Give some examples of everyday vibrating .h bbvha spjj0-.h7 2pb9k (lrobjects. Which exhibit SHM, at least approx bps -.pahljjbh0 krbv927(h. imately?

Is the acceleration of a simple harmonic oscillator everj;fpt3 f:+ - wo5dvbbz zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately simp9tic )qf *no:ple9nqco *)pf:i t harmonic.

Real springs have mass. Will the true period and frequency be lar1 rg7z :drg,/a5yk yvtger or smaller than given by the equations for a mass oscillating on the end of an:,7/gvzrt 15 ykga rdy idealized massless spring? Explain.

How could you double the maximum spee w m8be:5tekns)m36ged of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached *av kj1o;oo /lto the hook of a vertical spring scale, and then is released. 1ol;*ook v/ajDescribe the scale reading as a function of time.

If a pendulum clock is accurate at sea lefg hv4ux;i*r(vel, will it gain or lose time when taken to hi ;h uvrxfig4(*gh altitude? Why?

A tire swing hanging from a branch reaches nearlbb+o5gsa5sg cv.umt 2u k3a1-y to the ground (Fig. 11–48). How could you estimate the height of m15+-uu aov b .3scgs5tg2ka bthe branch using only a stopwatch?

Why can you make water slosh back and fodqld0 v :y+e5zr,ezj.n, sq .k+d.ahc rth in a pan only if you shake the pan at a certain freq++nzecj5, .: dhkrvysq0qd zal.e,d.uency?

Give several everyday tfu tx 8w:.m*cexamples of resonance.

Is a rattle in a car ever a resonance phenomenon? Explain.z s(sk* a(5myyx,qhb-hmno7d k; 0+l t

Is the frequency of a simple periodic wave equal to *bnm dv3lnv g77a*c-pthe frequency of its source?vb v*dpla n7- 73cm*gn Why or why not?

Explain the difference between the spej95fi( byacuc2o7i,(j4 m +jf s(fspked of a transverse wave traveling down a cord and the speed of a tiny piece off(cj( 5b 4fj(i,kjsy p29s7+ aiocm uf the cord.

Why do the strings used for the lowest-frequency notes on a piano normall:y( jwmqjo qep0fx lm::vs2 q-9- o-vxy have wire wrapped arounpjx:9fw0m-oq qq( o2vj- xls - yve:m:d them?

What kind of waves do you thinkl dsc5h5r16-r5 : stuflj3r7wq az 3rw will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paralqr5wr7zrd5afj3t h35cws61 u:- slr llel to its length?

Since the density of air decreases wi k8tq)apr0twn- r1esy*z i4-xth an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect ther) 0te8-yxi-k z14qtn*a rwsp speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in am(:mv8h k,vnf yplitude as they travel away from the sour(f n8y vhv:km,ce.

Two linear waves have the same amplitude and speed, and otherwise are identical, rgde/:wd z:9z except one has hr:g we/:9 dzzdalf the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the bout37jo cwb*nax8 ++rdl ndary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and8od+3 tjn+*r bcxl 7wa velocity do change). Explain why.

If a string is vibrating in three segments, are thervr*a(n4g4cwim 2 q sjpk.6ed4 e any places you could touch it with a knife blade without dic vi.2*gpa6j(4w d n4em4krqssturbing the motion?

When a standing wave exists on a string, the vibratioy5oh5k4d u9 zp.9iie7a ed8qm ns of incident and reflected waves cancel atq m9 p i5uhdy7d489eea oki.5z the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, c 6spw(ub0 ai(sg wj):how might we determine whether the energy was being carried by particlei caub6sj w(wps(: 0)gs (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, whatlaulm h4sn- 40 is the total distance it travels in one peri0slha4 -n 4mulod?    m

  An elastic cord is 65 cm long whwmuj7030y qm:*obtc m 7n pm-ren a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. Whay3 n-c0:pr *b7u 0mwmtm7qomjt is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car5:b 8*opolns b compress 5.0 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 vibrati5l pb :so*b8onons?$\approx$    Hz

  A fisherman’s scale stretches 3.6 c-:0yv;yh(d k r klyh s06jez;wm when a 2.7-kg fish hangs from it. (a) What is th ye;:k- w;shk0rz6d yjhv(yl0e 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 frequ-o7i 6xebhmwn-2 rt.nency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs fro w2mex7h o6i nbnt--r.m it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 o/ wj1:gvfk)hnfz)- y at times t w/g)k1z hv)jo :fny-f= 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(6 vcw/8 tta7 ;jrit9w(e h+qksm)kwuqcv8 r- in a spider’s web. The web vibrates predominately with a frequency of 4vtrj6)8/8setk k+cqw( a;uwqrh7 (m vtic 9w-.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. miubkfd602. p9il*gij0n niv*l .v .sWhen an additional 680-g mass is added to m, the frequency is 0.60 Hkif.i*6v . jsm*iu09pl20. inlvnb dg z. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with auz 9rk 7j*lf80 9pbbtcn amplitude of 0.13 m. Deterzpbl9j cr f8ku90t b7*mine
(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 equilibriu)d6n3z;w3)zqkp d- 4jb o8wl3j 9dstc+ fgtwom is the speed of a SHO half the maximum val3;jz)d-pjg4zww3 bd c 6ts9k8lf 3q)doto n+w ue?$\approx$    A

A mass attached to the end of a spring is stretcl5nrz*a 5wk/ e/vcefpj(-e.xe0c z5lhed a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. Ifj 4u)szgep d/.p*xock j/0ihq8qp8;c the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?u0*p kgc8pc/dspx) q eq4 ;.johz8ij /    s

  An object with mass 3.0 kg is attached to a spring with spring 9et84qeuy m.2 d,fs giam02 xzstiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium poem9ef42tuya8x 2d .g,m s0iqz sition, 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 sp (m rr:supv dthai;m8.5n;2u fring of a toy popgun 0.200 m to “loa .dsimp;h2f uu 8t nmav(r;r5:d” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless suy+w *6z emmkt:rface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J oe*t m6+kwz:ym f 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 g9wobxl;mm3fi b-(,tmnr*) a= 0.45cos6.4t where x is in m (* on-;a3m,mbt xr9wli)fmbgeters and t is in 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 equilile :pt wa9t7-gbrium is the energy of a SHO half KE and half PE? -:t alp9gew7t ±    A

  If one vibration has 7.0 times the energy of 88y 5x5vd nh njfkm1w(a second, but their frequencies and masses are the same, what is the ratio of their ampv(jhxf15 85 wdnynk8 mlitudes?   

  A 2.00-kg pumpkin oscillates from a verti06ebhacpx 9-j 66zduhcally hanging light spring once every 0.65 sdzhax-09 6c b6ujhp 6e.
(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 sup -u4f*tqzx +gv.lof f)ported by two identical parallel vertical springs, each wiz -v.q)4+uff* gltfxoth spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accordingms n 49xst)a 7iawg,5z to the equation x = 0.38sin6.5t where x is in meters and t is in secon,a547w)x iz s 9anmsgtds. 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 jrghbj rl6,pus : r.r m;w8c hbs(0-1bmbq7;oB. 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 horizontrg31aroz ,0*k b)+n7fsps q dyal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed o7yn+gz a1s0 rko)rp 3d*bs q,ff 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 5id5g(hx- dyz;tnz:e constant 305 N/m vibrates with an amplitude of 28ye:55i d -;zhxdgzt(n.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 springs, with spring st /1wsu2z.krzyvq 0(4 qy)admniffness 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 fixed horixsbi 0j);7ojbvel;ch 6 n1)j ezontal spring whose spring s b jh7ni;)b1eo0j6j)exc s;lv tiffness 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 mas2(mn zkzx6 k8bs 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 lbkm z6n(8 zk2xevel 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 j1sx e f-h/z93xot 9qws. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulumebeo)cea6,hjp8 5:; hcl j7dn be if it is to make exactly one swing per second? (That is, one complete vibrationc,aohj7lhn)c p:8ee ;5e 6dbj takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. Whathhs0f i b:+m1y is its period on Mars, where the acceleration fyi:+sb hh0m1 of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendv+:po21 k ewnhfsh +qga7y1 k;ulum 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 pendulum bob ha n gm(.q)w fu7aa5*/t jdy+aaxs a mass of 365 grams, and it is released at an anglmqu t.f5ga(ada7* n x/+jwa )ye 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 losczn7 k c(k7,ldes half a minute per day, how should you adjust the length of ,kz(c7d nl7ckthe pendulum? shortened by    mm.

Derive a formula for the maximu,/ li x 6kcxxozz9h0u 1yr-8mrm speed $v_{max}$ 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 21h 6r 2pko7wognnas50.5 Hz. At it is released from rest starting at an ng sknp25ro01 w67hoa 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 qc -geqfo3; ;uhis anchored boat every 3.0 s. He measures the dista;g-qc q ;uf3eonce 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 an(wdk x)u1(k pfd travels with a speed of 343 m/s How far apart are the wave crests (cx1() (dpfwkku ompressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (k)9 ,,1ew o n5xbuxqbe)sai1 zdilohertz) and travel with a uz9bedi)wxq ne,5a x,1ob)s1speed 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 longitudikueimzj++ ,fe2bf)l ilg*+d7c b/5vrnal 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 tvam rem ::g/h6dpq 0vm98hl8qwice as dense as the other. In which rod will the speed of longitudinal :mmd6phlg:q0a v8 ev8qm9/ rhwaves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. c bu3ow-g/ a8jyhx. 8bIf the tension in the cord is 150 N, how long will it take a pulse to travel from one sb3c hoybx8-a/j.8 guw upport to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable sv*x g81kna q+oms0,uao/i .bof length 620 m and diameter 1.5 cm. As the gondola comes to thebi.*as0os ua/vxq,nmo g +k8 1 end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surfac.dmv*xa4 3cx7 ef*jl je of the sea. He hears the echo of the wave reflected from the ocean fx x4fje ac*3.mjvd l7*loor 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 differen x0 (xvmcx7jcs58rgw-rv )o/- gbrmq(ce helps in locating the earthquake “epicenter” (where the disturbance took place).g-x /xj5sr)bv (c08 -r xm vmrgwo(qc7
(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 approxzb:yvg0 7dp1 ,(ap7 n c)npnllimated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencie71:nglv0 (pln a dnp,y)bpcz7 s), 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, and (b) the amplitudes, of al pvmk4cr ;n3*n earthquake P wave passing through the Earth and detected at two poin;mrv 3pnl*k c4ts 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passinct -+f5mhum /og through the Earth is measured to be ho m t+-5f/ucm$ 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 teqlp.p 1ef7( yravel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the ampli.p7fe(pely 1qtudes of the two waves?   

  Two waves traveling along a stretched sts 88 eah,qkjh mk2/mfc:i+zc,ring have the same frequency, but one transports three times the power of8,k,cj/eq:c+m2 8 s ifamhh zk 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/ykj+l 225nk k2ruat r a total vertical distance 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 2ra/j5y2ltku k+n2 kr the bug’s maximum KE change?   

The two pulses shownun7 )l, z2r asv5s/fnr in Fig. 11–52 are moving 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 happened5ur, anl /)v nss72zfr to the energy at this moment?

  If a violin string vibrates at 440uz b2guw+k+r , Hz as its fundamental frequency, what are the frequencies of the first four zk bwur, u+2+gharmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what fw5e c 9q s:dtltm1db)-requency will it vibrate if it is fingered one-third of the way down from the end? (That is, oq:w bd5)s9- tlemtcd 1nly 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 lebh2 t38)v +oq *zoawwhast three other frequencies at which it will rawhht3b*z+o o8vw2) qesonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is bp90gttl e,)tms b z:-1quog+92m/s If the frequency of standing waves is 475 Hz, how far apart are t1mtstgbto+gz )9,- :lbpqeu 0wo adjacent nodes?   m

  If two successive overtones of a vibrating sd l/z/( +3g 1 w0w,jivkollrvytring are 280 Hz and 350 Hz, what is the frequency of the fundamentalkgv1,l +iv z/o /wyl0dj(rlw 3?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance frn )k9;fv0 cmlhom the bridge to the support post isl)nmc 9hv f;k0 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 string is supposed to vibrate at 200 Hz, but it is measur 75kjhlrxh 9-ted to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies lt7k9h -5jxhr are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured 2.(udj 7w h3,uib ; z8ymjlcdfni*x kv*j)en. to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the f;ik n7.8)mn*e jjzdhv*2.jc fi (xwbuyu3, ldrequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanica8i4e (loxle*p l 60-Hz vibrator. ( * 4eel8lxipoThe string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may rvt1xmn 3-a)w be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varyi1 vt-w anm)r3xng L between 10 cm and 1.5 m?   

  When you slosh the waterp-i;k (kl/kw5viz.vm back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a stz/i-(lvi;.5vw kkmkp anding 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 s0;nqy0lnxy mr6.1 tbr3 mhf/ itrikes a boundary within the Earth between two kinds of y .rr06xmh;l1fm0nqnyt i /3b 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” whvle+5xp i,g/ rere the velocity changes from 2.8 m/s to 2.15 g l,e+xri/vp m/s 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 it hits a layer of cold, z l1mz;urwj;6dense air. If the sound wave hits th lu;1z rmw6;zje cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rock at a+;6 pnil3):qkankt6n- xglrjjap-3k q+t: r6in; x6 nk)lngl 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 about 0.5 m in diameter. According tog.npyo )jk :f0 the user’s manual, the dish has to be pointg0ypo.jf): kn ed 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 kmzguhv()gf x0 h51v86(v njewq and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledvf(8g qun51)(x gvh6v jhw0ezge 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 5 ous9;; .ebu:)8f7 c qkzs pmkr.jrr-v50 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed r9mu 8b ;s 7rresop;.zf)v cj- kq.:ukof 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, whicf*oa:yoc v d6hy)i1y/ j,aky3 h stretches the net 1.1 m. Assume that the net behaves lik)3vfy:i 6*cdayy1 a ,ohy kj/oe 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 theomab( */ lx d hrpu6hg7.ht5a, end of a freely hanging spring. The mass then falls 33 cm before it stops and beghx gb.udpm5ah,h(at7 /l*o6rins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a h l05n zztmf;eg6h 3/z.rooj1iuge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m.tfng3 zh.0o5zmroz1/j e i ;l6 (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) at just the right pace of abz/ /l)zy-vmxm:vva/6k4h xe2g fn b z7out 1 step per secx -yz4ab: z6)g /vxk/vefmvzl27/hnmond, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from 3cs +ogjl b()*i2im kfthe center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the s cksi g*+jilb(32)mfoound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40tu 1-p u0kgyivi) q;3zo where x is in meters and t in seconds. Dete10 - ;vkiu3)pzugyiqormine
(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 p05 f.tsrimb7bv7+8phpwjv6b x;jr) f. What is its frequency if it accelerates at 0.50g (a) upw+j xvppw7bs )75m vt0rb;b 86rijfh.p ard,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raftzzom *:4(bukbjba*b n2y c;ub0 evw .7, it sinks 4.0 cm deeper into the water c ju ybbz7bb.;z0 v42:bwuokn *(ma*e. 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 musiu ngav+itr8, jte;e *)cal instrument are tuned to play at 392 Hz (G) and 440 Hz (Avaut+e*,8 t; iegj)rn).
(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. 11–3,yx4 :zybub 2m. jop1lu1*iqy3. 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 freq4y2yquli zm1*o.pj, xb:b1 uyuency 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 0m+(vw)d*ohxtno0z -. u i; 6hsgetw wtip of each prong moves 1.8 mm to either side ov*u(+g).wtoxdt-his0z w he w0 o6n;m 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 oscil xx*d 9y6:jhcelates with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contacxj:yx6ceh *d9 t with the board during the oscillation?

A string can have a “free” end if that end is attached t93(cwoe:o1f g+spwz to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed an31 zww+stogf: peo9(c d the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-waig5sz0rx a7/yx-a6g ey swing takes 1.0ar igzxsxe0a/g765 y-00 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 oscillatefk1m8q wi;d.ev5iz/:/ zu egq in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which on f1:gmeq8 /izvq;5e d.i /uzkwe 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 1pd tx v.5l+bh*4ecun*23 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 ou5.ch+tnbxd 4v *l*pepposite end. Where will the two pulses first meet?    m

A block of mass M is suspen/.r nx/1y5p ,i8sdtl4ph k lkaded from a ceiling by a spring with spring stiffness constant hki/ rtpay5px . k4l,l/s1dn8 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 126pjv tzcb2x)3 10 ej8ip5ai sjl82mov00-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. What is the period of the bouncing? [Hint: Refer to Table zxo26jts8ic)3 mjvab0p15jv ep i8l2 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58jn+)o9:6ypm 3+s2orri wtr)ain 7 r zg (which also 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 the shear modulus 9wijz+rory:t7n n)rr3 +)p2 a6imgos(Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz