Give some examples of every.e6sdn e; ow6rday vibrating objects. Which exhibit SHM, at least appr w en;rod66s.eoximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where?h3ppc ,vloqv)ai0d;q :.yie6

Explain why the motion of a pist2hxvxcug- 0f- ;p9.imu;l; hlx xcj(gon in an automobile engine is approximately simple harmoni0-fu p.c2 h9livug;xgxl m x;chx-;j(c.

Real springs have mass. Will the true period and frequency bef(,zl: a osw+.hixv g4 larger or smaller than given by the equations ff,z(x4vo g.ail+h ws:or a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple h6dax hm,vuw )/armonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook ofq+ m ,forn (siv6d: 7pf)lo8nc a vertical spring scale, and then is released. Descc v noqs8:r n6p)o,d+mfi7(lfribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it+l0w4lquec4 / oyi 9ct gain or lose time when taken to high alti9l/04wcyeqiulo+t c 4tude? Why?

A tire swing hanging from a brud-a;hl ( y,ypanch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch usingh(p-d ayluy,; only a stopwatch?

Why can you make water slosh back and forth in5vk*irt6v fp. a pan only if you shake the pan at avf6v.p* k5rt i certain frequency?

Give several everyday examples3wod*hk44m,y(h u s na of resonance.

Is a rattle in a car ever a resonance phenomenon? Explajm-i 3ad*tiogt()w9y in.

Is the frequency of a simple periodic wave equal to the frequency of its sou4 d*af lb spepj+-gs3o2bk63drce? Why or why not?djk-3*b p2dogs la +b 4p63fes

Explain the difference between the speed o7)7ov htyc5usx4( lo8 np +mpaf a transverse wave traveling down a cord and the speed of 7 mct yu7a4os85 vox(+ppnlh)a tiny piece of the cord.

Why do the strings used for the lowest-frequen :x gmo9o)dab4cy notes on a piano normally have wire wgdm4)o: o 9abxrapped around them?

What kind of waves do you think will travel down a horimb ;htz /f64phzontal metal rod if you strike its end/bmt6p;zfh4 h (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decrease v-g nq.ug(l.j 6 (cd*h1nv.uxb6gphrs with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how woulu6-.6 (r.* cqn bn(hg1xhdvluvjgp.g d you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease inq uuofhbn4,;e2s:*rt amplitude as they travel away from the sor;:f4 uqu *2, besohnturce.

Two linear waves have the i6j- lln+rp n*y8e-jy *9 mnknsame amplitude and speed, and otherwise are identical, except one has half the wy lkynl-9m+p-nr* en8n 6*jij avelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betweev*kx6 h:udc7j n two sections of cord as in Fig. 11–33, the frequency does not change (al7kdxc hu6 *jv:though the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, ru1 m9jyam-m 6are there any places you could touch it wmr19m mu- ay6jith a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of in808bjefdhmcag);fg94x 7l+huw z u(acident and reflected waves cancel at the nodes. Does this mean that energy was destrjflh;4g)xa guuh m(8cf7 d 0+a9 bz8ewoyed? Explain.

If we knew that energy was being transmitted from one plac6w,z*bgwofesw12 l6 7byv*vl) t)jsv e to another, how might we determine whether the energy was being wyzt* wf,726)g*)1swvvbjv e lo6sbl carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18k19cg cwuo19;ez1.) h wairrb m, what is the total distance it travels ineu wocag.bir ; 1 1rwc1zkh99) one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hv4x2 p1nlw n5bangs from it but is 85 cm long when a weight of 1804w 1p2x5nl bnv N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-xlpgzok+qh3y6 7y l6zr3vs s;(0 ett( kg driver gets into the driver’s seat. If the car goes oqp(txs;(re6lzvz73 l hy +6ygso0k t 3ver a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What66rkxcyb0 cda ;d 9*ps is the spring stiffness coc*;6s 9c0d 6k rxypdabnstant $\approx$    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 3.0 Hz when a a ik8sxqi vbj9pkjl;,n xeh0u0-;6 ut:rw(7smass of 0.60 kg is hung from it. What is its frequency if only 0 u7s0i8w xh,jtqxn;(kaipj e:6;kr-vs l 9 0bu.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at am /a6y .4ovxktimes t = 0,t =m .64vx/ayo ak $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 0.25laq/f-fz8a 9o g is caught in a spider’s web. The web vibrates predominately with a frequencf8fq a-9lzo a/y 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 vibrrwv5fd)0p* b iates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value ofv)* rbdipf50w m?    kg

  A 0.60-kg mass at the0rerz*ohzt u; zd8-x8 end of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determine 8xh -zt uoe r;0zd8rz*
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maximq5ap;yjry*g( 2o2q5vidh0 r wum valueo;q5wi5gh2(qr2j v y aydpr*0 ?$\approx$    A

A mass attached to the czu - o6n8r5.f6oiu6+rk w fuk8aoc .9*tngkrend of a spring 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 ve7izo 4:cvq3. qip exu/rtical 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 positioiuqv.3q:o/p7 i zcxe4n again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnessd*/ 1 3uwxd0qyc(zcm b constant k = 280 N/m and is executing simple harmoncu*0y 1c 3/dzx (dwbmqic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.d(pio + 1f1t yau8cww4mur5x(0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave8o (fca1x (ir1+5mudwy4tp wu the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is ad7u.ss*moxvo10 qth jbz;(, gp :oda -ttached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compresjvxud 1 :ss7b*zmtg.0 ,o (o; h-qdpoased, 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 accordin7psrv. ;y vw)rg to the equation x = 0.45cos6.4t where x is in mete.v wr ;y7svp)rrs and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half nw9 5. +keudyt t7 .uujp(jpj9s ,(wmvKE and half PE? (uwnd9.j , mj.j 9e7vtutk(sp+ w5u yp±    A

  If one vibration has 7.0 times the energy of a second,1 gt0wobpyq 5. but their frequencies and masses are the same, what is the ratio of tg o5y. qw1tpb0heir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once everrg)oo9qe ---k(slabgy 0.65 9r so--) bgk(eq lg-aos.
(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 supporta+v/1ul+w6ksa y uu g/ed by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?sl 6 uwa/u1a+gk +y/uv

  A 300-g mass vibrates according to the equation x = 0.38si t32q+ dvlh wdf5ng,p1n6.5t where x is in meters and t is inddl 1+vf h,n53 gw2ptq 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, labelqun .p(39-tie lbuy: q9 j)wqaed 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 horiskj9f 8m8 (pgzzontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed ozkp89s(f m8jgf 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with an ampli+i *f km xuo :wquw0,of+hps23vm25tetude of 28.0 cm when 0.260 kg hangs frvxmukf,qo0wip +to:e2u m+w*s5f3 h 2om it. The 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 connectel3q*l3fy)qvo d to two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal spring b:42c 5 hv8vak5zuwiv +sq/pp whose spring stiffnesw55s+i 8vqa/ :czhukb vp24pv s 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 a high bridge. After reaching his pqh)mbmf+p3x;1 7f(wd5 ugze9k b7dwlowest point, he oscillat pxguwf)3z+km7ew d hp5fb(d1;b 9q 7mes 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. 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 60 s. What vs(;86of,ta qwq(ib5op / jqois its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per /o.am, +5h xvnd keay+- tv-kesecond? (That is, one completexd/.ok +mka-v5e +hy-ea ,tn v vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, whdw26 -v nlj t 95qjq0))z-xmjatge7plere the acceleration of gravity is about xl enjm qqj g6jv9a-w)z2p 7-dtt0l5 )0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lond6c7cls+cu ducqsm58 vaa7 ,;g
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, t5vq4 a y* ks;)hnzgx5vhe pendulum bob has a mass of 365 grahq n;x*s)kg ya4v5vz 5ms, 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 pendulum has a length of 0.*d* tc jn-qh;x81m+ilw; olyb9930 m. If the clock loses half a minute ll*h nxom*tiqw;8; -d+cyb j1 per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the max ,j,p7wknf cs-imum 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 ya y:oqjln9gu:4e- )tof 2.5 Hz. At it is released from rest ) gq9yj:e:4ylat uon- starting 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 anchored boat everhvg 2 v3ylv6h+jg6mo5 y 3.0 s. He measures the distance between two crests to be 6.5 m. How hhy6ovmg 6+5j2g lvv 3fast are the waves traveling?    m/s

