Give some examples of everyday vibrating objects. Which exhibit SHM9 x- qml(w8 nf2d0nqcqqm.*uz 1sg7nx, at least approxima7-f qn9gc* n. s(x2q 8n0u1dxqlmqwmztely?

Is the acceleration of a simple harmonic jh/:edgj7g-w c/l h t/oscillator ever zero? If so, where?

Explain why the motion-0sbxy -pf5xg of a piston in an automobile engine is approximately simple harmoni0 s-xy5gxp -bfc.

Real springs have mass. Will the true pe7tw+rjp /p4yfriod and frequency be larger or smaller than given by the equations for a mass oscillating +jr/fppw 7t y4on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple ha 2xx/l:*bwdxi rmonic oscillator (SHO)?

A 5.0-kg trout is attached todkl9xfi4i zg1-uw 5 yc;v:i y+ the hook of a vertical spring scale, and then is released. Describe the scalec;4f+zu kyi1gxi vi w: d9yl-5 reading as a function of time.

If a pendulum clock is accuryx)i51 ,6,lhh0 sa jfb ym9pisate at sea level, will it gain or lose time when taken s0yaxlb iym)9s5 ,1 6jpfhih,to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 118+oyvq os0, kt–48). How could you estimate the heightv8+ ysot0k o,q of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the pan 5wnvr d/y pld.v(y-x/at a certain frequenxrv(.ld d/yp5-ywv/ncy?

Give several everyday examcj.uos l+ej+0 a6rb-mples of resonance.

Is a rattle in a car everrmcr7+ud **nmdwb3(rrq )ub+;f7/ xhsj i8bs a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sourc+e z b9xzm br5b5 fcy1kub(w/:e? Why or why n 9 m/ br5bf:bw1zye+(u xbk5zcot?

Explain the difference between the speed of a transverse wo8/o ;ncj2xw zave traveling down a corx/ j2cw n8o;ozd and the speed of a tiny piece of the cord.

Why do the strings used for(t h 6b8atjvoem :ad;. the lowest-frequency notes on a piano normally have wire wrapa8ttj(o 6d vemb;:ah.ped around them?

What kind of waves do you think will traiom6u :mkc1 la*h j2v4vel down a horizontal metal rod if you strike its end (a) vertically from above and (4ajommv6h*1 l2:cu kib) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, buqk 2eehlq t)))u3e 5blt the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with )k hqqe53 2)ue tl)elbtemperature?

Give two reasons why circular water waves decrease in amplitude as they trf*4lyexa*bb 1avel away from the s ley1 ba4*xbf*ource.

Two linear waves have the same amplitude:.,thki uf z.g and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits moz,. g:htkufi .re energy? By what factor?

When a sinusoidal wave crossesmxo+ls lv.y +q(29hfny- o:uhc 7: ces the boundary between two sections of cord as in Fig. 11–33, the freq +o7c:lf.-lm h9yq +:evs(uxosyc2n huency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there atud bp- 89z1u6xyn9uo ny places you could touch it with a knife blade without distxyuztuo6n9-u 9pb d81urbing the motion?

When a standing wave exists on a stmmg y xlf97,(lt9h*eqring, the vibrations of incident and reflected waves cancel at the nodes. Does thism ye,9hlxm7f9t(q lg* mean that energy was destroyed? Explain.

If we knew that energy was being ta oif 1)a*,i8odlms7 x 8t(mpuransmitted from one place to another, how might we determine whether the energy was being carried by partm )afil,o(8*8dut17o a mpxs iicles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distj/b bf(6 a(am 7vs2bxwance it travels in one pe(b2/vaa6 fwb7(jbs xmriod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but int:xc9 k* 7 7ewm- imh3.jooxkil.b*fs 85 cm long when a weight of 180 N hangs from it. What is the “sprin9mc*oe3:kjtk.*fw hi7xbm7- . xloing” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into thb:vt ff+l te*0e driver’s seafe+*vl t:ftb0t. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretche;j-n1up ,n.drk m x5aas 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness con aa;xj-d mnkr 5p.,un1stant $\approx$    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 of 3.0ktpy7 3.f2q fu Hz when a mass of 0.60 kg is hung from2qy uft7p. k3f it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 wap:bi 0nsj,uv,g5 7r 5fs+ ovat times t = 0, awb50+,p57 ufjgosr,ivv n :st = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 c/cg/wbu-hgy 9aught in a spider’s web. The web vibrates predomingu/ -gwb/h 9cyately 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.ss, fa ,p+5d 5,at.idoxq( egi88 Hz. When an additional 680-g mass is added to m, the frequency (oq5, +d a.edpigs5saxi,,ft 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 )u*end5vxbcq zc;3 igr.3 9wksecond with an amplitude of 0.13 m. De9 v .w c 3kb;)e3uigxdcrnzq*5termine
(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 aj wg( ura;s*nv:r 2 wy:9taq9equilibrium is the speed of a SHO half the maximum valu(y: jqw9a:;v* r2 9aga unrwtse?$\approx$    A

A mass attached to the end of a sprjlhs 5 n7 *upscql:il*oe46* urze+u 7ing 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:t,1z l1hx91li qh;imy e/jbh 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) equilibrium position ag ljeb19ih/m;1yih:qt1z lx,h ain?    s

  An object with mass 3.0 kg is attached to a spring with spri2qns3 : dw0a+ lamiv3gng stiffness constant k = 280 N/m and is executing simple harmonic mot3 a0w3i vdsl+ 2agnmq:ion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.20(i4 c z7xou*gx )l+c30v hmhii0 m to “load” a 0.180-kg ball. With what speed will the ball leave t 3 u xx )0vg7mz*h4olcichii+(he gun?    m/s

  A mass sitting on a horizon59 6 -rzn9d-h wmjhbfgtal, frictionless surface is attached 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 with the spring compressed, the mass experiences a maximum accelerr9-dj65gwmf b-hznh9ation 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 = 0ss ,cq*k.x52t jb njb0.45cos6.4t where x is in meters and qx*b cn 0jjb.k2s,5t st 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 is the e34mb 5zkfxcs s1l1 /hi -thx.c;;nnk bnergy of a SHO half KE and half PE? ±tszxs fhk4-ncb 1l c5nb3/x.m; hik; 1    A

  If one vibration has 7.0 times the energy of a second, but their frequenciesu zte5s*gcxu*u*h8 :k and masses are the same, what is the ratio of thh*5 gu8z t:*euks*ucxeir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangi0xkw f6vou0u4bsv 8e1ng light spring once every 0.65 s. 08ueo6104xkv sbv w fu
(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 vertidulne 7 (cy:(hcal springs, each with c(e:h(u7ydn lspring stiffness 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 whermo3* vry96u gpe x is in meterp6r* ygu9 ov3ms and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For eacw bkm4xx (2z8z,dep/fh, 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 = 12j 7v-dk.yv /+9l0w 5pvin(xiy e(afyt4 N/m) is struck by a hammer, which gives the mass an invx +a/yv(djy.i0vwfl7t-pny5 ek 9i ( itial 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 constandx dhf6ajy g.2f:ls9 1t 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. .fda: h1gf 9jsd2 lx6yThe mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring sr-:a:t conucwm2lw:.w0btcau ,z; 9t tiffness 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 6; ptnq9ssw0)gs n.u3xhk n3p21gjjc attached to a fixed horizontal spring whose 36q1s3) hxs ucn wg0pstk np9jn;j. 2gspring 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 massfj+us j 4yjc4( 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. Calcula jf 4cjj(y4us+te the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. Whathyl+ 0ab-u xy( is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is -2/d/lsc( ff aepj-yg to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 -ygf2lec /-s d(a fj/ps.)    m

  A pendulum has a period of 0.80 s on Earth. What is g oh*dmzz+f u a4nq: yb07 7olrs9,h5jits period on Mars, where the acceleration of gravity is about 0.37 that on Eandjah 75om*hgl :z,z7y 9+ q4ubfor s0rth?    s

  What is the period of a simple pendulum 80 5:r 2hn47mnh e8 sbvsucm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 pxv73(a +m( gfkdurlk3d2 f+cm, the pendulum bob has a mass of 365 grams(d vf+amxfu+r ldk3g2( cp3k7, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s penduluyz-bp 6a:um7mm has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of t b-:au6pmzy7m he pendulum? shortened by    mm.

Derive a formula for thee4jqu:)+aps c 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 9x7 ymo p)n*bm it is released from rest starting at an ax9nmp)7yo*m bngle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow ofmvg5k57 bzg z,7fpx7f his anchored boat every 3.0 s. He measures the dis b 7xf7gv,zpz fgk7m55tance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with aoxan ,u0aqg:kkqj h4l(at- q+9/u n ;r speed of 343 m/s How far apart are the wave jgtoq u-:4 0n;qq k hr nk,u/+xa(aal9crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and ujb9fh47jbiy /hl24lrk 9-t v 1600 kHz (kilohertz) and travel with ayb i4bj9l 7 t4jhuvfkl-2/r9h 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 ofr/by4ikfd u, . longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as denkw2w,+ihvd he-qq4 w3 rhii-:se as the other. In whicwr --i+iw2ihekh 4d,qv3: qhwh rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between twcp;vhoy6 (c0ah2 5rq6/h;0wzn a zgqbo supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the oz hya25/hqn;q6p;z 6 bha0gw0c(c v orther?    s

  A ski gondola is connected to the top of a hill by a steel cable ocr1 3b) vuyz63(4vxqui:m vrtf length 620 m and diameter 1.5 cm. As the gondola comes to the end of itvir)yr3tvq: vx( zb6 3m1u c4us run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his sapll+ (5be i0bhip just below the surface of the sea. He hears tb5e0(b+pl li ahe echo of 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 earthquake travel atfw+w k8wb8tx- different speeds, and this difference helps in8w+ w-kfb 8txw locating the earthquake “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 sinusoidal transva.k/j v8a/loui7da w+ lrkc: ;erse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is neeuali7do/w :kc lajv+; rak8 /.ded 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 ea,2:ke : e(qektm*lhofrthquake P wave passing through the Earth and detected at two points 10 h2 etl*e:ef,qo (kkm:km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave pascr: h9 *ybxbw8sing through the Earth is measured to be 8b*hy:cbw r9 x$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the safh- d8 plnwjg1iz/+ 7cme portion of the Earth, but one is carryingi7+wp -1/nd8czl ghf j twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the samecoup:l9 12g ,skam /b16tccnitoa6 9j frequency, but one transports three tk9pt 1 6ung,/ctc9aobl m ji 21cs6:aoimes the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and do15rkq6u: gwml5yh;qpz9wbga aal*8 7wn a total vertical distance of 6.0 cm, from the lowest to the highest point,*7ug;wgaymk bqz19p ral ha6558w: l q as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving tow3x8 uhry gve,w-lvg/-ard each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this mvlg3r/ ,- 8-wexhyv guoment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, w4njorhw kw+, 12we6 hehat are the frequencies of the first four harmone2+nr jh, e1kh w4oww6ics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unf7cs6pcym0 t-asct;1xingered. At what frequency will it vibrate if it is s a6m0c1-ytctxs7c; pfingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency oozdulk lze b df)t*79u21b/k8 f 280 Hz. Name at least three other frequenciesbe d1duz2ktkob)/7 l8f*l uz9 at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of staq- gw//9jigtoz zcb+/nding waves is 475 Hz, how far apart are t bgzjico/+9-g//w tzqwo adjacent nodes?   m

  If two successive overtones of a vibratb+ vpvw 6 ii(agq)g8e1ing string are 280 Hz and 350 Hz, what is the frequencv6pwq)( 18eiba +igvgy of the fundamental?    Hz

  A guitar string is 90 cm long +;8k m2bs 3t2pqql)r0tlcl dyand has a mass 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 overtones?3tb220) trdk+;qqllscm y l8p    Hz

  A particular guitar string is supposed to ,gr.d:3bhdcu5x0k jd (dl/8gbke6mz 9y of/b vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By w/d8 cbd (ho6dedrb.j 5 ,lybfuzxk/ gg0 m:3k9hat percent 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 supposyaa7se3v0+ jpk;/ xe c2yppy7ed to vibrate at 200 Hz, but it is measured to yppjy;+ak2v/0sa7xyc p73 ee vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal stringnt 1e w7n5qxtxzh2*/h is attached to a small-amplitude mechanical 60-Hz vibrator. Tt2t5*xe whqz1n nx/7 hhe 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 mayo ,8 ;vnf qa/wk;ydq4r be adjusted by moving the pulley. If the hanging mass m is fixed atr/4fodw nqay; 8q;v,k 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 watexsk7s a0;cen: ub5l(srgf(/h r back and forth in a tub at just the right frequency, the water alternately rlb x sug /0kr;7 secfn(s:h(5aises and falls at each end, 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.0 km/s strikes a boundaryhyq0 cxu xx y7vr;7o(qb.g1( u within the Earth between two 7xr(q gchxb oy(;qx1u7vyu.0 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 approachb 43hezo7y n 6qs,ov;g an underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incvsogq74nhezo,;6 b3 yident 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 it1+ hb2:m(,p+sovmed8 cftvrd hits a layer of cold, dense air. If the sound wave hits the cold air id+: 81sr vmcv p2,bm(+oehfd tnterface 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 bounoi j+ qbzbj. aq*0n 0zlowbz7m5tu8+,dary between two types of rock at a 38q 8wo bjzuz7+.a jb0o5t n0+z*m, ibql $^{\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 manual, txu+e 06rgfw7u he dish has to be pointed in the direction of the 6fugu+xrw70 esatellite, 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 xuz,0 9 e6nsqkthe 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 9ns keuqxz, 60knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m F;uqujsl +4s .mhfk55 nind 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 (approximatels+k4 .nmqu;luf h55 jsy 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a wi:fx,uz vzd6/fsb0:h ztxq8id, jh(r) ndow to a fire net 18 m below, which stretches the net 1.1 m. Assu,if /t)z hzdsxxhjzf:0 (d, burvq 8:6me that the 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 hanging spryxq)w1z q j) pgx0 ohs8)ryh79j82cxfing. The mass then falls 33 cm before it stops and begins to rise. What iqrf x8jhw8 )g2q)o1x 9sxyzjy0)cph 7s the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 1bd1 gnkxc f oswle)g(jf( /1741–54), compressing the spring 5.0 m.oc(lxgsgb14 /ek 7j f1(wn)df (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 p7 ftiwnpu 4 4)fdh9u(cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11– upu9ptf)w(d4 f 4n7hi55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certai8uc7di apgm-(z - 1ht+hyrh s+5h0bp azmaa.2n groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. Whagah rau caihyz70-8-hm52( +ms+zp 1pb. hdatt 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 e x fxm3i06-tpis in meters fimx60-pe 3tx 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 frequency f. What is its frequencyd5;xj d ,izba* if it acceleratzjxi *,; bd5ades at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg manrmbvhi2 m zar8h/r9 0-q8 hzi. stands on the raft, it sinks 4.-h2/8ma9 rmhvrz 0qrbz i h.i80 cm deeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are le6u8 su4 cngiy1o2/ftuned to play at 392 Hz (G) and 440 Hz (A). i8 uf4guc12/neols 6y
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fieibk; ;1b.xypxz , 2dyg. 11–33. Determine a formula .p,ekb;x 1z xydy2;ib(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. 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 eapgt s3 yu0m f/8nwd:9sch prong moves 1.8 mm to either side of /9mp fy 3tnws0:d us8gcenter. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillatenn 1lwd46dn2 ls with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pew42nn61 nldld bble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if t1su uk y5gz00jry*a ;o qrp;f/hat end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.fp/0y ;zu*a krs1uo5q;ryj g 0

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way su:f otr a16z:or21dswwing takes 1.000 :z:ar1w2ou f6 1dtrs os.
(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 springmpi8com 9 qvf90gok322 i zb8b can oscillate in the vertical direction or can swing as a pendulub9z8 mo8fk032iv9b p o2qmgicm 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 masz6baeb )7:kd szi2j q,s 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two p 6b: zs7jiz e,)kabdq2ulses first meet?    m

A block of mass M is suspended from a ceiling by a spring withyf6)fwr r 6whpt3t:7f 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 pefr :wrfyt p76twf36h)nny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at /(jnmytjwydo5s) :f6huzj d47hz. j. the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the perio.hdn s: j) tj6/4yydzmj ofhj.u7wz( 5d of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a tr(uvax)jbiy 5 3jku.4/fx9zm7o, fhplate 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 shejvf y3 u j7zmfxi/(kra)u5.9t,ohb x4ar modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz