Give some examples of everyday vibrating objects. Which exhibit SHM, t 2v*fx* b)gipat least approx2xg pb t*fi*v)imately?

Is the acceleration of a simple harmonic oscillator ever zero? If so,dibt a+: qo/4p*eglt) where?

Explain why the motion of a piston in an automobile engine is approximately s)7fj uh9h) gj--plvly8e+o r)xw1yryimple harmof-h98he)) +yrwy g7)- ojypvujrxl 1l nic.

Real springs have mass. Will t54.ilt 3lwdxmq0 nv3gt(ioj a zb)(i;he true period and frequency be larger or smaller than given by the o5.(xtm4djbn 0 t( ql;wv3ai3 glz)iiequations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simpf kewaxd/ ,pn v26hm1.le harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scalev6hc -*n. wfrx, and then is released. Describe the scale r-hx fw6vn .c*reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain ork1dn qn/3d8s 9hy v5 ny-eo2rw lose time when taken 5y2wn8 hd/o3 k-9veqrndsn1y to high altitude? Why?

A tire swing hanging from a branch reaches neifwrim r z:t* e*f.a(1arly to the ground (Fig. 11–48). How could you estimate the height. zarfewmr* f*iit(1: of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan + w(h)iskn22lo7glou only if you shake the pan at a certain frequenciu 7(+wg)lo h2ln kos2y?

Give several everyday exgtcquxv/sa;jx u5 q/6:8c x2 iamples of resonance.

Is a rattle in a car ever a resonance phenomenon? Expla cmg pir-z7v e3l;8zc*ug 5x *aisk6s* ji9m8ein.

Is the frequency of a simple periodic wave equal to the y3 r1hj 7bbo9wl+wvy)frequency of its source? Why or ww+bly vhwo7jryb3)9 1hy not?

Explain the difference between the speed ofl2esd -t7q0ztka u.o-cz:o3 b a transverse wave traveling down a cord andt72tbuz.k a3oo q-:ds0-lc ez the speed of a tiny piece of the cord.

Why do the strings used for the lowest- +lj(l av+:saafrequency notes on a piano normally have wira: ll(s+aj a+ve wrapped around them?

What kind of waves do you think will travtn.b u0hy:.r2 -b7 cvxwl .vwuel down a horizontal metal rod if you strike its end (a) vertically from above.w7bhn vxrytbvc u-0.:2wu. l and (b) horizontally parallel to its length?

Since the density of air decreases with an increase ihzaq57 p45 jmbn temperature, but the bulk modulus B zmahqpj55 4 7bis nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitud+kb6qk*1pvci e as they travel away fro*k+ipcqv 61kbm the source.

Two linear waves have the same amplitude and speed, and otherwise arjj5gxw /bt) 6fe identical, except one has half the wavelength of the other. Which transmits more energy? Bxb 6)jj/ gf5twy what factor?

When a sinusoidal wave crosses the boundary between two secc-r,zajd,c).1,c u:iywi g p mtions of cord as in Fig. 11–33, the r,-1da wiyz : ugi),jpm c,c.cfrequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, a. p,*uue;1igejct s7g u9m5g mre there any places you could touch it with a knife blade without disturbing the ;9g* g7iuj pgcs51e,m .tumue motion?

When a standing wave exists on a string, the vibra -pb(ig1 j2 xkqj6p2.e xyc; qn,a;mx2wcoh:utions of incident and reflected waves cancel at the nodes. Does tebkh;x-; y1pj 2qc,px6 :wcoqxugia (2 n.j2mhis mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, howt tc(: y(sqcm4 might we determine whether the energy was being carried by particles (ma4(:s tyccmt q(terial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance drfq(rhkk.,veoq 1go.q/ )z 4 it travels in (o,r .rg vq1q qd4khf ze.)/okone period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but7p l; .u3aj9oqx2c ons3w4jo h is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant.oj wscu hnoqlpo7j49;3x a32 k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver ,kmt/as aztxk 15/+c bgets into the driver//kk+bzt cst5aax,m 1 ’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale strenlong- l3 b2g:tches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffne:-bgl gnno 32lss 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 frequenc xhr6sc,bz /.uy 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 hc6x,/ur.zbs from it?    Hz

Construct a Table indicating the position x of the masp1 t9wp0yz sn*s in Fig. 11–2 at times t = 09pt1nzsp*y 0w,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 cauf5-zm 1 kqjv)oght in a spider’s web. The web vibrates predominatf)5j vo-1zmkq ely with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. Whenw t 89i gh;ey4)dv:uyd an additional 680-g ma9wtgh vdyy):d8e4u;i ss 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 of a spring vibrates 3.0 times per second icb-ho ko,o,5 rlh95iwith an amplitude of 0.13 moholhr55b kco i9 ,-i,. 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 :2ob)0f:i 3.3yd+pd ihgctm 7xztzgh half the maximum value?2hd:)gy zhoi t73 df3ti z .m0pxc:+bg$\approx$    A

A mass attached to the end of a spring isrdvfjq4,b px7z9x)q*u.i y( b 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 vertlp/o. pf ;-wabical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how lonp/ albo ;-f.wpg does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness k 4p9y3)2j ;pnswyq bgiol+v4constant k = 280 N/m and is elypwoj) +i2 y43n;vsgk q4p9 bxecuting simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 Nere+t7 g7b0q y to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. r qbg+t7ee07y With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfaco ;zwwe+bj5 m/e is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of b/ wwe;m5jo+zwork 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 accorzurk6 ws 1cfm6:f(gx4ding to the equation x = 0.45cos6.4t where x is in meters and t is in seconds.: cz16 fufmxg(kws46r 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 equilibrium is the energy of a SHO haa4 -zo;d llub),jtkk3 s0 q-2k3ofacclf KE and half PE? k)t3; 4olaldc o-,fk ckj20bz a-3usq ±    A

  If one vibration has 7.0 times the ener /q/kt1y3whbd5 ida(pgy of a second, but their frequencies and masses are the same, what kt(d/hq / y35awdpib1is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hj l cu b 0l9lu)2adf-;daj5+loanging light spring once every 0.6u+2lj-j0)a5lc df;d b loaul95 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 iokspa ;, n*:4cj fyvx6dentical parallel vertical springs, each with sprif nyx:asjk6o*4,p;vcng stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to ttzi-3eee f wo(q( 2 fj2bvbc)7he equation x = 0.38sin6.5t where x is in meters and t is inebb)3 fj- iw( ev(zc2qf2 7teo 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, labes+d-gdf 8c)b-kny4bnled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on4 yj;-zfl, q3,lzdaxhz 5gz/ h the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives thyhll4zz3- zjx/za ;,g ,dfhq 5e mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with an amcj8p) 5b;0 mvldyw /f*p1te 7tqg fez:plitude of 28.0 cm when 0.260 kg hangs from it. The mass passe: 71g jclvp b efdm/zfe5ty)q p*8t0;ws 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 connected4)bvdsgi l ,n8 to two springs, 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 a dh60p4l 1tyvnttached to a fixed horizontal spring whose spring stiffness const dp6t0nhv41lyant 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 fro+l/z kz w32zdwm a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the3wd +z2l/z zwk 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 vibrat52tk- fp48m dnhm+ oveions in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly y.-vv obi nklo5r4q4 /one swing per second4/r.lob n vv-4qi k5oy? (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its vmpt4 i ndb+7;period on Mars, where the acceleration of gb 7+;mpi tvd4nravity is about 0.37 that on Earth?    s

  What is the period of a simple , q- )i6dmowt ytyks:6 sb: :k94wopyypendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.76hwia9xgd83 nm+,n 3v i0 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12vghia,n9w n+x 8 idm33.0 $^{\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.yjz(-y . qh-chx0oqb:6v3h +f fb0htc If the clock loses half a minute c- c+yyb6.3 v hxf-jhfq:(oqb hh00tz per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula forli hjx6oq.*a7 f i*b)n the maximum 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 2.5 Hz. At it isj4 i u4ipj;/tr released from rest starting at an angle ojju 44pi;it/rf 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 pasym3on1u:c7mh s the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves trau71yo nmh3 mc:veling?    m/s

  A sound wave in air has a frequency of 26ahv *rou8;7t v2 Hz and travels with a speed of 343 m/u;r7athvv o 8*s How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequef i z.luz-c2br:2ibij b7/ (iincies between 550 kHz and 1600 kHz (kilohertz) and trave i(ibiziz.:ui/jbfcr- b72l2l 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 o7x,eg:nv ef :of longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have thjw 9i)is9i *zem c8oc9e same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves bec j z iwi9i)om989*ces greater, and by what factor?   

  A cord of mass 0.65 kg is a: m7jouzzjfdr6(y sg68ag(i, as(p. stretched between two supports 28 m apart. If the tension in the cord is 150gpa, 8sa6.:j r (i(6za d(szg7ojmfuy N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620.v qs pivpqrz:ls,7)jea5jahh( 5uk f5/x z // m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse alo psja,fqe5zs (i/. 7/v :kxv)r5hzalj5h/uqpng 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 theosb6mzw gk) ll, (drm-,cf7/b side of his ship just below the surface of the sea. He hears the echo -gm/, 6ol rzsw(l ,c dfm7b)kbof the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthqu+.;0-iaa4uwe jaeju p ake travel at different speeds, and this difference helps in locating the earthquake “ iaw.uu4pa-eaj;0 ej+epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoi6d5)eem neza8 lb6 +1(e cviysdal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually6al8(eynd)v ezs i1ec+5 eb6m include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an eartw:s o3o1n0dcjed h5s8p *ddc*hquake P wave pasonj05 *cd:13sdhse8*d pwcdo sing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Eemsn2vv b *m-n j-rvn/9a 03pa pv4amwh7;x5narth is measured to be pwen0n4m7amv /9ab v -2a5;sxnphmr3v-j v* n$ 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 travebtho .wrq: m9(l through the same portion of the Earth, but one isb.om t:q(r9w h carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the samedn6s i,*lc7v0vt 5syo frequency, but one transpo,nc sivd5yvo *706l tsrts three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pocq5u,go7su t)wx 0v* dnd 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 gq7 )vu5 w*xd,stuo0c 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 bqej 4-6bg*ri rctg 6;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 6r c g*et bqg64-bjr;ithe 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 fundamu*x:tu 0baov--mqd8 qental frequency, what are the frequencies of the first four*qt0 -u-m vudo:8 qabx harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz whene.ti7- u 2utsm;o 4itfb9bqg-nhw94a unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-tq9s 4e-b9f-nout 7t;bmigi2t4h uw a.hirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frepldk25 2gcp 3tquency of 280 Hz. Name at least three other frequencies at which it will restc23pdkpl52 gonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a str vxfz(yv: oj9)+q(hhking is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent nodesq9x (jvz )(yv +ofk:hh?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, gqlgw ge 8yham7psj/ r1y,144what is the frequenp h4 y/yqgj8w ,gme 7l1r14gascy of the fundamental?    Hz

  A guitar string is 90 cm long abz7 ba 4nd52wtf5g h/ind has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and t5 5ntahb24idwb zfg7 /he 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 vibratrz ew*euokls)-14l jd ..n 3hte 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 fhtu we)*jr.-lz3 1dke. sl4norequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is meat qu(tt31/g iixrl bpml6ir-,ql x;8:sured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct ,lt6rqt ip: ig uib1(-3lm;lr8t/ x xqthe frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude3kd ehh:k2:sli avbn/21hm4 e mechanical 60-Hz vibrator. The string’s mass per unk2l :2:n1vih/4hs k e bhdaem3it 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 bhum. l/imbwm8qk)6,v/fe,i j e adjusted by moving the pulley. If thj mw, .6iq ,vmuib8klmf e//)he hanging mass 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 andaka.u6 t ua1krz48.f j forth in a tub at just the right frequency, the water alternately rises and falls at each end,u.6fatka48 zja1r.ku remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k. g;jl9 fi+(+eyi dqq bik*odng8i-z 270 km/s strikes a boundary within the Earth between two kinds o zi +e;+n*78 iil(fd2g-kdgiq9 qbojy f 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 frod-x.k mg6u zuk dd:sm3 0de9/mm 2.8 m/s to 2.1 m/s If the incident wave credxk 9g:em-d6dd ku .3s zm/mu0sts 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 itz hn oj9vm3f5vp,: f+k hits a layer of cold, dense air. If the sound wave hits the v kj pz9vh:m5no ,3f+fcold 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 b,a bhx6z3+rd+zg uy5 fetween two types of rock at a hb u3 r+fx5+6ayzg,d z38 $^{\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 i1bfutjup1x2 7 n diameter. According to the user’s manual, the dish has to be poi7xt f2jub1pu1nted in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across ubu- fdz9 j.a/ +djlftx61,ekthe 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 ofdz,kf6+9e t j ba1uj/x .dufl- them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m *(ur qtn)o 2iuFind 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). [Hintru*2 u)i(tnoq : Use conservation of energy.]    m

  A 65-kg person jumps v7tlirn x4grbr,+:6*8 4s +kae bcddcfrom a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behavesd*c8 4n+4t krgr vc,bl +ds7:x6 reabi 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 freelyrd80 ;a 2ddklu/i8hz nb6-pcv m6 v8bt hanging spring. The mass then falls 33 cm cdr ih-n umd;l t6/ 28a8db6zp8vvk0bbefore it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22r-ebbl0 i 0x*jfrg* q0 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spr0fg00 lb bi-x*rerj *qing 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)nue-l opt7s-) at just the right pace of about 1 step per second, the co u -7snt-p)eloffee 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 the center of a 33-rpm phonograph r tj iarjvkpe*,:9((u record have a wavelength of(p *eiravtkj9,(r j:u 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to thelyna3:asp9 uox(so l)j1 h- xcuw.: k; equation x=0.650cos7.40t where x is in mete1:hoa: ;. sl)39xjyuxnowplcu(a k-srs 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 fr1q*c9+g/a ge(gpipkl57 tgea equency f. What is its frequency if it accelerates at 0.50g (a) upwagg5 t +gpp(1/kiaqelca9 *eg7rd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75wmpb rp2t/ c02g7 tq+a-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrag2tpp/ wr7act2+m bq0tes 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 instpkf6,6 ks n8slx0z fb j.llzq6f4b0 -yrument are tuned to play at 392 Hz (G) and 440 Hz (A-xkk.sl06 f nj4qsz yb b06,6fpl flz8).
(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-pam4 p(lt ob9 e9dq64pakrt cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the r9o 4pl 9m4td6eapb( kqatio 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 3kglk9ilkrijw * -w;yg/uf 6*4u .fnnmoves 1.8/ gu k*g-w;kiruyilf69 3k *lwj.nf n4 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cycles pep js8: pvnzka* 6c/ez4r second. What is the maximum amplitude with which the end of the board can vib6zckav 4esjp*:zp/8 nrate 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 attac1he/unrnfa qmt7ew 3o)6 tc:8 hed to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of sae wmn1u7q 8)3ecohtrn /ft6 :uch a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-wai)g wy8lbjy 80y swing takes 1.000 s. i08)yjl8gb yw
(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 oscillaurlbg 9t/u*5sy ;gtz6+nt :px 24 zlpoln63cq te in the vertical direction or can swing as a pendulum of small amplitude q5bln c2 rt6z lgu6px+u:sn;*t pog l43zy9/t, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tensionne ic vb *txb . rkqcgm/df289jm0l5.8 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 two pulsbv.c8me x jb* l8k f0r ctn/qd9i5m2.ges first meet?    m

A block of mass M is suspended from a ceiling by a spring witbkq ve9lpidy 34alni:.h7 ;p4h spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of4y 47d9e ailqbpvn3.h lik;:p oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the scm t6tjl mop0;7a vy)j462vtjunkyard. 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: Reyj 0p)cltt4m6tv;2oa v7 s6mjfer to Table 9–1.]    s

  A block of jello rest)hafs*zox pq/ye8hq(dtwmp 1 3l0l (-s on a plate as shown in Fig. 11–58 (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 (Section 9–5) of jello i(8 yfml-wxq/qt z*0 lp)h3pd(aesoh1 s 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz