Give some examples of everyd 7r)l/ jp1)djqmmsg2wp7 *uplay vibrating objects. Which exhibit SHM, at least approximatelgm7dlq2)l/ jp*7rs1 m)wupp jy?

Is the acceleration of a simple harmonic oscillator ever ze* k 4qw3mtrleuwr:9 m+ro? If so, where?

Explain why the motion of a piston in an automobv ,ao*av9hh0q ile engine is approximately simple harav,h9h0q avo*monic.

Real springs have mass. Will the true period and fre*ynseoen); 8p quency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized8o s; p)nyene* massless spring? Explain.

How could you double the maximum speed of swcr*ap q3kch6z f7 4/a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scal; 8qe.o quf 2kdsr-a,ye, and then is released. Describe the scale reading as 2 q.s d 8k-yoer,ua;qfa function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when 8pauezf7j)- x; x w soik0e:6vtaken to high alteo7ifx-ps; jw6 8ek az ):0vxuitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). 3:0)s/sypokjw ri k )ue/ix;gea c,w0How could you estimate the height of tpu,)3/jkywk :)iex0;ri gaes/s cw 0 ohe branch using only a stopwatch?

Why can you make water slosh back and forth in a pan on tq*hz 9 l;i8ozuvkdpes7y+7xc37u/lly if you shake the pan at a certain i8 ok /vzhu;p7el c7d3qy+lux9z7*s tfrequency?

Give several everyday exaa(ho7 vp iz:mz+ /x)esmples of resonance.

Is a rattle in a car ever a resonance phenomkrjzv;8/o *15xh(ame 8,+rb dbp ecvd enon? Explain.

Is the frequency of a simple p yv6h d3(8gfuo;z 5 7prs)vxwberiodic wave equal to the frequency of its source? Why or why notzv) rfvod6 ys3x 5p;ubg7 8wh(?

Explain the difference between the sp+vr/ln of*d2zeed of a transverse wave traveling down a cord alfr*v/ nd zo2+nd the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normal, xo8 n-,hehlvb* hx-bly have wire wrapped aroundh,8hn ebob* xv,-h-l x them?

What kind of waves do you think will travel dostplbl3 :9 dxz;8tgw3 wn a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its len38 gbl9sl 3t:wzpd tx;gth?

Since the density of air decreases with an increase in temperature, but thejzy5 do5q 6zg n:if hamxk,i75 ,/;sypcul3f, bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to varypyzd : h6yu3;7 gsf,km5 /ianxj5z 5fqicol,, with temperature?

Give two reasons why circular water waves decrease i acih lp9u(;a6n1+uhln amplitude as they travel awaylh;1 lu+npc6h9iaau ( from the source.

Two linear waves have the same amplituk* wap2x1tbjfd:(bttq) n9 g8t7jk7wde and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what fa9k pg) ja w8b7t k2q: xtj(tnft7w*b1dctor?

When a sinusoidal wave crosses the boundary between two sections wfw54i : l*8yvpzanlkn+nx;6 of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain ww:846n y;xkwlf pav5ni+ n*lzhy.

If a string is vibrating -7(fqxnje l:n/y,upoin three segments, are there any places you could touch it with a knife blade without disturbing/ eqn,7 np j-ly:uxof( the motion?

When a standing wave0lnn/ 5jc9i1f ;pc, sfaskyb ( exists on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explain.fsiyp nl ;/b(ac1c,j0kf 9ns5

If we knew that energy was being transmitted/ hb3m um5hn-n from one place to another, how might we determine whether the energy was being carried 3m-/5n h hbunmby particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what isju)8znuy rh7 th/q9wy :qv1: v the total distance it travels in one perioyu 7nz: q):h/8qt1uw vvrh9 jyd?    m

  An elastic cord is 65 cm long when a weighs5de9r8 nxmx3mx. ;uht of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of9mse;.5 nxumh3xrdx8 this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mmf ;uq jfl3m;/;niek1f when its 68-kg driver gets into the driver’s seat. If the car goes over a bum u;f m;k3ifj1nl;f/eq p, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 covtl8j6odtu 1 ,r vr (o*+n tuvid/1:km when a 2.7-kg fish hangs from it. (a) What is the spring stiffness c ,:vv (j l8k or/t iuv1+*nddtot6oru1onstant $\approx$    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+rc-wr7ayq2bze k u6; mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from it?b7kq-zcwr+ ;yu 6ra2 e    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at timesb *4lh/xdn3a0g +vbkb t = 0,t n*bkldvh bx a4b03+g/= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 web vibrat(f8hptok v35kes predominately( okpf8tk3 hv5 with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a sprinmmi9l k*.aru 2g vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the freqmamu9i.r* l2 kuency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second wijfdw vjp.664b th an amplitjjpb w.46df6v ude of 0.13 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 from equilk 0:6q 4wfuxa0upnv(a ibrium is the speed of a SHO half the maximum valux0:(pf6 0uq aavk4wune?$\approx$    A

A mass attached to the end azrvho3) (oxq0( k 1x y/9wfibof 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 vertical spring 0.315 m. If the spring is st 0 (pldg5miudhd4k6m6retched an additional 0.130 m and released, how long does it take to reach the (new) equilibrd(5d m6mkd hl0pigu64ium position again?    s

  An object with mass 3.0 kg is attached to a spring with s eab: l2jymw vr718opz(3*m xcpring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibr*(7a zo bypx:lvj81wrme3 2mcium 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 hi.s4+ fmb9 q(04q( zqmr-jo8ip j hvqto compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will mi-qqvhb4phz(r.o f9(j 4q 0+q msij8the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end h 2h-r;+ / ,gc pd)hfm4mebqacf1 bo5kof a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of/c hkmhq-e)42 m;cgaf,f +o5h b1 bpdr 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 aod us(ck49 rhf g1eu/9ccording to the equation x = 0.45cos6.4t where x is in meteofe(srgu h1u9 d49k/ crs 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,9qdh; o:pi beyt1-. ooiiw3j from equilibrium is the energy of a SHO half KE and half PE? ±y qo.9dt 1heopi:jw-b,i3;oi    A

  If one vibration has 7.0 times the energy of ne 5,it49xxf9ev z l1fa second, but their frequencies and masses are the same, what is the ratio of their amplitude9nz f1 f 49lxtx,5eives?   

  A 2.00-kg pumpkin oscillatesh-q+ z hc;w0-vn*nvj q from a vertically hanging light spring once every 0z+qh *0nvw- j-v;qnhc.65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical paralutb-3rz/2e -u i b1bam* o*npflel vertical springs, each with spring n2e*ufo*z -br-/am ti b1p 3bustiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.aot/w,do nup9 cncu83 g0wt(ywz7+a-a)m q;l38sin6.5t where x is in meters anq-wa0(g+c3 zmu)n, /9adt; oya op8nwwc 7u ltd 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 d l0g-,lnt x1 s+ewr*oSHM, 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 horizontal spring ( *m03esxmqinsv +r+(mk = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s smvs3 + nm+0(*e mqixrDetermine
(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 constafqcog j; t4d+j *ji,+gnt 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive ve;j gji, q*4otg++cdj flocity 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 constanwh+nt bjp6uz 2(lt3htc- r;u0ts $k_1$ 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 0.6: jktqt7- y8ov3y frx+00-kg block attached to a fixed horizontal spring whose spri8 to:fk- xqtyv3jy7+rng 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 a high bridge. After reaching his y*ru 4olr tg;o ; iqb;v;yi0)llowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below g;blr *out; q) yv0l;ri;4 oyithe 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 is i ehf zax/j,dp- f*x 3rn2hgf:)ts
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make ehw ;.stw/aj 3xxactly one swing per second? (That is, onw.s3 wt;ajxh/e complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. 2lusi3xn(amte 1 w.0qWhat is its period on Mars, where the acceleration of gravity is about 0.37 that1me x3(2iwnats.qul0 on Earth?    s

  What is the period of a sjardg1/ij im.sj))j2 3 d5rwf imple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendu) 1kp-* dumomfaa9lee qn3z66 lum is 0.760 m, the pendulum bob has a mass of 365 grams, andz96fqo mn)plka- 3ae6e md1u* 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 l59augu:bf8 z 1pb9ngtength of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened bypfba95 1tgbu z8u: g9n    mm.

Derive a formula for the maximum speed 4jr*w4(mz-f vv3ud.e1m e tia$v_{max}$ 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 fre0+r,y2xdn v r+v( azkz4wj8jtquency of 2.5 Hz. At it is released from rest starting a4+j08 d z+a(rnw vjt,xv krz2yt 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 crckj. l ,;9mkutests pass the bow of his anchored boat every 3.0 s. He measurestl.ukk ;9jmc, the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency1-lq5ytm1q6.y g;wg 5wsgkyp of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests glqw gpt6sqyk1;g m-.yy 5 w51(compressions)?    m

  (a) AM radio signals have frequencies between 550 :kb+p v(j 7 7vivdfr+mkHz and 1600 kHz (kilohertz) and travel kbj7mvfvp+(r:iv+d7 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 nmvoy9z6-vwm1t4fy1pox 0 jtt:v 5l+of 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 tww* mad.(,c r2ixn1 ljt cqc; d.1cn2vmice as dense as the other. In which rod will tm 1 j*in.racn.q2(mlc2xcd 1vd,tc;whe speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the tens 6u6z/arg3t dkvk, q5oion in the cord is 150 N, how long will it take a pulse to travel from one suppotgr6 ku /d ak3z6,5ovqrt to the other?    s

  A ski gondola is connected to the top of a hill by a steel caw)u( a sztb( riil-n7.ble of 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.zl7t- rbia u(sni) w( 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 h*k 6ym)ug4i38n xurtsis ship just below the surface of the sea. He hears *yiuxngs 8 3)4mtru6k 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, and this d()tzk 7yvg4.hs w,zz(rmz ;ogifference helps in locating;z7r(4gszy) zhzmowt (.k,gv 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 beb.:j dd y2t/eygp k9)i 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 witkdejyp2y:d /. )b9gith the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an y 5q5s4qg1 djj7hjs 8zearthquake P wave passing through the Earth and detected at two points 10 km anj8q1 gj5ssdy 4z7q j5hd 20 km from the source?(a)    (b)   

  The intensity of an earthquake df ;(zjsv(r*zwave passing through the Earth is measured to be (szjz* r;vfd ($ 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 the53 hy0 j2xy;jpn d5, *hbojust same portion of the Earth, but one is carrying twice thdh3*0ytub2ph5n5,ojy j ;sj xe energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling alon5sujij16ie2f 6.lh yy/kcfz*dk*2tr g a stretched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplf6 hefli/yky. r*j *2itkc zsu6j12d5itudes of the two waves?   

  A bug on the surface of a pond is observed to move up and do ig)zlsk30fn map :(u*wn a total vertical distance of 6.0 cm, from the lowest to thg(s3 *mf:al i)nzp0uk e highest point, 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 mx5yk1k 6lmz4/h/ xvk goving toward each other. (a) Sketch the shape of the string at the momentkh6xm5gk/zk /vy4 1lx they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are w+8fidcit9.z2 eu 6hm the frequencies of the firsch8+w tiu9i6m2fz e .dt four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 x-)io . 6h6yfco *wgtcHz when unfingered. At what frequency will it vibrateo 6 i6-y.cth*ogwcfx) 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 wave.)    Hz

  A particular string resonates in fouj*4mtom0i ar6y3g 2 qor loops at a frequency of 280 Hz. Name at least three other frequen mm j*0yo2ao3gqit4 r6cies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves i6fe 8w6sig rjxm n.d :ql,k48:uoe1lon a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart ar8we rkilo,:i1:e8nl6f4g mjx uq s.6de two adjacent nodes?   m

  If two successive overtones of a vibrating stre vbp 405w/zyjing are 280 Hz and 350 Hz, what is the frequency of tjb/45 zvwp0ye he fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The acfcz4eh. mv n4hfaejr:4mz*6 4 (5ds distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are5(ccs .4d f4 ammzna r efhvj*6z4eh:4 the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suppoh4k f9/zt:ue7ff t(py5kd ,ybsed 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 correk e(,7tzd ffk h4fbp:/9 yuyt5ct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposepyv 7ez uofj75j(ws2 1d to vibrate at 200 Hz, but it is measured to vibrate at 1(zj7u5eypj27vso wf 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is an9nhz gjt/kbuh8d+1i) 8 mky: ttached to a small-amplitude mechanical 60-Hz vibry8u9 it+h/g hd1n8)n: jk bzkmator. 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 lgogf 2 (i:dkn2mw2)y hength of the string may be adjusted by moving the pulley. If the hanging mwmki gfyd )hn22(2 o:gass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequenc(lkt1qa f*ju 7y, 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-wide tub is 0.85 Hz. What is the speed of the jq fl7a1k(ut*water wave?    m/s

  An earthquake P wave traveb jz ky/-.fa11xx,t ioling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at a1 jtxbx1y ., iozk-/fan 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 fue .xh8xwn-fv6sg a(nm(23g4 oxs2x “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave cn.n3emx6sf(8x4g2xug f-s x av2o (hwrests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelovq6 ino/u (/zing in warm air when it hits a layer of cold, dense air. If theuz//(oo nvqi6 sound wave hits the 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 between two types of rock/j7p(l-yhlmqr i,2t i at a 38- 2ihmltr ly, (q/7ipj $^{\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. Accordl. x4:z*c,z8z wvak fg*4daw iy58epuing to the user’s manual, the dish has to be pointed in the direcfguk*. 5d,lxv88a*wa: zcw zpe4i4zytion 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 an dn*dbn cntpc(;+px:-d velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attxncpc n dd(* tpb-+;:nracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumpeum 4tc vu86wr/hi o*55(ag* -taistp dr has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the c/upta5t(tvd*o rmsa8gi 64- 5i hwu*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 n bq3nx) u4ygk5et 18 m below, which stretches the net 1.1 m. Assume that the net 3n5yug4 bqk) xbehaves 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. Thes m-r9/ aho6dc mass then falls 33 cm before it sto6oc h-a/r d9msps and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a spee)m7vy+xrsgm7 0m8n l0a3o tfsd of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring s+)nx0goy rl0tm87vsma 7f s3 mtiffness 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 pace : l9+g9: mbh as(kyeh97vt ke8d1sdze of about 1 step lk ds1:h9zt8eybk9gd(+:7a e e hm9vsper 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 w3.mbf v(ag:rgroove 10.8 cm from the center of a 33-rpm phonograph rm:bga r.f v3w(ecord have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is/kca0t)b o ltri ,pj4d.t r;qr5) h:tn in meters and t in sec5t,:bn/trk oh04 cq;t)li j )pr.tdr aonds. 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 it3zuvjj u4m 7m9;z0fs* upx c8v acceleratesj7c4jvx;uu zzm90 8 sm fup*3v at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a aodo2u6em( 8yn/ +dkc lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the wacneoduy6a/ mk 8o2( d+ter. 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 instrumen;ki p,rkndf g.jar,6cb+blt) 8 om5p +t are tuned to play at 392 Hz (G) and 440 Hz (A). ,g+kb;j5) l k pi,o6n8tfpr arc.mb d+
(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 travelinggimrb 363d6bi4 k)ffm down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for th) mf66i 4ibkdfgm br33e 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 frequenxps70 g. a suhl-3mqakckcdf+*.- i0tcy of 264 Hz, and the tip of each prong moves 1.8 mm t7 +3xl0c utdaacqh*psgi-sk.m kf-0. o either 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 motioqhr: vqm6n:dp9,gk w: dh*n.d n of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the boar9mk:dvp6., gqdqn:n *: dh hwrd can 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 “free” end if that end is attached to a ring that o 7:o:3z wtq1i o7llfa4du/wjotf. v( can slide without friction of17z:. l: lqfto/iu( ao7jwdv w34o otn a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each oned.ffzj* fsi .qh.d3dl-c 0h,z-way swing takes hzdsff-3,z. i. q ldhd *f.c0j1.000 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 ine fl: (/qa7mbqrux cj)q1 zza6s vq:fn3090nm 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 tzcn0qff m:/ n zbx(13 vjaraqlu 96q)7se:0q mhe horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A ;hr/agv e iq5;pulse is generated at one end, and 20.0 ms latervhq ;e 5g;i/ra 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 a ceiling by a spring with +f0g0sq rj kk)f7pr1:zjxcg 4 spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on topx pr1gsg0j4:q+7 fk)zjk0cfr of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cxb1 fk1mxvrk1l3eyt/vi 6 (vxih,nz 6k1 2f1i rane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the trzfi1 /n, 3x i b61x1 x vvk6f2hikykme1(1lvbouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gnqz m k ankf;-(9nn*3dives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear moduk*man(-n9 3 ndnqfkz; lus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz