Give some examples of everyday vibrating objects. Which exhibit SHM, at leastg.os77 )*, bliho583cjrymzvao y1 hq approxima y hs7 alb3 mji.gz*)8rqoh5vy1 oo7,ctely?

Is the acceleration of a simple ha1q7zxp(+j g mpl 0,ac2 7ma2chilpf,grmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobilei7kw e+z+. f 7xkqe8x f(knt8d engine is approximately simple harmonicf f8qe7(w.7nkz xd kik+8xt+e.

Real springs have mass. Will the true period and fr)k,8ctl3 bq 5f q ;,lr;t4 mbegiksjs4equency be larger or smaller than given by the e msk 3gjb8c 4;kb,);t5 fiq 4,ersqltlquations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speun w;38s-rri 6;cxl: 6 xrrgcaed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to t-q.wh ,*qy,yr,c narihe hook of a vertical spring scale, and then is released. Desc aryrc,h,q -. iy*wn,qribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when tami*4k z+ph q)nken toi)zmkpq n4h +* high altitude? Why?

A tire swing hanging from a bran6t2*ux5zx0yru b u;s och reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwa6zyxr;05x 2 utuso*ubtch?

Why can you make water slosh back and forth in a pan only if you shakq qnvymli/q;h)ld;x:fah62. k4l a e+e the pan at a certain freql fh2ll:a han;q)ev4m qk.qx+id 6y/;uency?

Give several everyday exampxe+3 z o*zoa phct)7c:les of resonance.

Is a rattle in a car ever a resonance phenomenon? Expfo8ty9p ljo5+5a3v idlain.

Is the frequency of a simple mj+09 oexqldse(g4 v,n/ye0uperiodic wave equal to the frequency of its source? Why or wh9+yuj 4o x0dsv/mn(ee0l qge,y not?

Explain the difference between the speed of a transverse wave travelm :/ 1 z8ui6mtuu tzk1wt9d1zoing down a cord and the speed of a tiny piece oo9 u6ttduzz i181:z k 1/ummwtf the cord.

Why do the strings used for the lowe// ig4ckf :,gbfwqurx.pwzty(*/t3 g st-frequency notes on a piano normally have wire wrapped around them/ kbft/zxq ciwf(* ug.g/r4p gt3w, y:?

What kind of waves do you think wiem(u4dwn8q ynk 4)2 ijll travel down a horizontal metal rod if you strike its end (a) d4mw4nyj2nkiue )q8 (vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperatg3t mr//s cht8(vnx0oure, but the bulk modulus B is nearly indv38/t(toch gnrm0x s/ependent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why cirzv4j egs t/+7 t* rui6m(kwy*rcular water waves decrease in amplitude as they travel away from thezeyi7wt(/g * j*rumr+sv4k t 6 source.

Two linear waves have t8y3ln i81p8 oi w-(f5jachxmm he same amplitude and speed, and otherwise are identical, except8 wni5hp ml13 ja8y-8fmox(ci one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave cr-t vv(,mf vhj)osses the boundary between two sections of cord as in Fig. 11–33, the frequency does )vv-(tvm jf,hnot change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segmentstcc x ml1. k**)yuatv0zmpu 8-, are there any places you could touch it with0pvux*. 1yck- m)a 8mzutl*tc a knife blade without disturbing the motion?

When a standing wave7pet,+1udvwvxtzm 2v9qw+ . e exists on a string, the vibrations of incident and reflected waves cancel at the nodes. Doex ,v+vzuvetw2m.t 91 qe+p d7ws this mean that energy was destroyed? Explain.

If we knew that energ1h xwlpbn6n0a wk12h3vx;6x r y was being transmitted from one place to another, how might we determine whether the energy was being carried by particles (mawx vwl 0xx13nk a6;hbp2rhn 16terial bodies) or by waves?

  If a particle undergoes SHM w/e 8x/-ns w+iyz bow/uith amplitude 0.18 m, what is the total distance it travels in one py w e/o/8u-/bnwisxz+ eriod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fromhz0fz4 :na/s e8t .biu it but is 85 cm long when a weight of 180 N hangs from /f4.ie:bzhtuzs8 a0nit. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg v a ,zd-xay/l2car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what- /z yvdx,ala2 will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm whex::ew)9rzz8v*gg c e gn a 2.7-kg fish hangs from it. (a) What i:zgreew8*:gvxz9) cg s the 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 vibrates with a frequency of 3.0 Hz whenifi4kn 9q 8;iqyu2 r2b a mass of 0.60 kg is hung from it. What is its frequenc2f84 b29iiikrnu;qqy y if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the positionjdj2dw h kqe55qb4l*q th4s;: x of the mass in Fig. 11–2 at times t = 0,d h2b4; qq4*w5l5 hkejsjd:tqt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 spidew9e- pw 5*zz3to1n/ab3sfiv nmm 2 fz:r’s web. The web vibrates predominately with a frequency of 4.o5imaz1* 32: w n z3s/pw-z9f mfventb0 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 .0bobgsmf ;p7gei(i3 vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequenc(ip.fgsb0im7b;3 oeg y 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 with - t4hcmhk+p4hv/ud j-an amplitvhuhhc+4tm p -k d4-j/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 equilibrium is the sl1bxel(msco r 1.k19n peed of a SHO half the maximum valbnl kmr 1l(.1cxs 19oeue?$\approx$    A

A mass attached to the end of a spring is stretched a d(vps4 qhwl 24mistance $x_0$ 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.t om+(gdc61 ib If the spring is stretched an additional 0.130 m and released, ho+gi6d o(c1b tmw long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attacqmg /lrh2s5b ,hed to a spring with spring stiffness constant k = 280 N/m and isl r/h,52 sqbgm 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/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 tokj1,kl x +dzj4k ony/7 compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball./ kdj ljk4,on+x7y1 kz With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictioh5fg 8m/u q2qqnless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maqq2qh85m u /gfximum 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 accordin8joy4g/nswv 5bjr8:zv6 tdcf,oo z3;g to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determine,4;ojvts/8 onwdo8:z5c6bjz v3grf y
(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 ehou4 g+1vuns .6f5brc-g im *uquilibrium is the energy of a SHO half KE and half PE? 6-cub4m5g1 .nu+ vrg shiuo*f ±    A

  If one vibration has 7.0 times the energy of a second, but xwr*1l41osp sf- +jw qqjs:3x their frequencies and masses are the same, what is x431o* sx:fwsql+ rw1jj pq-s the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hang:io fmifg 2*qbl;9*ky we-ea.ing light spring once every 0i2* *-a;ef wmi9.gokylb fq :e.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 parallel vertical sprib73;ox8se6s wv)8e pondn x :bngs, each with spring stiffness cons3 b n;8xxv)son s6:edbwo 8p7etant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.3j+- lard zdv0ks7 ) zj2lq 42j qroh.d/gaj,:o8sin6.5t where x is in meter0q/ao -rvqa2:4ozs ).ghd d+ z7j2jd,krljl j s and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and82xc- st kfo1a 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 (k = 124 N/m) iscnprw be68 5-yj (n;dk struck by a hammer, which gives the mass an initial speed of 2.96e- ;p58ckyb(nr jd6n wm/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 g rd )wl/8lz-o.tpc0cstiffness constant 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=0t)r/zo0-c8l.lw gpd c) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring -b*1s/ xjq ywdh2o+ zwstiffness 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 att j/z0ao wzditq4 ,04l,2 fwasvached to a fixed horizontal spring whose spring stiffn044w,javs zf ta,2i/d0o zlwqess 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. *lmzep +dje:h;uhv; xc 04;faAfter reaching his lowest point, he oscillates up and down, hitting p0*vzx ;+h;h;lcf:ema deuj 4a 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 ,1, 4wvhnasyb in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple z8 oosy x*a/;j(;cewipendulum be if it is to make exactly one swing per second? (That is, one complete vibrati;osjzay;(i8 w /xe *coon takes exactly 2.0 s.)    m

  A pendulum has a period ow2i9 hu (mlsnz,- x1zof 0.80 s on Earth. What is its period on Mars, where the accelwslz129mzhi,nx(o u- eration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 chh(6wv vsz5o9.9 evk:h6lgpub/b g. wm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendul/ypklg 1z30j s1d0a )ckzti9rum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is relejs1rld zi/ 100zt39k) cakpygased 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 oflcs)kxkug m. 0pdm t-0*;f,zk yq dj)7 0.9930 m. If the clock loses hal udmp-mkxz cf,* k lktqj; 0y.d0)g7s)f a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed lfz-6n*ptq5u f,gwa: . fpza,$v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscilliqu12ly9qn9 k ojcw0sg97/ no ates at a frequency of 2.5 Hz. At it is released from rest starting at a0gk9sqnnl oo 27wqu9i91 y/cjn 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 thatwk 6i2bx, (alsd8f6(7slpenn wave crests pass the bow of his anchored boat every 3.0n6xp (ikab,(lef6lds 8 72sw n s. He measures 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 frefcij 2, dh-f *3. ucc.jkhllo9quency of 262 Hz and travels with a speed of 343 m/s How far fhojcj.* h9 fd3ku ci ,-l.2lcapart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies bewzlalkitkuu:c a/0.b/+ 2/vb ce )h/j tween 550 kHz and 1600 kHz (kilohertz) and travel with a speed +bucvzbitk.au // l ): 2cewjk//lh0aof $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in tb vwky-yft c *;7q8-t
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is *e8dcvo7vh 09 fs z-)wf2gqa xtwice as dense as the other. In which rod will the speed fv*dxwh 2 q c7-eza9vo)f0g8sof 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 te w(g12p bt qmdybr 6o,rc43x5insion in the cord is 150 N, how lmp3yo(4b wi5, r6dx2br1 gqtcong will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top 3o3-rjw dance4e7 3da of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it buwcej3ndd3 -a 3oa7re4 mps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below t4ttfmi+3q cl9 0eyb x1he surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this poi cl4yi1q90xtbt m f3e+nt?    m

  P and S waves from an earthquake travel at different s:mi sv :f5v 1 xy7mme7:vgh1ykpeeds, and this difference helps in locating the earthquake “epicenter” (wh m: em :71vyfivshx7y:g vm1k5ere 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 transve,y 4hwoigq c2:p0c2h; q.bddz rse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of freq d,:hh gw; 0i2po2.ccqbdyqz4uencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudesgo0 r+e/0kpdiwn5 e 5s, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a) +p e i0drng5wo s5ek0/   (b)   

  The intensity of an earthquake wave passing through bexnx zr),0u:the Earth is measured to be u,0n e):bxxrz$ 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 6lb)bk6f)my 6fdr 0 uzsame frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wz b) r yfu6kfb)6l0m6daves?   

  Two waves traveling along a stretched string have the same frll, iprr.2h v6equency, but one transports three times the power of the other. What is the ratio of the,lr6ri2p hl.v amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a tota,xwsxz43;0 re vgxv)bl vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripplev e4sxvwgb3x;rx z 0,)s decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 ne a7l7p r(ant m9ny/,are moving toward each other. (a) Sketch the shape of the string at the moment they a l, n nenmr(ty/9a7p7directly 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 i 9zrk9j4-(tal spy eqcn6 5h2rts fundamental frequency, what are the frequencies of the first four kr9jh s y ral5n(p4cqez2 -t69harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfin:.6)gqahtb+bvn 5 trtgered. At what frequency will it vibrate if it is fingered one-third of the way down from tt+bhn6bt ) .g:t qar5vhe end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at p( qtbwsx;k8ug5l6q;faei/h 97 am4za frequency of 280 Hz. Name at least three other frequencies at which it will resh;4fibw 6/auka5;zxqp tmgs9l(8 eq7onate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing waves isy dwlt;y9,ggtyxtvdpxswd 5 66odb .4 75 wf03 475 Hz, how far apart are two adjacent nodes?otw yg wgb6ddw v;sf 0 tp6ydt,73ly9x4dx5 5.   m

  If two successive overtones of a vibrating stri* orka(m(m*l ung are 280 Hz and 350 Hz, what is the frequency of the fal* m*ok(u( mrundamental?    Hz

  A guitar string is 90 cm long and has a4a nur1 feu83a 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 ara1 8n4 3ufuethe fundamental and first two overtones?    Hz

  A particular guitar strinvz-5i: ndcne3 4d5tzwg is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the stdni n5-e:34twd c5zzvring be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar st8w2/ tka,:ocvv dl6*p m +t; ia(obyfaring is 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 ;l dt v*b w/2p+t6aaoy(v,:c afom8ikchanged to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanicab:.z-y fn9 gl55od2h+1u2np idb sqlwl 60-Hz vibrator. The st:5+5.ln pou dzhwf2d9-ygqbb1nl s2iring’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 hb rah3 uv15q4string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L betw3h4hq5av bur 1een 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequencybky,n m8jz+. p, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standingpjnz,8.bk my+ wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 kmh psca(4s: vy-/s strikes a boundary within the Earth between two kinds of material. If it approaches the boh -ac (4:sspyvundary 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 velocityl 6g:qy2f)w ji changes from 2.8 m/s to 2.1 m/s If the incident wave crq y)fi 2w:j6lgests 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 l ,sjr)jpi8pebal- c8 (ayer of cold, dense air. If the sound wave hits the cold sricp8aj,-)bjl8ep (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 str jwc *dkxy;oh ucvu89 .k);qz,ikes a boundary between two types of rock at a 38uco).w hkj*qy cv9;u,dk; 8xz $^{\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. b/yywlb zn(oz)*;lu)*q dnut4 i 5 ej9According to the user’s manual, the dish has to be poyw(*o;ullz nz 5enjq t /dbi 4*u)b)y9inted in the direction 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 zwn ),q,;y04xtyvgl y-jt )c t750 km/h travels across the Pacific Ocean. As it tz))qynj, tlw; 0g-c yt4yxv, 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 attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kl,dwkk-.t 7jm ng1c* zN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides withkdj ,1l g km.ntc7-zw* 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 t*vey9oj n( b.bo a fire net 18 m below, which stretches the.yo( enbvjb *9 net 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 freelq3 jw+*j,h 5faa.nggsg0y iv1y hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of thegj jvnw1gsifayq .h g3a50+, * oscillation?    Hz

  A 950-kg car strikes a huge sprin+c bv)63is *br, (a0 mewwduweg at a speed of 22 m/s (Fig. 11–54), compressing thbdv, c *wi+rem b3ww(s0ea)6u e spring 5.0 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 a cup of coffee (diameter 8 cm) at juss-ag e*n3mmkic1kw 1 5t the right pace of about 1 step per second, the coffee sloshes more and more uk5a -1kmse1 wn*3 cgmintil 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 grooveh2 s- im,,sguldm7vt peit vd;o;p.te/+, y7q 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will behp .m,-o; p;2s,gdvetl du7m,itti/y7qs+v e the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is in tvoe2 kdvfr/ a4*v/9tf i)n4gmeters an r2gt vt)vefkod94f/i*anv4/ d 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 frc2t bevhs5uc 1faw n ,-+de()9 mwi7shequency f. What is its frequency if it accelerates at 0.50 ifs-9+ hd1a)wech2t7b w nvcme(su5,g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floatv af2 9 t:zemwzjml4nd)2 b7;bs on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm db v4nm :7; zawljtez2d2m9b)feeper 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 5spr 8ulv;-e:;t e quutuned to play at 392 Hz (G) and 440 Hz (A). vlut;us pee r8:;-5qu
(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 Fig. 18cm3p*wooqr5r9c,x dtua2yv:a 3nj 11–33. Determine a 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 co2tj33*a uqwr1 mox:np 89r,avy cd c5ord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the0yj 3:xzcdqb, tip of each prong moves 1.8 mm0:q,3 zdcbyx j to 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 motion ouy45rw yjfi4is4b85h f frequency 1.5 cycles per seci4 wb5i8y f4 rsuy4j5hond. What is the maximum amplitude with which the end of the board 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 can slo*wecw fy.72ph+:xc b ide without friction on a verticae x.:+owwyb*p fch27 cl 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 fy v5)qgdo3 :1md,ryyhas a period of exactly 2.000 s — each one-way swing takes yyyqrm fg :,o)3vdd151.000 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 in the vertical direction or( 5wc diy.1ehw 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 pec(1dwiwh5ye. riod of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched abgcb.e.2,0 8 :x jc zof3jxenunder a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a secondjg 82z:o3ex b ec0x..bnc,fja 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 w afwj6 (u.s57jz 9.vrt.psq:tm dwy 2 4.ytddzith spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude o4djywja9qrz . .:.d6 ttd f7y5z.u(2msps wv tf oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1201n sfvl4m,ux 30-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car boun4mul1x,3 vsfn cing at the end of 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 shown in Fig. 11–58 (which also gives thel(y ;cgv61 5ddxnim d0 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 modulu(;16ydd 0d5vc ln imgxs (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz