxc7speed $v_{max}$ 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. Aii6.knd gi8; wp),hdrt it is released from rest starting at anp)iw,kh;d8igi drn. 6 angle 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 efqn 1 o9c8,ve91urzvanchored boat every 3.0 s. He measures the 9c91oq8 ,enfve1zrvu distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency o hw3s(.hkv6l zf 262 Hz and travels with a speed of 343 m/s How far apart are the wave csl zkhwh6v( .3rests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz a p/mes-efg3 k/q. -q,(t vzeeba:s y8and 1600 kHz (kilohertz) and eb8 3/(,ta ezyp e-gs.: aq-mfe/ksvq travel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed od2yxk3sx+n xv bvt7 .b/tcg8(d+0gmof longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as )0 sbm/ c0y5zeudnbc6 8an a7zthe other. In which rod will the speed of longitudinal waves be greater, ab)05ancm e 76ny 8 cs/uzzbd0and by what factor?   

  A cord of mass 0.65 kg is ,a ; wxp kad n;p,,t;fazt2ng,stretched between two supports 28 m apart. If the tension in the c;g,a,2f nanpz a k,;xwt,; dtpord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connebj6hno,r(9n twxsmcb56(c +n 3/xwnm cted to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and send 5 (3 t(b/wbc,x 9cn6w x6+jsnmnomhrns 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 bel 02p)tgs6zp.z( urijtg8*yjnow the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How du*yzptgisjp).n(zj6 8r 02gteep is the ocean at this point?    m

  P and S waves from an eartt*t ,ih ,lf0srhquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturt,*tf0islrh, bance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximate2w1j5og3up kn ;henkb,xf u,5 d by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequenciegf,5 ubk 5o12;kn wj,h3eup xns), 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,y/ow4 bke i7wt-z4gip x2m 5;e and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at tiz- e ioywg5p/4 72k;4xwmtbewo points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earytp1g s,bm q83thquake wave passing through the Earth is measured to be sb3q,8myt g 1p$ 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 portion2r47voocrsdnt hc,rm083m7 ja l.2o j of the Earth, bmo2chmcrjv0d .738s7 ,jor4 ln ora2t ut one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but one tpr 2im 9ex-(icransports three times theemi(ri -x29pc 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 to move up and down a toasa,v gu8/1 k7-yuted tal vertical distance of 6.0 cm, from the lowest to the highesk1/v7 -utea,a d u8ysgt 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 moving toward each other. (a) /s0;sc , ncwqbk;m az/Sketch the shape of the string at the moment they directly overlap. (b)cw, ; m ns/sb/ac0;qkz 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 moment?

  If a violin string vibrates at 4m;sk:14 yy72s xu4 w;lmiu mhs40 Hz as its fundamental frequency, what are the frequencies of the first four xsw2:u mmyhk474ym;lsi ;us1 harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what fre1c*1j;q ymnfhfg1xn 2txtk j 1zi5:+ mquency will it vibrate if it is fingered one-thi:*f 1;1knzm1g2 +qc5ntf xtjihmyjx1 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 em o2sodp m8,9four loops at a frequency of 280 Hz. Name at least three ot o28 me9pmso,dher 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 frequ m/ m3dn+t;gu borhv*b h4u;u*; 4agazency of standing waves is 475 Hz, how far apart are n*;uv ;3dhmag/t4g4m zub;*rab+uoh two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what isp is o0n(x9xzr8h8m ld 2.z sr4x2r;4 gehze:m4rzxloz2e( xh 8i8 .eg0;rm9:z r2dx p mnshs4 the frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distancersu3h 20 rutpzbj0: d0 from the bridge to the support post is L = 62cm and the string is under a 0 3dbrjptsuz0r 0u2h:tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibraty;;n1l 9cdv ele at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tensll;yn1 c; v9edion in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar 8v0qkqkokpme 0; st .2string is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decrea80k mvtk s0epoq;k2. qsed by    %

  One end of a horizontaax(yn)i );:acipt z.vcz 3tir qb;+f3 l string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per ztxaq;:+i3)b v;c(zt rynicpi )fa.3 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 stl5 gf -krcbe v*mty2l+yw ,g7/ring may be adjusted by moving the pulley. If the hanging ma2m/*yg y 7vwt+5c,bg-lklferss m is 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 typg-zuqil)m0y(x( 1,g s 7wugub at just the right frequency, the water alternately rises and falls at each end, remaining ysqz-,ui(7g 0 yg)pxulm1 (gw 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 strik s4sl vvd)7:ltes a boundary within the Earth between twv t7:vs dlls4)o 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 4bg; k pmuo6,ysu r5(e“shelf” where the velocity changes from 2.8 m/s to 2.1 m/s ,g 5beyo46kum up ;rs(If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when ilkzw17n q8mv)q)m w7f t hits a layer of cold, dense air. If the sound wave hits the cold am 7)qzqlvw8fwn )7m1 kir 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 ow.-y axec(lu swl;hz-,g 49va boundary between two types of rock at a.a -luvcy (h;w-xl94o g,szew 38 $^{\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 abzww,1qy aum p92-q2od out 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of abouq d,22 wmuaq9 yzo-p1wt 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 travels across the Paciabl* .qhxp;*ow/lg;; pw:ldvfic Ocean. As it approaches Hawaii, people observe an unusual decrease of sea levexpllb/;h dlp ww;q:v*;ao* .gl in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring sq ;w/3+(plh 6yeptjvhtiffness constant of 550 kN/m Find the maximum compression o6yl/pvhh qt(p;3w je+ f the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 1hld((qjs6 rz 6lqgbtpamk-h o:d ++,:8 m below, which stretches the net 1.1 m. Assume that the net beq+ k(o:j ,s(lz6dd h l-6rpbhgtqa+: mhaves 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 .awwxyn at v41f9i+o9 ygl*i9hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?nwit+a*419via lx wf 9.y9ygo    Hz

  A 950-kg car strikes a huge spring at a speed of 22 mk7 *kqc4h xhz5zc 63ec/s (Fig. 11–54), compressing the spring 5zq k heh6xcc5*kz4c3 7.0 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 of coffee (diameter 8 cm) atfi .yr ch*l2.v just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of walfv2rc. *ih. yves in the coffee.    cm/s

  The ripples in a certain groove 10.8 j).1 goau;yp fcm from the center of a 33-rpm phonograph recoyupj )fo 1.ga;rd have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equat6kfrl 9zkq3+ 8o4 tmswht;k6t ion x=0.650cos7.40t where x is in meters ank66qttkl4;r+ 9m tohw8f3 sk zd t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates(d n 7m)csvi;s with frequency f. What is its frequency if it accelerates at 0.50g (a)m in(s7vdc s); upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on thec6l fhb +9utt;1yebv ; raft, it sinks 4.0 cm deeper1c9v e + t;fhb6tuly;b 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 i.rjlawj (7pi8wzs (:w nstrument are tuned to play at 392 Hz (G) and 440 Hz (A). (l.: pwwisjr7(azjw8
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. nrzsrfu01sah ,55+: grb kfh211–33. Determine a formula (a) for thefhr10busa r+sk :n hz,2grf55 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 lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong movue) oglev-pajfn/ x p/ g(6.r0es 1.8 mm to either side of center.g/aor6uvfx e l(-g.pj)epn 0/ 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 harmoni8.v z:kahbf 2hc motion of frequency 1.5 cycles per second. What is the z8 hvab:k 2h.fmaximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a2ue +5los-n 1/pabopg ring that can slide without friction on a vertical pole (Fig. 11–57). D +p2egob1ulop n5/- saetermine 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 j3vkyyej) ,rmee s+).— each one-way swing takes 1.000 s+)j )y3j.mevse rye,k.
(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 o0g51awb b dj)yltbg -m.u3o u-scillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the verticb-o0l.-b1tg ymu 3guwajdb 5)al 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 ma pn/88)iyvbuass 123 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 bayv u8np8 )/itwo pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffne)a f m)ofvv46oojl129 k/qibvss constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillationsvo) j219/4 v6oai lvqmkf)bfo that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-k630ucgd os sazn m3crd1;l:nhqs16( kg car at the junkyard. The steel crane cable is 22 m long and h0(c6 s6cqgz o311msk3;na dd rhsu l:nas a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives tyy1z(.lu*stvxtc e f z(42zi9he dimensions of the block). You push it sideways as shown, andy(y(i9t ul f2ecsv4.x1tz zz* 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