Give some examples of everyday vibrating objects. Which exhibit SHM, g 3 9itzqq *yps:zu*/hat least approximatelz9y:q*3 z *p/gsuht iqy?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wherwjkz:)7bqrp* f yo5u-e?

Explain why the motion of a piston in an automobile engine is appror) yly)ul8kws (da; 4/tja :maximately simplm;k u4/8)yll(ryadt: wsaa )j e harmonic.

Real springs have mass. Will the true period and frequency be ym0s0 s:1n2r,q t g,ipm4lnbvlarger or smaller than giv yt:4q00l , 1prvsbim2nsgmn,en by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of awd olxn/q:1lqx ((b) f simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook o-qez4(y 4vca of a vertical spring scale, and then is released. Describe the scale rc(aov- ez4y4q eading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when8y80o0iuffs.z:x dk q taken to high z0f x8doi. kfuq:y 08saltitude? Why?

A tire swing hanging fro6i-*er :i(gs xy8c gfim a branch reaches nearly to the ground (Fig. 11–48). How 8rsyf g6g:-ix ci*ei (could you estimate the height of the branch using only a stopwatch?

Why can you make water*tdbf 5el g3o0 fskrrlc q+9o+20jg* b slosh back and forth in a pan only if you shake the pan at a certain frequflr kg* 0eqo do2+ sj0grf5+b*3t9bl cency?

Give several everyday examples of resonance.j;k/g v. n+cedala n6/

Is a rattle in a car ever a resonance phenomen7abkip 2r v 6bxwb7+.aon? Explain.

Is the frequency of a simple periodic wave equal to the frequehu 6ahpw *s1j4ncy of its source? Why or a*h4h1jw sp6uwhy not?

Explain the difference between the speed of a transverse w0cs23v))nc:/kct 9 jha z5fuks-p oidave traveling down a cord and the speed of a tiny piece sdkv32s0z )c pcuoa9t c/ihj:n fk) 5-of the cord.

Why do the strings used for the lowest-frequency notes os870od- l-z kevoj)j rwitk;1n a piano normally have wire7wro0 koevktj l;1 jsd)8iz- - wrapped around them?

What kind of waves do you think will j7 gm:r v0jpqg5/sy. 0nyjhq3travel down a horizontal metal rod if you strike its end (vrj yqg5m pn/0 3j0sy:.7qgjh a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase i ;ia+ hfkvzp qht-sw( q5f xa:o1,;4ztn temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperaturex-41kztq,;5 fhzaaqs+(wof ;v th : ip?

Give two reasons why circular water waves decrease in amplitude as tc )-e1n nccka8d60zzahey travel away from1 86a )ckzcnd-a 0cnze the source.

Two linear waves have the same amplitude and speed, and otherwise are idenv 9ahncple .p.,t+f4 mtical, except one has half the wavelengthp+ 4.9hvcft,am plen. of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses th nl nj :i6)belz8lj ls,+ke+6de boundary between two sections of cord as in Fig. 11–33, the frequency doelk6d+l,)l+ j i6n jlnes8bez :s not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three sesm53m:id oer 8gments, are there any places you could touch it with a knife blade withsdm8r3moie5: out disturbing the motion?

When a standing wave exists on a7s2;ql8u eo jv string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was de jl2v;oeq7su8 stroyed? Explain.

If we knew that energy was being transmitted from one place to another, hvvla gcj;4qjn4m7d f3d-9 (qp ow might we determine whether the energy was being carried by particles (material bodie;qcv-9 74ja m 34(lpdfgvndjqs) or by waves?

  If a particle undergoes SHM with 1b*qo fy,btq9amplitude 0.18 m, what is the total distance it trave ,1q*bt 9qbyfols in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 : c n4r5 ,sex.3cygpzecm long when a weight of 180 N hangs from it. What is the “spring” constant k of 5crzc,3 g4:x. enspye this elastic cord?    N/m

  The springs of a 1500-kg car comp+ c el3;a)-t, o8uywh2 wy/ pvumvbba;ress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, whata32h taw;)um+ pv bwboevyu;y8 c -/,l will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs frzm4ny9q- 9,jnby)fb hom it. (a) What is the)nq,9 ybb4fjm-n9zy h 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 vibrg8c/hsn)w *wh cb-l0rates with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is 0 wnclh-rg*h /sw bc)8its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the pospj01( i,dl*ilx xwo5p7 2yr kyition x of the mass in Fig. 11–2 at times t x1pl*5rl y 2oi 0j x7dkpy,iw(= 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is cau34i/b v kqd3lv+:fcbmght in a spider’s web. The web vibrates predominately with a freque:bf33k/dqimv 4+cl b vncy 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 v+9 /4 exv8ah hqhkvh+of 0.88 Hz. When an additional 680-g mass khhv4/+xaqv9heh+8v is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 qrmr hi nl123x de+7wa t+r,q.times per second with an amplitude of 0.131 + trinrw+qem.73xl r,h2aqd m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement slo+nu,.qag c0) trf6 from equilibrium is the speed of a SHO half the maximum valu lngto f+usqrc. 6a)0,e?$\approx$    A

A mass attached to the end of a spring is stretched a disf 4f+2vca e0lytance $x_0$ 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 vert uv7womser (k2wxv-c, 4is29 *pg+sdpical 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) equilix siw+c,pm rs-seuv4g7 (92 kdvp2o*wbrium position again?    s

  An object with mass 3.0 kg is akf k9 v 4ns,scuo8i3+attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s9i cuf +83skno,s 4vak
(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 spriv 4v ;e0b bmz4eun: v.hpjqb2t3 3ubi/ng of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the balmp.be:0h2qzv3b4u 3iju n b/ ;ve4vb tl leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end o36hg7 x5cvh,xah u w(xf a spring; the other end is fixed to a wall.h(x,3hva c hug6xx 7w5 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 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 = 0.45cos6.4t whb (.q90jeohg*ql 6orfere x is in meters and t is in seconds. Determinhq9j6o.g(lq fe *0 robe
(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 oq4i 4)9zn z6hlzzjq,l9ziy5KE and half PE? 44qyn zl5 h,z 9zi)9o6 zjliqz±    A

  If one vibration has 7.0 times the energy of a second, but thei;wcei g::ak02x ib kviyg(rf +imh;uw- r17l)r frequencies and masses are the same, what is the rat)-+ikbi 2 wihfrvw(m0k1ye:a ;;li cru:7ggxio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanginl3t 6ihu(ry,6y )s wze;yhjn(g light spring once every 0.65 st wne (z ,i)jyyhs36y(l6hru;.
(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 su5z(g4t)r1xr, e3l hz4sodzzr pported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration? 1z4 zdrotrex,h)glzs3(54z r

  A 300-g mass vibrates according to the equatr s3+z4ef( khy b0fw:gion x = 0.38sin6.5t where x is in meters andf hsye0bfwg4: k(3rz + 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 et7.k2iyl :tn vxamples 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 end of a ,l kt -+:askvhhorizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an int h+kv:l-k,s aitial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates wibsm.j,5 vanj+e jhju,;)-o 3 oqjh2acth an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass pas32e5jnj u-mso ,cab)qhh +ov. jj,a;jses 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, wif5(4582s6b/ yuwg ;wbi zojhvm bvb.wth spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizonto3ej.zh 4lfh br14 wy7al spring whose spring s.lez 47y4fwhh jrob1 3tiffness 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 -:cd9bg8 k eonfrom a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. eg :-cok8nbd9 He finally comes to 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 vibrations in exactly 6kqa;k2b)hy0 p0 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pwo*zdv)-+*t90 yrxduvfe/e yendulum be if it is to make exactly one swing per second? (That is, one comple )u+9* etf/dd y vz-oreyv0x*wte vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period oriut9zceux2lxai10 j- ( )ky2 n Mars, where the acceueu) 9cxakly-jzxr (i1i 0t22leration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pel)1ix5 d)b5a 4-i2xu+xxgwt w+h bx smndulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple .8 08b + bvyuphv-vjxtpendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle ofh8.+juvv-8 bvyxbt0p 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 m. If the clock lonln5.as-yye51tcbmh4w,6 ld fx-o 8a ses half a minute per day, how should you adjust the length l d5ton6 s-h.a m xf1caew48l,5nyb- yof the pendulum? shortened by    mm.

Derive a formula for d*b;kfhegz e* t)x6q5the maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released from rg anvi1.tkix*j (;t1nest st ;x j(*tva in.1it1kngarting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchorfjb2x r c1b9t6ed boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fasr jt x91bc26bft are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 tj323yshkoi ; ro9nr-lzyw :);bcmf5m/s How far apart are the wave crests o zrh3wf nb:coj2imtl; y;s 5) k3r9y-(compressions)?    m

  (a) AM radio signals h- l 1lkq0lynpfov2z3*a:fm-c ave frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed ofyp 30v1l*llo -z2qf:-nm acfk $ 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 ic58 ;g3 cg1ngd 2svgevn
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastipjyqm8ubl+38 c modulus, but one is twice as dense as the other. In which rod will the s3y8 qub+plmj8 peed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m ap8iz -ku2 k j;w(j;kl:etgwnf*art. If the tension in the cord is 150 N,8;n( wzeljjk;wkgi2 t-f*k: u 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 w r1md,:wi-yaof length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for tryid aw- mw1:,he 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 ship just below the surface of the sea. H53n.qtsmw df6t4 5aw ve hearsdvn5f5 ww.4st6 3tamq the 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 at different speeds, s;y og7qa5jbv59ri:r and this difference helps in locatini;5gqa7rs9v 5:by r jog 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 tra6oaif3e f,q30 : mnwbansverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that, n0ie m 6b33awf:qafo 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 am6dfqo/jq c-r3 b6ng;hww8ohk63pd ; jplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 kj6ho6gd8kr 6 wqnc 3o;w-jbpf;q/h d3m and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to be )0 v zlcj.z8ru)juz8 zv.r0lc $ 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 travexo :snu4:6hg bl through the same portion of the Earth, : su4gnobh6 :xbut one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a se cwss.uewt3bqa6x: 1. .p6 hhtretched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudea: 6eq hh6u 1sbe.c3.pww. sxts of the two waves?   

  A bug on the surface of a pond is observed to move up and 0 )xzjt axk:b zf)26oxdown a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to)af02x:kxx ) bjt 6zzo 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 other. (a) S kw ra7*wqo4imx,sq+1 ketch 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 momentqwm*i41 s wx7o+,k rqa 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 frequency,41 kvx5ykcp/ov -ls7 gv/q6qx what are the frequencies of the fi1vvxso 5k c-gp qq //6xvyk47lrst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz whenm+j: o2 ec8rdfe)6ktq/z)vs h unfingered. At what frequency will it vibrate if it is fingezmj):v t8e6+ks2 h)r/ ecfq odred 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 mvsoel(d*pz w/)r;2x in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will(d*vzer )lsx;omwp/2 resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If th v6vmjanf)* +ze frequency of standing waves is 475 Hz, how far apart are two adjacenvmf6j vn+*za) t nodes?   m

  If two successive overtones of a vibrating stringxw vnrtb.76*zhi(3e c are 280 Hz and 350 Hz, what is the frequency of the fundamentalx(.w*rbv7z ci6 h3 tne?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 6 jae,g 7a5vy:snaa.3b n xdf(9d sx,ag. 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 fuajnx 65vs yad7xdae (,a3g.ns 9,b:fandamental and first two overtones?    Hz

  A particular guitar string is supposec6rmnj8 c,5cyboqt .(,d im;/jmg1 tfd to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By1fyj(q.b 5g;o/crimjm8,6cd ,cmt t n what 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 fl d/i6zadb l :o87z.jis supposed to vibrate 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 frequenc7b jo dia/llz.df8:z6y? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mech-rlx-t(lnc xb s v6k9d9 ldjy87ijx*9anical 60-Hz vibl l-8ji-r*dx 9 y lsxtc x7v(jk9d96bnrator. 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 adjusted by moog)lio gti8(tsi31n1 s 0qw 8zving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved bolgziw ti1 (t 8o)igqs30 8s1ny varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right6)yj5eddi i;0o)v nvt frequency, the water alternately rise 0 vn) dy)t65dijei;ovs 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 an dy2ijr6ir0,3 zx, mst k.0 km/s strikes a boundary within the Earth between two kinds of mai3r,dsj 6xzry2m,0i nterial. 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 veloxg ubiz8s r(27city changes from 2.8 m/s toz27 i(rsux8g b 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 qlp l36f p:bj gd:0gc:i:x+urhits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of 2q+x:dcf03ilgp : :bjru6gp: l5$^{\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 wavesfexv:a/, y p: strikes a boundary between two types of rock at aey,a:xs/ f vp: 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 q5 wdz;l mifnwx9:4q.5obif* manual, the dish has to be pointed in the direction of the satellite, but an error of5z*n4fiq:mw 9lxw5dq.fb o;i 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 k e6w 0qmge7bc5ow;h8p m/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how mu6pwohgeqb5 m c078;we ch 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 car bumper has a spri :0zo )i -mownhhl1kl 0pb;,cang stiffness constant of 550 kN/m Find the maximum compression of thn0-kml)oh0:;lz ao w1 bpch,ie 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 toibvq 7zp-j9l; .: sif k4,oj*agvp n;+sr. vyc a fire net 18 m below, which stretches the nets:p*ijb ;zfipvc k.. g+v4, qnal yo sj;-7r9v 1.1 m. Assume 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 spri*mvy( +d:d rg6nx8rnn ng. The mass then falls 33 cm before it stops and ryn:v(m+xdrn 6dg8 n* begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compressi no*bz jj8ts hu)s -/pd)ja.v 9agwb2:ng the spring 5.sjjs2p: vda9 nt )8owa/ b)zh -u*gjb.0 m. (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 abp6bf2esk rb ,q50y-w 1oe0 lx cup of coffee (diameter 8 cm) at just the right pace of about 1 s6esr xe 10ob0 ,w2ypqb-l5fkbtep 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 the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-)zn6ing f i/hzrjz pwwfg768a;66v u6rpm phonograph record have a wavelength of 1.70 mm. What will be 6 6g8ah/fnzw6n6g);z6pi uif z vr7jw the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is 5l9hr gwi32ahin meters and t in seconds.9hril3gh5w2 a 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 if i1tdx f 7e,qvog:ltq,csw8h4 .t accelerates ae tx.,v1qw7g,qotf8ls dh:c 4 t 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the kevy 2 bs7b9b3i t9 86jzue*ocraft, it sinks 4.0 cm deeper into the w v3ce9b6e*o 7 bstiy8u2zbjk9 ater. 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 (G0h5ji k* mw, oc3rsf2j) and 440 Hz (A). hj0ck52j* mi,w3fsr o
(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 stretchzt;4 ttbqrglwdkz)+o15l j-/ed two-part cord of Fig. 11–33. Determine )l od gt;wzjbk-tzq/l 5r1t +4a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 2wuhr kkq2y0, gxxf m 2,ddu3,564 Hz, and the tip of each prong moves 1.8 mm to either2m3xfgdu,0, ,dxq2w k5rh kyu 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 frequen-cym0i 8+ wd yv b+b3fhxg(6ticy 1.5 cycles per second. What is the maximum amplitude with which the end of the board canwv tm-c0 3hx iig(by8 +b+d6fy vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “fre0/ z: *j0zakhk5 o+.:ynsxh taxwqzn+e” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths5znaz0skho/kjw x.t0: +hn+q yxz*a : of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactroqb(hn 9)jb)1r t)ys ly 2.000 s — each one-way swing takes 1.000 s. o)j)y1rs( tqbh)nb9r
(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 oscillate in the vertical direction or can swcjra152o s2 hli dp(.xing as a penduluhl2pj( 1 adico5. s2xrm 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 z1 0as;c/pe mveph:+ pwpc)a0 mass 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 mzs m0cp a/+eapwh); 0:e1 pcvps 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 frhfjgd5 +jn(1lom a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that willgfnd+(jlh 5 j1 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 steel crane cable is *b/ v 5liy5pkp22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end oibp l5p/y*vk5 f 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 show9xu kqw(u*l*pn 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 frequenk* *9q xpul(uwcy 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