  A sound wave in air has a frequency of xqbquyfggrk .g 5x/- /jq(y( .262 Hz and travels with a speed of 343 m/s How far apart are the wavegugy bq.xj-5f(. /xgrq( k q/y crests (compressions)?    m

  (a) AM radio signals have frequenci2nh.jmr5oh -ies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed ojr nm.5h2-hiof $ 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 o.zq:jm ax +x0u8p y/mbf 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 dense agen0m :6 1uby if2;fpts the other. In which rod will the speed of longitudinal waves be greater, and by what factorg n2fim16e ty 0fbu;p:?   

  A cord of mass 0.65 kg is str5 t+p,m uwg1mldsyz v0j+5ax3etched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support1t0du 3gpw s x55 zmj+l+my,va to the other?    s

  A ski gondola is connected to the top of a hill b-x- ,ly*:6ad ewcqk ray a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end wa,ay-lxc 6*:k-eqdr 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 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 hisld* g 8pjkh8a 7qhk8g- ship just below the surface of the sea. He hears the echo o88-p7d8hlqkg hj a *gkf 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, and t /jg ,*bmrnng*his difference helps in locating the earthquake “epic rgn/nb*,*jgm enter” (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 hr01e -. dcbn;f6ywvqsurface 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 leavn6y ;rh -d0vefwcb.q 1e contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the int sv)t lq7yw8lyi*3g): kumva2ensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points sgqiw l8mv*vtku372al) y:) y 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake1( fmv 7,y )jp6sjqgt)pu+z cu wave passing through the Earth is measured to be 6pc ,1qyuz u(tj7s )jvg+fmp)$ 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 theq8/yaz a-b4xl same portion of the Earth, zq/y b-axla 48but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but o0gc2 mtbet6e t-1:ggv kj4(owl6*yu bne transports three times the power of the other. What wjvt :bcme4oeugt(62*1tglk g b0-6 y is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to movmq*6jhmb0n vk*ep q6 ,- q-/ba k6vwthe up and down a total vertical distance of 6.0 cm, from the lowest to the highest ptven*p66qm ,-6v -h/wb k0kqmha*bqjoint, 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 toward each other. (a) Sketch the q33zr19scsu h 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 otss 9z hr3ucq31her, 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, what ;,ys r r1u( esbrynx38are the frequen3rx( ;e8u1byssrnr , ycies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered.to )r:3iv zh+k At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That isro)hi +k3v zt:, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates innnbxf55/y/ ,e1w kd1b ,+rzqf urg-xx four loops at a frequency of 280 Hz. Name at least three other frequenciefk 51nbx /5nxg,udb, f zwr+y1 xrq-e/s 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 frequxx 84ptb9 tri4gtb4( t udr5g8ency of standing waves is 475 Hz, x 4d rb4it8u rpx5tgg4 tt(98bhow far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string ar+u/recx 6 .)5+fmv t fhffp9nqe 280 Hz and 350 Hz, what is the frequency of the fundam hmf9c) 6fu5v./f+rxqp +fe tnental?    Hz

  A guitar string is 90 cm long and h kj2/wb 16f gonx9lux6as 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 thel9u/1 6 2xx fongw6kjb fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measurej1a5qv-8c q75g jqprqv5uju (d to vibrate at 205 Hz. By what percent should the tension in the string be changed tq(quj5v 7gu5apjq jv 5c8- 1rqo correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar str 0yecv* pytny:86- bxuing is supposed to vibrate at 200 Hz, but it is measured 86xvp0nt buy c e*y-y:to 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 stru-ztr:,vatyo(h7 h o0 vb(4wxing is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per btryv(at0vxzu (:,hho 47w-o 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 mazc 684bufrcedi6t :9*ka myva4 e 2ld/y be adjusted by moving the pulley. If the hanging mass m is fixed at 0.02d4*8z:/ea66 9iktc ebry4cvfudaml 80 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and foyow k1ff)o2 /q yw0z4grth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-widy/ o oq )10y42wkzgffwe 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 boundary within the Ea+ 9o b)n u/cb 8gphiue0f1hc3tx,dl*hrth between two kinds of material. If it approaches the boundary at an incident anglxh1uf 0h93p *,obtb/dc ui+elc n)hg8e 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 - 8aifkr ,ofp0q,qz-funderwater “shelf” where the velocity changes from 2.8 m/s to 2.1,kfaqi8zp--0 ro qf f, m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a la6 s6pav n 9tpl,ircg8-yer of cold, dense air. If the sound wave hits the cold air interface tgn69-l 68cpsvri ,ap 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 bound),ma p1re9zqsqxd: mxaa 8.,v) pc3jfary between two types of rock at a 38r1)) pdz,a v3.xamq9,q: f spa8 xjmce $^{\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 thdrk:lh)t/ -xjjr z*1(ny,x poe user’s manual, the dish has to be pointed in the direction(kjoh,n/ )dj- lrzp xyt*1rx : of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h tragt 0tjm4cl 1u9vels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and uc4 0glm19tjt 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 ub: u,jcz zr)nq-7m s074phj4. b mjeqof 550 kN/m Find 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 (approximate7 ),4n-zsj: zurmbj chbjqm4e p.uq70ly 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m 5 ,7ucjjf 9lcxbelow, which stretches the net 1.1jc,u 9fx jl5c7 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 spring. The mass w7yg h 712vjkjthen falls 33 cm before it stops and begins to rise. What is the frequency kwjhyv 12gj77of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), co+ 1ehdf 7- 7mr/myuxjw r2swv*mpressing the spring 5.0 m. (+e r j*2mhwrydwxf /7- 1vmu7sa) 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 cm) at just the right po:iur*oo,n+l-*esbku jp 80h ace of about 1 step per second, the coffee sloshes more and more until eveo8:euiosnj0 u-r, h+lo*p*k bntually 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 grivzx; qeqw)11*e/3w b ttmo z;oove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound e vm1;ioex t; w/z3qtqzb e1)w*mitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is t 4gpu)f d5n4mc(urq8 in meterf)gpqmu u4cr(dn8t 54 s 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 frequency if it3+lbwvryt aatp (3 ra+sdl7je4k :c92 accelerates at 0.50g (a+rk9 2ewp33a :lcja+ 4tvdl7bt (asyr) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Whetbi + 9qk+ hcw:ffd8.jn a 75-kg man stands on the raft, it sinks 4.0 cm deejhff. q+c+98bdtkw :iper 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 y5l 88qkp7cr4lq0sxr 392 Hz (G) and 440 Hz (A).cl0q78r l4qrsp8k5yx
(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 .t2a6o/n3ba ti mqus0 (j:-dottyd4xFig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy s 6qud:aotn/xbt0 s-do3imyjta42 .t ( ection 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 kt *xtm*/1woky,hc,y the tip of each prong moves 1.8 mm to k m,k/ty,** thwco1yxeither side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency u zc2ois;n:9usy0 *lw 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a2yo9:lczs wu;0 in*u s pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if thajvf(*z n4 mkh)h91;pcshhyy/ t end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant h 1yhzfp/mn *);s y(k4 9jhvhcvibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing7i l u+(upljb2bnzk-- takes 1.000jl-lz7 i2p-b+bnuk ( u s.
(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 i5u*c 0lgf1ne1ge +vs1iunmh6 n the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and +s*euvlfn 16n51emuhgcg10i by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pulse qiro: ti .41ljvrw-*a is generated at one end, and 20.0 ms later a second pulse is generated at the opposite enr iwarq.t4:j 1vi-l o*d. Where will the two pulses first meet?    m

A block of mass M is suspended from azrnp0bkmdp u2z- 9316rz*p eb 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 than0e1p*rz 6zzu -2bmrk93b p dpt 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 s j5du 2 hkp*amr9oz9e:vl/+z 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 crp s 9 z*+vuhd/mj9eazlo25:k able. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate anmexxkkv1w2b /1 h 0.(idkcf3s shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as s. 1ix(1xnwev 3 k0cdkkb/2mh fhown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz