Give some examples of everyday vibrating objects. Which exhibit6buez:ya3+ pe SHM, at least approxima:z e+63a buypetely?

Is the acceleration of a simple harmox3/ygt0h ;j e,gl v7canic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately simpugsykt.g m+ * xc6k:lq8g9l ul8pw)/g le harmon8y8x w6g)q kl*/c up:u9kgllgg. s+mtic.

Real springs have mass. Will th03in3bt*ns ox e true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an ideax3no3*0stb n ilized massless spring? Explain.

How could you double the maximum speed of a simple harmonxx b8+bz ya5.i;pvw2 xic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical k( wvxou95s8 bspring scale, and then is released. Describe the scale reading as asuv5 ok(8wb9x function of time.

If a pendulum clock is accurate at oz6.y htyy* j:ix n99fsea level, will it gain or lose time when taken to high altitude? * 6onj:x9f9zyytih. yWhy?

A tire swing hanging from a brantwdg; t vph:;:ch reaches nearly to the ground (Fig. 11–48). How could you est g:wt; t:dp;vhimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the pa03hp ini:jo fc zn8*iddbr/ (:n at a certain freq3:d cpi*:o/i 0nijzhbr df(n8uency?

Give several everyday examples of resonan)i1*g* zf(+4atng zysa d1n .4dambd/chmma: ce.

Is a rattle in a car ever a resonance phenomenon? Explainf49 gmv g1x 9tm2vksh5.

Is the frequency of a simp0 kd0 q6r5wn7 )jismqlle periodic wave equal to the frequency of its source? Why or wrq0m0 )iks7w5 l6dj qnhy not?

Explain the difference between the speed of a transverse wave traveling down a qv/t,fc8 krk)2z)l go cord and the speed of a tiny gctv,q k)/z )8olk2rf piece of the cord.

Why do the strings used for th,dxn)q.wrrz1 qo.0v,g *n eo me lowest-frequency notes on a piano normally have wire wrap) 0en.1qz,mr dvng, ow .*rxoqped around them?

What kind of waves do you think will travel down a g 20yd7tfy0qp h)l4 s2l+cf hohorizontal metal rod if you strike 4cs q7 2l yfh+lhgtodfy20p0) its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but thp;r(b-lqfc39eksy6 r: 5o dyme bulk modulus B is nearly independent of temperature, how would you expect the speed of soob6lrk3c fym -9(s drp5ey:;q und waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as tqu 2)z*-91:fij( li*yw kp2b csxgnt phey travel away*)l(uzxks2:-ft2q i*g wpinb 1p9 cjy from the source.

Two linear waves have the same amplitude and speed, andgj0 rij ifs)h1 /bte;9 otherwise are identical, except one has half the wavel; eb 1hjrjfg09sti /i)ength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crossez ;/,tqluhh1 hs the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why. ,hhlh 1/ zq;ut

If a string is vibrating in x9yt*9tl z2 nsthree segments, are there any places you could touch it with a knife blade without dl9y ztx2ns9*tisturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflec ap nk9dlbw3ip550gg b)fv k+7g;lol.ted waves cancel at the nodes. Does this mean th. l aklv b7o5;b+f ggpkd9 wpi5g)n03lat energy was destroyed? Explain.

If we knew that energy was being transmitted frgry5byu r,r ,zg,9au4om one place to another, how might we determine whb9ayy,rz r4 5guru,g,ether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with ampvn.p a3o4sjv:litude 0.18 m, what is the total distance it travels in one period? v s .4apj3vn:o   m

  An elastic cord is 6n2qn3mria9 -wx6 n ha75 cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of thar -76n9n q2xmhi3nw ais elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg53)buzkc hs(0mnqc. 8)i ncss h3.zie driver gets into the driver’s seat. Ifqksnc 3z iusm(ni)hc0)s .h8z53c e.b the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What k8b34w ebl:wpis thew:lwek4b 8b 3p 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 b)ksmlj01-h0,kc ssva frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its freques1l c,j ms )-k0bksvh0ncy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at time:ovd 0h+,5ur lcox8sjd0p )sts t = +d jutov0 ,:d)8s0 sclxpro 5h0,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’wvm )yi;xx x;3s web. The web vibrates predominately with a frequency of 4.ymw;xx i; x3)v0 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 frd6s-8596knkge jkdaiequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value o9jkk dg8sak6e 6 -5dnif m?    kg

  A 0.60-kg mass at the end ofx(8nn11hils nd btp0h:e,e:n a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Detn11np::(0x slnhh ei,b n8et dermine
(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 equilicu j,kfyb8 6w;-qlx9h brium is the speed of a SHO half the maximum valfxy,68-hk;wlub9 j qc ue?$\approx$    A

A mass attached to the end of a spring is stretched a distancfir:xjv6l 0a;i( ;n nanih 05ee $x_0$ 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 vi2mr:i8, e5ql-qok a)xgda n-ertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new),qdi: 5-glk )e2 qima no8-axr equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness const:aw224s4t b cfl2 igbdant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium positcwf22sidlgab4 : 4t2bion, 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 si5nkll f4s1iye;dpal3rh0 63a3ph +80.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the g5ni 3hpid hl1sa;lpef kyl 4s33r0+6a un?    m/s

  A mass sitting on a horizontal, frictionless surface is a0 *kj5ejb chcmh*(9cg(l:wq t ttached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest witj m5cqgwbt9: kheh(cl* * 0(cjh 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 the7c/utk* )b k: (iak1rpp8 )ij1fb giiy equation x = 0.45cos6.4t where x is in meters andcu a7pb) krkp( / iy8)igk1ii*t:1bjf 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 equilibrium ib pilr 97)fcc,g/lqa:w2yx65 r2rja is the energy of a SHO half KE and half PE?g bir j /22pqr,)6ix7 : 5cy9raallwcf ±    A

  If one vibration has 7.0 times the fj8ac +1anug/d) p)fq energy of a second, but their frequencies and masses are the same, what is the rati1+ u/napg)f8 d)fq acjo of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertica cyoc/xaf* z5imm/,r (lly hanging light spring once every 0or cm5*/zi/yf(m,ax c.65 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 3lbj/)kf t y/atwo identical parallel vertical springs, each with spring stiffneabf)/j /3ltykss constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t w4ky,jg f1 w*ag0. lgmqhere x is in meterw0m ql1 fj kg4*y.,gags and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples b)h oh/, pfcelk9f74lmd3g x (of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the enve) cbi v5 rxk9p0a6wdli+7w5d of a horizontal spring (k = 124 N/m) is struck by a hammer, which +kx)vil6 pw 0wc rbive597da5 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 co .i- *-k* mkfvh 2qef omz0(ae;9dxjvgnstant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive vvm 0q-kv9gd -ef2ka*xm.oh ( z;*ifjeelocity 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 g*c 0di0vixi ./vrg s3springs, 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- *rca xrx1m0/pa.yn7 ekg block attached to a fixed horizontal spring whose spring stiffness conrn1/7cae *xpyx.ma0 rstant 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 withpm b+p5te3x7r mass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Ca3re7p mb p+5txlculate 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 exac9,guzlsqn- :wp*vn * mtly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is 45ns dqb/vgwl78ca8 g to make exactly one swing per second? (That is, on8ca/ 4gd758nbslq gw ve complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on+mc/o b9-sa n m5wo5ki Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Eart-snmbom+/o k9 cw5ai5 h?    s

  What is the period of a simple pendulum 80 gl/bn675- pus4f a h 6n-preeccm 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 has a massazx-zv 68xz (l3mu)fb/i/1w etqejvq s *xs46 of 365 grams, and it is released a q6tfxvuzm8 q)j4/ex z3lesi(s1x6* v z b-w/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 lengv uf0yp7ne2, jth of 0.9930 m. If the clock loses half a minute per day, how should yoj0yeu ,vf pn72u adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxim,yjo2 mwiht- 1qq8q p;jps/ bd5wrj-3um 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 jad83fhn0 uf: it is released from rest starting at an angle of 158h0anfu jf3d: $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat p9y bp scyf9xu );olne9n/i97every 3.0 s. He measures the distance between two crests to be 6.5 m. How fx /fpo;c9 9l9b7u sy ip9eyn)nast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz w ;d.l f9 ee:yvtp 3grgr3f+l7and travels with a speed of 343 m/s How far apart are the wave crest+f g.9y3e r;edvgwp:r t3l l7fs (compressions)?    m

  (a) AM radio signals have frequencies between 5+vdn6mn +c ak)50 kHz and 1600 kHz (kilohertz) and trd ca+nv+ 6)knmavel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in:o5a xsi b3n4d)dt/ oy
(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 asuiz,o cop4r6 . the other. In which rod will the puor zci6o .4,speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between twof )q8,xtncxfv xjn 888 supports 28 m apart. If the tension in j8 nt8qv)nfx, fcx x88the cord is 150 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 m 2uhft;pqsi3;v+ g9;utc1 1yyt5 fdyp and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulvufi ;gp hd1;p9yc+uyft;t23 yq t 15sse 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 of0 4z*+hzl ofig his ship 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 the ocean at this pointolfzz hi4g* 0+?    m

  P and S waves from an earthquake travel at different srblzo3eg -a)1 6t/lmbpn)m 6b3sl . zwpeeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took place). 6) n s1.m-3zgbe /bll)m baol6r3ztwp
(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 7 a +zg-*qcokgcan be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthqua7c*ggkaq -z+ okes, which actually 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 int5c x fh:d7d8erensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and fedx rc :dh85720 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to tc 71l;sd urm/ri7wm, be wmr l7 s7 /c,rdu;mit1$ 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 j;u ,x vkwa5l 6i w91j5oba/chfrequency travel through the same portion of the Earth, but one is cara , oi5cj b/1la;uwkhx6 w95vjrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretcws2ii tw:,8o9 o3qlx2mxk bl2dh+;qe hed string have the same frequency, but one transports three times the power of the othtd:xlql3eo, 9 obi2;w +qisxm28 hk2wer. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed tr1id,m mp3w u6o move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, asr,m uwi6p1 m3d a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–zbnl bbf3+ 1c (g c)/0l8gniqi52 are moving toward each other. (a) Sketch the shape of the string at the moment they n 3 lbzc/lg q+bb1gii0(f)8ncdirectly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibr1shh 8 cy*sfq4sjfy,2ates at 440 Hz as its fundamental frequency, what are the ch84,* 12hfsssj f qyyfrequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frem/p ql7o49c ywquency will it vibrate if it is fingered one-third of the way dowm/o9qp7w4yc l n from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at l;vxmdv.zpmtf)k1-qqwh 3:4h an3p7jz8 m0 hdeast three other fr38w4j zpa ) qvk3-.0d1; n:dt7mfmhzxhmqhvpequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s8 i .qrvqi-wv8 If the frequency of standing waves is 475 Hz, how far apart are two adjacenqri 8v-w qv8.it nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, wha1c n/3lhryo)zj-i)n ;j.xsbeta*j ln*(o) jrt is the frequency of the fu1j.nc3n;hbj xt enz l(o -r lsaj)/)ir)*jy*ondamental?    Hz

  A guitar string is 90 cm long and has a mass t -)lry,tlxbab .t6rg/8;r2whc m: 8nsks4gq of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two o: 4s x8 hrt,t8s ba2lg-r)rmkby. n;gwqt/l6cvertones?    Hz

  A particular guitar string is supposed to vibrk-px .bq4t j*yl3 qq0bate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So th.b0q*jxpq -l btqy 43ke three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrateusna)a u r7 -qb-u6:qi at 200 Hz, but it is measured to vibrate at 205 Hz. By what perceu6:rnqau -s ) ua-7iqbnt should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attasd7+,cfhis 8u/ r4as a8xme. 4ba7cktched to a small-amplitude mechanical 60-Hz vibrato d4+ hc87xca8 4.imrs u,bas te/kfas7r. The 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 be adjusjvrvl8chb)4-jhtyci +)6e 2xted by moving the pulley. If the hanging mass m is fthv8 ) ij)-xy6rhcel bv4+j2cixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a t-mq3 y4ym7wdi hgp.v)sq8b/ g ub 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 standing wave in a 65-ciq 8 yp 3g/myhb-w47d)vgsqm.m-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 st8f46 se nogbz8rikes a boundary within the Earth between two kinds of material. If it approaches the bounon ez6sfg84 8bdary 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 changes7g k-5q)xonyebrvs i 65gec-qv+2rj2 from 2.8 m/ -x5sg -qbkj6)2ny2v7coiv e +grqr5es to 2.1 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, dense aiacg tsite 46dg)8uwz+ln67/nr. If the sound wave hits the cold air interface at an a6gts eidzu7 8) cw4l+/nnatg6ngle 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 between9 r*h4 :wty0i82o:zjkrvuvo lks:(u a two types of rock at a: a9vizho rj*l:4 :8ut vu(kryo20wsk 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 to the user’s ma;t7q - 9on c ;*y1wxixgnih*wzc)wn5onual, the dish has to be pointed in the directio 5q;nic-onwgitxzc*)xy 9h w*won1 ;7 n 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 kme;muwn ga 9 l s(td( l4v/6-k0,bknakl/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? ( d/ 6l0;amb (esktg9kn4a ,vun-w llk(In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffnesaqzgp eigv t84h;c b 64:z3md.jsyz 1:s constant of 550 kN/m Find the maximum compression of the bump .:4t zp43azhgizeqs;8jgcmvy 16db:er if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m bel;r7ye xly* 6xcow, which stretches the net 1.1 m. Assume that rxelx ;y6*c7ythe net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging0c 3qiuuou;ht vz9 0 vj3vkt,+,bbo;r spring. The mass then falls 33 cm before it stops and begins to ris i;0tku 0u+; vbojbcvuzho9 3r,3,vtqe. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a h0 0x9z6x ll0yan )ripguge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the sprixa)0 0zigpx6lr90lny ng?    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 +i rs vui8ye c1r3.da0cm) at just the right pace of about 1 step per second, the coffee sloshes moa+01irye udi. r3vcs8 re 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 x;gnr3ob-kk5 p s ms7l2+ eo9z10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. rxl5s;-kzn g27o p3ksmeb9+oWhat will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x :eyvg4qxe8*iuom+w)b0 z- s e is in meters and t in second0+zvmieo*ewyqe g-4 :8 su)b xs. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency i/9qdnav8 z ;0ts7f ontwf3;zgf it accelerates at 0.50g (a) upward9 38zd; fn;zov g 7fs0n/tatqw,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stana ku+(ozi+. hdds on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whiahoi(kdu + +z.le.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 85np i*go.f3w x 53sa4i/rgfr3bkqgt Hz (A br3x rfqi8f.w*k53o3ggtign/4 a p5 s).
(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 travell2f-j5gg4 vke;qrgzut7r/) xr:i )uying down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (exg;vyg7f gtzir) u 5urjk)r4l2 :q/ -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 26 z87gg:goqsb ;4 Hz, and the tip of each prong moves 1.8 mm to eithe gogzqb ;s:g78r 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 cyd82g1.k onaeiu3p)vbu q3bt6 cles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed eq i.3b ua k)1gu683pob nd2vtthere (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to asep 0ez: h*io1 ring that can slide without friction on a vertical pol hp*oi1se z:e0e (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 — eac 0b1hmfu+w e 4svg ;.qk)si,kkh one-way swing takes 1.000 ssvhg+)s0i 1 .;e, kqb4u fmwkk.
(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 6ys*--ob gl(37tu)fowjhyae can oscillate in the vertical direction or can swing as a(l-y) uw st7oaybf *o-g6h 3je 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 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 tension of 255f o;pp:-8w4k9 mrqxi z N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. W-f 8m:rw pkx4io9z;qp here will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffness :5whxpzsjus ql .+*4bzhh 36oconstant 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 theps j+3so46zq h x5wzhh.l:*bu block? (Assume $m \ll M$)

  A crane has hoisted a 3j*ybkr8kmf )1200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze startsyjkmfb)r3*8 k the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which a//r: o+gm pdp -qa+ oibe7mq+tlso gives the dimensions of the block). You push it sidewayoep-ombpr q :mitq7/+/ag++ds 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 is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz