Give some examples of everyday vibrating objects. Which exhibit ks5(yc k:ecudl9b2 )kSHM, at least approximately:2 y 9) slkbe5dukkc(c?

Is the acceleration of a simple harmonic oscillator ever z(+irsfbk72pi uy 40qaero? If so, where?

Explain why the motion of a pisto-y 4 0u7*vrpt.sh 4iw1lkkneen in an automobile engine is approximately simple harmonic.1 py4*euv.knti w0ehr4k-7 s l

Real springs have mass. Will the true period and frequency be larger or s*df k: hnx/w3opl:d7 hy ,ul(tmaller than given by the equations for a mass oscillating on the end of an idealized massless sp*y dlu tdw:3l 7n,hxfh( op:k/ring? Explain.

How could you double the maximum speed of a simple harmonic oscillato np 6q5hi)i;unr (SHO)?

A 5.0-kg trout is attached z svy.,l:yy;n4mno u6to the hook of a vertical spring scale, and then is released. Describe the scale reading as a function of timnyv 6ys ,y .m4o;u:nzle.

If a pendulum clock is accurate at vs)-jivb9 b.;neci + psea level, will it gain or lose time when taken to high altitude? p)v.v9+-n;i esbi jbcWhy?

A tire swing hanging from a branch reaches nea9 no2cba y3r.prly to the ground (Fig. 11–48). How could you estimate the height of the branch using anr9 yb .po3c2only a stopwatch?

Why can you make water slosh back andx.j* +t j+u5hr2l9g up nt-udd forth in a pan only if you shake the pan at a certain frerj.dgt2+j *utu5l-d n+up9x hquency?

Give several everyday examples of resoiuyc 2-ab*+ fanance.

Is a rattle in a car evg7l;7tp- omujer a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to th++au(*fnujve ( b,mgj b.0q rje frequency of its source? Why or +qj u,fjv0ge m n.b (r(ajb*+uwhy not?

Explain the difference between the speed of a transverse wave traveling doqhtl:1 35fqj(r wap- iwn a cord and the speed of a tiny piece of 5jrapiwqq(l3:- hf 1tthe cord.

Why do the strings used for the lowest-frequ7zw ww85y ym:o7p(brtency notes on a piano normally have wire wrappedoywyrp7z5w(b: 8t7 mw around them?

What kind of waves do you think wil 7eqa-7a9fqv(fes ji. l travel down a horizontal metal rod if you strike 7.sqa9eia- e qj(f 7vfits end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, buz/g e1e+v bd9k-l .bwet the bulk modulus B is nearly independent of temperature, how would you expect the speed9- egv bl1zew/b ke.+d of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplimnq,hr)k:jo) gl vt :bnz, t-;tude as they travel away from t),rn nk bz:qvt) jl; ,g:m-ohthe source.

Two linear waves have the same amplitude and speed, and othbl; 0 uwbm-mzl.p(. qperwise are identical, except one has half the wavelength of the other. Which tranz( .p.l-b qm ml0upb;wsmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betwse(ohh2as7.zj 0.ngq een two sections of cord as in Fig. 11–33, the frequencyos ne a.qghh sj.02(z7 does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places your/zk4g.yjcv 0 could touch it with a knife blade withoujc4 / z0.gkyvrt disturbing the motion?

When a standing wave ex6m/3nzft npgj04 yht,ckb9 x*ists on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyj,6hxg /zm4tf 3yntn kp9*c0bed? Explain.

If we knew that energy wab9i81 c3dpaxz dek8qk8o9p 2as being transmitted from one place to another, how might we determine whet3ded pa 8bkpazi k1c2x9 oq898her the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM withl1kjdz/ ed4jrn9 ss -u6v*xr 4 amplitude 0.18 m, what is the total distance it trusd z v x4nkr 6*erj/j1d9sl-4avels in one period?    m

  An elastic cord is 65 cm lonvrq mf,2jfh(jq.h *(fl((kylg when a weight of 75 N hangs from it but is 85 cm long when ,rh(. klj*lyq hq( fj2mff((v a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kqwvo /7t5 sx8:3oppl*y)ub dt0j8au dg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the ca :5 *oosu3v0dt7/uwa8 p)bd8 yjqxptlr goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm why .av,jtn, dh9bn8 8mk3t5wrb en a 2.7-kg fish hangs from it. (a) What is the springt5mah , y8 dnb.8,jtn w3vb9rk 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 o ccxyexn6uri44uj . x7 8bk5.lf 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequencycb45 .nye xcxu8rkx 74iu.6lj if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 adepm r3vd. 3*vt times t 3 3rd*de.vpvm= 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 web. The web vibrates predomi6vtui lb;hg /.nately with a frequency of 4.0 .hl6gvt u; b/iHz.
(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 sprinairyn,/+ +g; l gbbp,yg vibrates with a frequency of 0.88 Hz. When an additionp+gi,g by ,/ly ;+brnaal 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end oqy;xg qb:qo 31f a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determine :gqy; qo1b q3x
(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 th+j)yy syqq2*ygr*r,i e speed of a SHO half the maximum valuy *)yi2q+ j* ryqgry,se?$\approx$    A

A mass attached to the end of a *o:qkkm un 1q2spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spri5d: p z /32xblo)tuslfng 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium positi ll2u3bp /d5 t)szfox:on again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiff:l,usx k, 4dbcr-ys*zj) )fotness constant k = 280 N/m and is executing simple harmonic motion. s)r*,j:cxk 4f,sy u-o)lbz tdWhen 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 t o7wolu.w bu74,d2 stvo compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg b uws7,4obv ltwo72.du all. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one ss26kum+g:ls end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the sprinss+lm k u26gs:g 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 = 0.45c,/m ej gm5g.c5 jovl5zos6.4t where x is in meters and t is in see g55j.mg5 mljv,z co/conds. 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 (kgqy/iud m(a5 zybh:e.gu:1equilibrium is the energy of a SHO half KE and half PE? z((kub ed/yh5mgayu q:i.:g1 ±    A

  If one vibration has 7.0 times the energy of a secoj fk 3n4w ih8)hhm.xu*nd, but their frequencies and masses are the sk*ihn4m )x h. wj38ufhame, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring onv-edafsdwqy:)ml++e2qt q x/n t685r ce every 0.65 q-:8 d qwledsetv5a xtf 2+r)y6m/nq+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 parallel vertical :j :5to 8(qevuguh si*;k3 uc(qwdy1psprings, each with spring stiffness constant k (Figvydkuc*38ih:j p:u (o(w15tq q;g esu. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x istz1n aomyn6o+x;y d,3 in meters andn1nyo+a,t; z dyxo6 m3 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 Bdv2ljou4c, o /. 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 sxkbuc-miyjvgz 6t 48p*2im)4g- ik( bog)3 em truck by a hammer2v)u(j)o4xi b6kiti -*e 4gcgmp y3bmkz m8-g, 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 vibrajghaqo7 cg9yh ; (m)-ctes with an amplitude of 28.0 cm when-o g()hj cghma;7y9cq 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, j uublt*n-;4k r,gl/b 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 fixed horizontal spria(bm .4u 8t:duvn4 yw btr*cu6ng whose spri.t umyd:v8rcn4bw6b(t* u 4uang stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. Aftee6gfpx ;oz /+pbhayi7+by7 h0 r 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 ;0+hpae7 +67g/ h pbfzybxyo i25.0 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 cgh02f a4 6kgeqrc rajbs22-7s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly onek.1t3o)wutf z f,-nt a swing per second? (That is, one complete vibration takes exakz-3f.w ttt,)ao u nf1ctly 2.0 s.)    m

  A pendulum has a period of+jv d hts 12g/1f3rtkq,0myef 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity isgfr1e3+yds0m ,vqk ht tfj/1 2 about 0.37 that on Earth?    s

  What is the period of a simple peny71z 3k.j7 ba hknkwp 6df*.fvdulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pend*hksjvs9ki:isyy 6(8ulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is releasey k96iki:vs j*(ss8yhd 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 le8 dqm8-/(.kuclz lg wungth of 0.9930 m. If the clock loses half a minute pqu8l .dc-mgzwk (lu8/ er day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximu 202-netcbu99qx *fjzi) j* d0carfumm 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 acu t i9y4hgrgqp 3m2(/ frequency of 2.5 Hz. At it is released from rest starting at anri 9g( qmh4p 3ct2/ygu 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 th1w1m c bn1 :hi7q* iddw4mq:qre bow of his anchored boat every 3.0 s. He measures the1:w7qr4*m1m bdn qih: qc1idw 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 of 4,alifdu- qo; ,w:rk.gaum;z 262 Hz and travels with a speed of 343 m/s H.guk:,l- iwozf,mr;u d;4 aqa ow far apart are the wave crests (compressions)?    m

