Give some examples of everyday vibrating objects. Wh5pph xboo p5c*vt6.l ,ich exhibit SHM, at least approximolo 6t pcvpx,bp *5h.5ately?

Is the acceleration of d .zdl5 0-kgi-y9zp dqa simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately +l+ alc-eu qp(h/ulj-simplh+plle+/- ( qj-uucal e harmonic.

Real springs have mass. Will the true period and faea6m.0s gos6u +9lt zrequency be larger or smaller than given by the equations for a mass oscillating on the zlg 6+.0assu9m ea6o tend of an idealized massless spring? Explain.

How could you double the maximum speed of a simplb2/m1mbtt5t le harmonic oscillator (SHO)?

A 5.0-kg trout is at u5 9) h9z dyqlntb-f7.xbtn)xtached to the hook of a vertical spring scale, and then is released. Describe the nb dnbl-x 9)x975yzh fq.tt)uscale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose timd g8g-dy+ tkm nrio3s41ed 3.xe when taken to high altitu e4 +xkr-gi3.18 ngodd3tdmys de? Why?

A tire swing hanging from a branch reache/7du 4w zcgwq7s nearly to the ground (Fig. 11–48). How could you e7wzgw q cu7d4/stimate 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 panki/)uavof5nv;jz: xz; nj:i5 at a certain frequenc ;k;5zv:f j/ onuxjianz:v)i 5y?

Give several everyday examples of resonance.xyi pl +lukt9.0u:q6e

Is a rattle in a car ever a resonance phenhk7nz-l w 3t+zrzmjxd3of3l*2 7 o i0momenon? Explain.

Is the frequency of a simple periodice cavmy ;*xq455es1ul wave equal to the frequency of its source? Why or whxa 4 eml5s;u qcey5v1*y not?

Explain the difference between thi+wgvilyzu5xc2 0mch o fn,:o,/ufp, *)d t-ye speed of a transverse wave traveling down a cow c/2*0,5) ,+cf ndhomixt- y:, fziopvug uylrd and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally h0eg+a:.wms y gave wire wrapp ywsm+:a.gg0 eed around them?

What kind of waves do ycxbclqsth909 : jfqx y.m9;7r ou think will travel down a horizontal metal rod if you stc:;q 7ml.ct 9 fxr9xqsy9jb0hrike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases wiheo-g+k47 g9c 4ne(belsbg op-m 0 9lhth an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed ogk9bhmpgheoo(b7 44lgl -e -sn 0e+9cf sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they fcmb f -o28jqci(ir,d,9(osn travel away from tnf92 c jf8,ir-(mqiodbc(, o she source.

Two linear waves have the same amplitude and speed, and otherwise pvdp+ 9qqdbgue7ii-oq 65z q0z0.+ djare identical, except one has half the wavelength of the other. Which transmi9.d0 qjp++i06d zpvu5qqe7bqz-g doits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in Fu a4nn6wnp86 oig. 11–33, the frequenc4w8npo6an un6y does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any plaw34uo7 p ogcg wcq)d64x4x -maces you could touch it with a kug47 mxcgo w wop-6cx )q44a3dnife blade without disturbing the motion?

When a standing wave exists on a string, the vibribboe1yj(7 z7/mn2y d h1j b9ns6a(poc k-g(eations of incident and reflected waves cancel at the nodes. Does this mea a p/d17 -ezn( 9g ib1eonyc6 jj7m((hok2ybbsn that energy was destroyed? Explain.

If we knew that energy was beip0n y8)mc lnt1ng transmitted from one place to another, how might we determine whether the energy was being carried by tl 01)mny8cpn particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance :p evi*e*j 9tr pyu3i1it travels in it:ep3*9* pieyu1r vjone period?    m

  An elastic cord is 65 cm long when ab*c ms+j(3 r o5. i2ezwpjy a-*1cldxk weight of 75 N hangs from it but is 85 cm lo l 5(jz3x2 dcarose+i-jw myb*p c*k.1ng when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car rb wayu u*+1lvc t;c(-compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what wilv -u( 1t+;ccyur*la wbl be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fia6bh 6s/mqk: fsh hangs from it. (a) What is the spring stiffm6qah fkb: 6s/ness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency oock v0:o0vghs5 +c0k wf 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kco00+kk5:h0g so cvwvg hangs from it?    Hz

Construct a Table indicating the position x of the mass .(iyuer up.l: zc*ftcitkj,tj. ) 38vin Fig. 11–2 at times t = 0,te.zku)iuypr it (t.tv*j.:3j,8lfc c = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The we8hm q)wp6vktn/ p/ b,d,.bqto b vibrates predominately with a freqd,//oqbwn t)hvp q,pkt.m b 86uency 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;ium:zaq982xks3v2a )qp ueshp jq2,.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the vse)2 k82x9,ji 2p:m3qa u uszh;aqpqvalue of m?    kg

  A 0.60-kg mass at the end of rq 9tnlpk 0;vs9 2bk:pa spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determin;kplk n0vbrqp:2 ts99e
(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 spe)ih;i w jd.b8aed of a SHO half the maximum val) ji b.8ad;hwiue?$\approx$    A

A mass attached to the end of a spx jge;9l)ot dbeh54g( a:: pfkring 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 spring 0.315 m. If the spring i6eym1*di6ze bl shk6ti-9 yv: s stretched an additional 0.130 m and released, how long does ithk6vtdezi*y:19elb 6 ys im-6 take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spr j )f2cetro 5ulm-h;e6ing with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from itsc)fml5u - e o2erj6;th 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 0.200 m8 24tge m2dhdw to “load” a 0.180-kg ball. With what speed will the ball leave 82tdmghew d42 the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one l5yaw3fs u xem1 k(+p6end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring flus xw a6(y3km1 p+e5by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6(cu t(g++o 18.rnlv u fx;lyya.4t where x is in meters and t is in seconds. Determf( +l (xyayuvu+;gtl. o 81nrcine
(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 half KE and kw 7y4g3qq**xkfkhn 7half PE? *y3 *q hgw4q 7k7xfkkn±    A

  If one vibration has 7.0 times the energy of a second, but their frequencies anso8fk5::zt 4yy n csoe w*w)c;g;mw-jd masses are the same, what is the rat)kom w sz onjtgwy-*fc;y4cw8; 5se:: io of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sp3v*f9s 2h csjvring once every 0.65 s. c*ssj vf39v2h
(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 verticfcan7mhskag6)r4oy8k * 8sou yu++z,al springs, each with spring stiffness constant k (Fig. 11–49). What will be thyz+ km8gu84h rf 7ok sc+, sanu)o*a6ye frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in meje5hcs 41k.zslz8p7 etersp7 zzjks4.ces hl8e51 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 S o+ i(l1 vxohvg4,jq*(azz (v7(z (ph qsqbtx)HM, 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 the2io0(d0 xthnv:v vm//wd( wgq end of a horizontal spring (k = 124 N/m) is struck by a hammer, whv/vnvdh2 mi/:q d(0 tw(og 0xwich gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibratoc7ui1 pz/3-oay1 ma ves with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positi oui-/vy 1a7am3p1ozcve 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 stiffness conu.bsiv3pz5h +stants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to/v/. :x.ezg j vozvp6l a fixed horizontal spring whoseev vjx/zv/g:o. p.l 6z spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from ay)5spex 65wguim 4*o;zsi q o( 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 spme6)o*o5qi(u ;x54z wy sgi rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrxsrf,dv-tro 9; (7zd)uehcp 2ations 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 one swing peg6(2m,lq tv o xk7du.qges7)ur second? (Tht)vk7gdm.7e62gquqs(l ,x u oat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on 1 8(vkkdc-ecp Mars, where the acceleration of gravity is about 0.37 th(k- 8pccedvk 1at on Earth?    s

  What is the period of a simple pendul7w +od t8: hvgq:ud,gaum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.76kvvg:p- : zrr*0 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of zvpv:grr- :k *12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m14 b/8wwktygb. If the clock loses half a minutb g1t/ywb4wk 8e per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximumlq (qpm6w)ec0wl )5* xdxx,bu+rt 5n x 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 is released fr(zy e9 x*ic4so d4wv3rom rest starting at an ang*zviry (4wo4sx de3c9le of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his apy 8k f45t evmtn v221rhvoz/*nchored boat every 3.0 s. He measures the distance between two crests to 1nr5h yt*tvv24ef o8zv2m /pkbe 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequen/o5nnpve 8iicq6w 5-gcy of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crestseicvi 6wog/-n8n q5 p5 (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiloherha9py9 *nyr(plomz 0+tz) and travel9*ynppa9 0 olm(+z rhy 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 rn3ux37ppnzv;i3 ej (bngy f 2rb9o15
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have theycl3hyxthq d 529k5g6 same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, a6 glxhk2d5hy c tq395ynd by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the w+q w ::ke7fk rb6rzn(asajw4hpf ,9,tension in the cord is 150 N, how long will it take a pulse kr ,kr9 w7sjp6w f:qh:+bzaf an(w, 4eto travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of ud6lty-za( on+ra d3)xv b-v6length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps o-u -z6d r+(3nvyv6l )dxt baainto 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 od 6sbt ,a8t4-5ryoy gbf his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directy8 yb,at5-rbg t4os 6dly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquae*i j*k +22f oalj67;xrbka ntke travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the dx*7k6 ikota 2nfe+j blja2;r*isturbance 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 surface67f wv7x owx+ik ab)v- wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint+kwo7ix-) aw bf v67xv: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, zzdrglhx ,ub3w/ g1,j+5vz3eand (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(3j/gz5glh+z1 ,b x3,vu edwzra)    (b)   

  The intensity of an earthquake wave passing thr: nw4 6xyom ur9:)m(j)oqg 6 dxc,imjjough the Earth is measured to be 6: xm(9mdx j )uony6i)4mj rcq jo,g:w$ 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 6 )dr -esi4vte6h4iwfsame frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the tw- fi h4e6ste)dvi6wr4o waves?   

  Two waves traveling along a stretch1bp5ht 0cs. l8rlhuw:ed string have the same frequency, but one transports three times the power of the other. What is the rwh.pu:th5 r b081clslatio of the amplitudes of the two waves?   

  A bug on the surface otc4(2fqeo:kv.kia fx) ; 9 zxof a pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If totc2 zo4fki( )q x.k efv:x;a9he 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 toward each otqojmky;+w4f 5iaa 8frk05:5u edh 6nnher. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few m m5aykejq8+knf5wi :ao;rn0fh564d u oments 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 vibrates at 440 Hz as its fundamental freqsau.,au4 ) 5v ildobk1uency, what are the frequencies of the fi ),kobusdiu.1a 5a4l vrst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hb uja;/sv 5qzv3b .8bnz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing w/b 8sq;zvn.ubvj 5a3b ave.)    Hz

  A particular string resonates in four loops at a frequency of 280 qd43p.wz (xxdHz. Name at least three other frequencies at whicd p4xxz.w(3 qdh 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 standinj;.9 chjah-oulb gnkb (g63*kg waves is 475 Hz, how far ap(9jljc bk 6- 3u ghk*hg.bano;art are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350wd c b5vd8pmk6-.5s qh Hz, what is the frequenc5qkh8-wc.dm b56p s vdy of the fundamental?    Hz

  A guitar string is 90 cm0-:vsvk(kmrsj;yy i 5 long and 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(iss0 :vmkj- kyv;5y r the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibratnpw,dyp w 65** vru(vte 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 the three frequenciv6puy v r* pn5,td*ww(es are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, bs e*;u5fep.:m (p z6a0-pc+y hck titwut it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the freq5p tmc he;uk :.t+sy6c*pi0e zapf-(w uency? decreased by    %

  One end of a horizontal string is attached tot4 -0edn6 -edmu nc/cw a small-amplitude mechanical 60-Hz vibrator. T 0/nt ce6-u dd4ncwem-he 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 ma)vb)xofs- 3dh y be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg,sf3 do)bvh) -x 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 tub at just the right fq d0h(e02q(kb), q omvx u,ootrequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce u,2voq0qqd0(ohxmk(e o,)t b 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 boundaj 4j.y p0 16nvx3n0hqqs:g csury within the Earth between tw03 614phg yv.njunqs c:0jxqs o kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity cha+o5ssg :s he8hnges from 2.8 m/s to 2.1 m/s If the incident wave crests o e8 :ssh5gh+smake a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in waz785qhxe q78-gfg mq hrm air when it hits a layer of cold, dense air. If the sound wave hits thh-x8775q8e zmfh gqqg e cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary betw4-i jkl, w5rbpyfi* 1oeen two types of rock at a k5fli,o*p1j-i 4wrby 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. -t6a)jbm x9vf5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the sate afx 6tb)-jv9mllite, 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 acr6k ngyqc )a u6z(9b(w - z9as4;myvfxnoss the Pacific Ocean. As it approach-(mwbvg6 yc4zf zsxknun)6y a ;a (q99es Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing csjl3h3rt:l6o y 7qsj1 ar bumper has a spring stiffness constant of 550 kN/m Find the m13o llt3jjry q7:s hs6aximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which xdeugbc 301 yx29m;pdstretches the net 1.1 m. Assume that the net behaves like a simple spring, and xxy9ugc2m 1dpeb 3;0d
(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 nb 6ic 7 o7hc(gcesfs( 1-m-neon the end of a freely hanging spring. The mass then falls 33 cm before it stops and beg-(e77ce1m6 inc hn g(-s cfsobins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sprint2,*,ni ) kgtb2(fwm d-oigoy-drjz2:wi* lcg at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is t--,:,l2ti o 2) gdb( rc*jtwko2fgidmny*z iwhe spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at f -pkhg m74-*g4lngeh rs .z,mjust 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. 11–55). Estimate the speed of waves in 4pgknrgmh, zfm sl*4g7 -e-h .the coffee.    cm/s

  The ripples in a certain groove 10.8 c ntkedhwwwa27, 44n;am from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will bh wd2eta7nk ,a;4n ww4e the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates acc;;g:+ t ujbria z;9+vsxn0zvgording to the equation x=0.650cos7.40t where x is in meters and t ir:ax;j+0 g+iv9tb ;z z gv;nusn 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 f;s pr0) )a82n:t twq(m ljjqpbrequency f. What is its frequency if it accelerates at 02j0 bjr8tnm p; :q)(pwlta)qs.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75w13zvrw 2*x v6q7 pljy-kg man stands on the raft, it sinks 4.ry v 36qvzjw21p*w7l x0 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 tuned to play at 392 Hz (G) and 44 2mytu *m1t;zy0 Hz (A). m*y;ty1t m2z u
(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 tb* trpi 2nax3 vyxj(-2raveling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeit vyxx( 2nj *2bp3ar-ds 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 to5st o/ +uaai-1u1y9h mv6mfrtwl.+phe tip of each prong moves 1.8 mm to either sid.+u y ftvpt- h1rwl oa+9i/aomu6m5s1e 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 m+ye3 kfet9 dza6g;3i(mx 6)j yyd5mz hotion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in;k3(9hz36t6m d y)ej +ye a5mfgdzx iy 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 thakaczhhm hao yk3:( 01r. ncx8 lz3az*9t end is attached to a ring that can slide without friction on a vertical pole3ak laz yh*(89c1 n:hz0hrx3 ckazmo. (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 2z :i zgnnt m,-y18;ehb9yqwx- .000 s — each one-way swing takes 1.000 swnt imzb;xq1h e -z8:y- ,ngy9.
(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 skp25u3wli y35/ne.p pt- h nqoscillate in the vertical direction or can swing as a pendulum of small amplitude, but not bow5synk/qphp .n2e5 -lu 3i 3ptth 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 tensial4ym; f62k( um3tuat d,kmriou (( a5on of 255 N. A pulse is generated at one end, and 2 5t4y3ku,kf6aouu a ( i(tamd;m(r2m l0.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from ax/9dm aa;v4f5cb6ybt ceiling by a spring with spring stiffness constant k. A penny of mass m is pybm;a 54dt9/vb x6 fcalaced on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steecfcbs b8 ,7lpnvgyu ;c7x,+6el 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.e 7bnc;8ycubps ,xvc7 ,f +l6g What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as show thddab0s6zk i3rc,62 n 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 begin 3 zt0cs6i bdrkhd6a2,s 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