  (a) AM radio signals have,502ilo+wjhb f+v ykw frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a sp+iy, 50johvw 2b wkl+feed 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 longitudo.*1ad y/4 wthp+ (levakx3l hinal 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 assnekw (gn6osg:s b mku000)z1 the other.()g0wm0k 1s s0k sugo:bn6zen In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretchmc) lk29x+e t mo7,shoed between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse xs mk2 cl,)m7 e9ho+toto travel from one support to the other?    s

  A ski gondola is connecte(d3h ). gn2l h-l15vqtfg)cgr z4x grpd 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 sends)2drg 5llfgr qtzv-( 4hxph g.cg3)1 n 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 shi,kwyz/tqw:(kir6p e .p just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is th,6/p:z rqwy wtk (ik.ee ocean at this point?    m

  P and S waves from an earthquake travel at different spec 7 l)ms37ma 8oqlv.p*bs c,yxeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took pp8amqom7c.,c)lb 3 vy7 *lxsslace).
(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 approximats;fpp cvs5s snl+ :**ded by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with *+ ;spssdcl pv*fsn:5 the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) thef)t1vjdfobej w5 x )s7,f49fe amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 kff7,) fejxt1s ve 9b5oj4)wdfm and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave p-sro9 pnohe4 p,hz ,1fassing through the Earth is measured to be ,n,hhoo1rfe4sp9 z- p$ 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 tm 3k4wdgx5k3 vhe same portion of the Earth, but owx m4g5k 33dkvne is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along o9p:5fg rm ( vml6kwh;a stretched string have the same frequency, but one transports three times the power of the other. What is the ratio of the w5;mfm96 g:vro(k hplamplitudes of the two waves?   

  A bug on the surface wsfe wf34n3flw s)k*tvwu9 4 9of a pond is observed to move up and down 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)*kl f93wew4 wt3w 9s fu4nvsf factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are movin/p hqj)+h52 g2e p6b i47txvopstg .wwg 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 Fxghqt s )b5hp7ei2jp v . pwow/t6g2+4ig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its funo o:b7.gone5d3* hjc1exwd.ydamental frequency, what are the frequencies of the first foud1 bg.odoxc 53*wenoj 7ey .h:r harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At whad ec( rqz8v*0et frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, onrvd0 e8zcq(*e ly two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at ajsrdjv t -c)*pyq7s() frequency of 280 Hz. Name at least three other frequencies at wht)prsy*d(- )7cvjj qs ich 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 fo x wia584; y2 8j0dhdahbl3jbrequency of standing waves is 475 Hz, how far apart are two adjacent nodes?0i5 bjxw;b8o3da2 y8jdl 4hh a   m

  If two successive overtones -yl )rn7lex8p2eql q bvp20a) of a vibrating string are 280 Hz and 350 Hz, what is the frequp8 np)l v bxae22 )eqly7rq0-lency of the fundamental?    Hz

  A guitar string is 90 cm long a s.-jl-l dto7end has a mass of 3.6 g. The distance from the bridge to the support post is L -s doj 7t.e-ll= 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 i-al6l: 0 kpbv8bav3 pgyco.w- s measured to vibrate at 205 Hz. By what percen 8vg3p: w0vac b-lal ky-po6b.t should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is s, z q7kp-zwd7ul soz+(upposed to vibrate at 200 Hz, but it is measured to vibrate at 20kz,spq+dou zw (l 77z-5 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplituds zt +btj5+a0)-loyfe e mechanical 60-Hz vibrator. The string’s mass per unit lenglasey)o j 0-+zttf b5+th is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by s7apri2)8 g q9 qwj-iwmoving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 2w7igsq- j9w8a) pqri10 cm and 1.5 m?   

  When you slosh the water back and fo 9 nry.3 of+y6ff7nmm71f,cwxnm )wiyrth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining re )cyr xn1 +mi9m7,y fn ynm6f3.w7fwoflatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within l9*afeq s/mrg x 4uu7:the Earth betwe9 aml *fxgru: 4/se7uqen two kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes j;8ro 4ghvwt fso)6n-from 2.8 m/s to 2.1 m/s If the incident wave crests ot8g fro vnwj4s;)h-6 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 vp mfoyfyb;ye( ) x71cv f;,o4of cold, dense air. If the sound wave h(; c,o)my1xf7ev pf bfy y;vo4its the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary5*.3 w/uaett5vrrt; a cok9 iq between two types of rock at aoe 9tw tia 5v.krq3 a/t*;5urc 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 diame5l dt0a c bt4j:t9sr4tter. According to the user’s manual, the dish has to be point 9l t45: actttbrd0s4jed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and veloc l;ud;w(p tg*fity 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 of them attracted to the shore to see stranded fishes and boapgu; *(dtwl ;fts.)    min

  An energy-absorbing car bumper has a spring sy v 7de 1snzrmdj,n47(9va pf9tiffness 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: Up794n(,v mrvfe 71zjdda 9 ynsse conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m belo d. dtae8 80kn fypq/4:iymd3ew, which stretches the net 1.1 m. Assume that the net behaves lpe:a4 0tymk8yd.8 d3 qeni f/dike 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 hangi ujrhmzsj ,1b -k7,rk9ng spring. The mass then falls 33 cm before it stops andu rm k,7kj9-hsr ,j1bz begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–5h*hgfz*x p92oo+g( cp4), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the sprinfc2h9 hxpgz p(og*o*+g?    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 rig, k8-urdo-; npy bvzh(( hfd6oht pace of about 1 step per second, the coffee sloshes more and more until eventuallydkonf ,ryo( hu (vh8;bp -d6z- it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center ofkd2psy k1nsdl kqjc e4kp7 k42,;a-o7 a 33-rpm phonograph record have a wavelength of 1.70 mm. What wk qkd7sca7jdpp,; 24-k1k 2o4syk ln eill be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrate(.ve5 d/e.8qwkdhfmt s according to the equation x=0.650cos7.40t where x is in f/.te wq.e8kd(5 mvdh meters and 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 with vfa fi0sc1i*babi.ah :9,x*w frequency f. What is its frequency if it accelerates at 0i,i: hb fcvfs.b*w*aaa i9 0x1.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stk g 7lq0-d 9gixlis0v3ands on the raft, it sinks 4.0 cm deeper into the water. W0ig ksvl-d90x73q il ghen 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) andc0 x;v3l; 7v 0dtychk *xj-6o mkls7ve 440 Hz (s ok c7 7;x;0l3vm k6 v0-eyctxhjv*dlA).
(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 coi (i-d )mxf:xi(lkur6 rd of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. W6iixi(r)uf (m-ldk : xhy?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 2 iuunkeabl-on w11u mi+;( 3q+-cqh9a 64 Hz, and the tip of each prong moves 1.8 mm toam9b +3hui-n o- qi;11kaw nc uq+(elu 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 oscillatecz:0v;o+wj 7jedvu *k whj *u6s with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which uu67 z ekwvj;coj *0+w* :jhdvthe 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 endd f z1dgvbuks9780u4d is attached to a ring that can slide wit4bd8d1 zg09u dsu fk7vhout friction on 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 on2kpxa4uz1nz-(ece9o e-way swing takes 1.000 e cen(z94ok1p2- auxz 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 c wi:0eder y4r ;a*b ri.i/aw,zan oscillate 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 vertical oscillations or the period of the horizontal swings, and by w.*rw e4iayw:err0zi, ;a idb/hat amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is strxeixrf0yr(-m roocp r,-27r .etched 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 theo ,7rprf(-r-i oxr2my0ec .x r two pulses first meet?    m

A block of mass M is suspended from a c2fc qw4l:tuc 55y j6hoeiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stac25ft 5cwqj6yho:l4u y on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The ste4 :9,4zs6fecn tmpg sd: fehr5el 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 th6deethgf4c::mr9fs 5sn4 z,p e 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 tva-xqv ;*lw*./p3ztws+ (o tc3q zje lhe 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 v *zzw3 (c;q t3teo-ls*qwj +ax.pvl/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