Give some examples of everyday vibrating objects. iz/l vb tq1:i3Which exhibit SHM, at least approximately?qitz1l b v3/i:

Is the acceleration of a simple harmonic oscillator eve:t9y s-oo6mher zero? If so, where?

Explain why the motion of a piston in an au 44zp/ehlal1 4r hvr7ttomobile engine is approximately simple harz t1 4r/lpelrv7ah44hmonic.

Real springs have mass. Will the truez4qt ea21*chjzrk rh +mf(u+1 4km 7em period and frequency be larger or smaller than given by the +2rujkr+ zq h7* kmec1h tf4em(41zma equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed pbn h: y 0axejecxa6x/g, ),y3of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook2 )d-uqm2cb qp of a vertical spring scale, and then is released. Describe the2cp- 2m)bd qqu scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or l )lznsos)r viw.i /q1+ose time when taken to high sw q/ln )zr o).s+i1vialtitude? Why?

A tire swing hanging from a branch reaches g8fr2x hp*o-cnearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatch?c8r*xog fph2-

Why can you make water slosh back and forth in a pan only e qc 5cq9x:zj- 7*4))aeqil*dfw3vf +xappm eif you shake the pan at a certain fi*x9jvmed)a*a lf + cq4wp )c7z3q 5ex-peq:f requency?

Give several everyday examples r 19 ujv,rvze cv3, t9u6wmr:+ pss;egof resonance.

Is a rattle in a car ever a resonance phenomenon? Explainbne9 *153cct( nb ax81 gypcpn.

Is the frequency of a simple periodic wave equal to the frequency of its sourcqjn jfc.e7:on09l0bb6i un+nn2zqf2e? Why or why not? fj0ni62j 0b+nz nnfq9lo: 7unbqec.2

Explain the differen:nn f j.cb8b-oknpx cw6*2q7lce between the speed of a transverse wave traveling down a cord and the speed of a tiny pieceo *qcn.bbx8kn-n6cfl72 j:wp of the cord.

Why do the strings used for the lowesk1 hk923(q+lugwl s6g f aoe/wt-frequency notes on a piano normally have wire wrapped around the w19 e lka2qgsol+wgf63 uhk(/m?

What kind of waves do you think will travel down ax5- gbw4j6o4/ 0*k(t bljdjjjaeuq7w horizontal metal rod if you strbujjqb5t(d7j-/ xjlj6 awg0w4oke* 4ike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with yq 9yj,dr:q:nan increase in temperature, but the bulk modulus B is nearly independent o9j ,:q y:nrydqf temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplfcuo76eh) k kr.1avan3q ) p*ditude as they travel away from the so*pe ouhnaq ) f1v7)3dk6.kcra urce.

Two linear waves have the same amplitude and speed, and otherwise q, opkxi6:q8 ae3,jdy3 9uab vare identical, except one has half the wavelength of the other. x q:ab3k3 ,, 8qo9iva d6yupjeWhich transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between twogi5rjb i64 ot7oe6x ;jqrgv7 :c5qq :c sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Expla: rcoqgiej 7bt:j6 6oqri vqc4g5;7x5in why.

If a string is vibrating in threlrt f2) h3lo*l3kmhj( e segments, are there any places you could touch it with a knife blade without do2hfll tm kjl*(rh3)3 isturbing the motion?

When a standing wave exists on a string, the vibrations zp.q wo2hk n;7of incident and reflected wave.7n;wz2qkho p s cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to ajw 8dy.-o- tj5+uzya hyd)3x r4e8 rihnother, how might we determine whether the energy was being carried by particles (material bodies) or by wava4ud 8w. )d8jeri3tyx+zo j-r hyy-h5es?

  If a particle undergoes SHM with amplitude 0.18 m, whalq gnl3 /c w(x-a0bh3ft is the total distance it travels iq3xb an(-l 0cl3fwgh/ n one period?    m

  An elastic cord is 65 cm 5) gh(lt;wsn)sjpcpb/ c+dl5 long when a weight of 75 N hangs from it but is 85 cm long when a weighwstp)l( bjg5lhd/5;s p +nc c)t of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car urfxke irai * mfqd8 38zj4*d :teb;78compress 5.0 mm when its 68-kg driver gets into the driver’s seat. k:de3re ut8jii *8ab;dmfzq7*8f4 xr If the car goes over 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.d1.ij quwvs 41 (a) What is the spring stiffness constan1ji dwvq14 s.ut $\approx$    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 mass of 0.60; w5hjtk3kz,ix k. v*v kg is hung from it. What is*;5v z ,it .3kvhkwjxk its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of z /mv1btw3l, xthe mass in Fig. 11–2 at times t =bz,v wtmx1/3l 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.29hk4,te 3ma nyjd,h d,5 g is caught in a spider’s web. The web vibrates predominately with a frequency of 4.0h enhd 4,jakd ymt9,,3 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When an aqt.iis 2ne /w*dditional 680-g mass is added to m, then w*t/.eqi2si frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per sec27/sso myz hi9ond with an amplitude of 0.13 m. Deterz sm2io7hs9y /mine
(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 ha/wi36 t 4igo optbreb9p2b *8. h5fjyblf the maximum val b*thyopi btebb28 g5iwj3p/r9f4o6 .ue?$\approx$    A

A mass attached to the end of a springhhyrrilz(53j6 xm;v+5 ys 7vb 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 vertias pp9u1.xngny0+w (pcal spring 0.315 m. If the spring is stretched an additional 0.130 m and released, yxpp gpu(1n. na9s+w0how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring wit,,dy1heamg it:: r cx6h spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving whxyme6:gr, dc1 ,t: iaith a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy pop1n bja5:rw.lg/5-jwc9ab cyros99a usm cu 55gun 0.200 m to “load” a 0.18ysw w5a9jbgc lacrso/mj-5 5 9b :5rau19c. nu0-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionvu5 n4rof.6yzeuvh f0h h9e6 -less surface is attached to one end of a spring; the other- u6f4fvy en0huhzvh.o956e r 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 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the5rla y +z,o7aw equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determin+7ryao5zw,l a e
(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 equilibrk o3 ta8g0,cfgium is the energy of a SHO half KE and half PE? ± gtoakcf 8 30g,   A

  If one vibration has 7.0 times the energy of a second, but their frequencies6v;zvoagcrp e ,4w , 2s3e,l7pon/9arc.g yhq and masses are the same, what is the ratio of their amplitudes?zogl evevaa6,p rsyn74 2phg9.rw , q;,3c/co   

  A 2.00-kg pumpkin oscillates from a ver-ao s:rzof81rtically hanging light spring once every 0.65 s. orzo-:8r sa 1f
(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 vertical0 :qh 5j p-qgmkg;wxb0 springs, each with spring stiffness constant k (Fig. 11–49)xj hqq b5;0 pgwg-k:0m. What will be the frequency of vibration?

  A 300-g mass vibrates accorduk5xr4ss g(g*pr zer-a 3a,f/ing to the equation x = 0.38sin6.5t where x is in meters and t is in /ra,f43gkp s(- zgx*are rsu5seconds. 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 and B. For each, what ipi 9x3 )zuu,sdxdvo 14s
(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 restsqqg 4dkk, ) 9snzb1x/ on the end of a horizontal spring (k = 124 N/m) is struck by snzqg4 skx/)9 k1,b qda hammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constal9et:pv 3 4 d6ilb7a2 uqcwd-znt 305 N/m vibrates with an amplitude of 28.0 cm whenwp elb9:46c 3z 7d-viulqdat2 0.260 kg hangs from 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 connected to two springs, withwt5zy1cf e fma9+8c(k 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 0.6flse ys db5:+m y9wux-(h i,2h00-kg block attached to a fixed horizontal spring whose spring stif( yh- ymlusid:hxbf,e5+9s 2w fness 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 mam;-/vgdp*-qg net v*(7kns xpss 65.0 kg jumps from a high bridge. After reaching his lo mgvsk*p- g-xve/p7;(ntdn* q west 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 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 ikjzavo,50 dksn i1 n--s its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per seconjmu.+p2fz np4 d? (That is, one complete vibration takes exactly pnm4u .f2 z+pj2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Ma phpw)ovh,ar ngu,fz2-;6-ll rs, where the acceleration of gravity is about 0.37 that -lp ;og2wh- uzh)pv,r 6, anlfon Earth?    s

  What is the period ofcnxg p , c6r*8ld 9-pi/mcvt,t a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pen7pan 1rndw*nnm 5yc59dulum bob has a mass of 365 grams, and it is re n9mp57wcdnn1y 5n*a rleased 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 0.9930 m 3z8/v mn :fqobdz;j1g. If the clock loses half a minute per day, how vbonj3z 1;zqfm8d: /gshould you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum ttvqk3mb8:i4x:fk jto gb,+2 speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released fr33t /.z1er/ msagyfwgom rest starting .e r1tg/f3wzsa3m/gy 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 9 zj6/.36vp 74uasyq uaznccxmu97 yewave crests pass the bow of his anchored boat every 3.0 s. He measures theezu6 a n9zp uqm/367 cv.cuyxsa974yj distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 juqqyp k uf s5v8-+k0-n)-ekjm/s How far apart are th veqj-0+q5-k8ns uk)kjp-fyue wave crests (compressions)?    m

  (a) AM radio signals have frequencies betweexoi e9rkju8 0pf *1v1tnx6yfj7 b8e9zn 550 kHz and 1600 kHz (kilohertz) and 1198prjveie9 jbno f k 70 z6uf8*xxyttravel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of r5 s3wd*g-yd/dw3h se;e ju1+ji xa :ylongitudinal 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 t j x (cb ;m;a;hw5bgsa61ftc3rwice as dense as the other. In which rod will the speed of loxc6a bgab ;th3scfj;mr5w;1( ngitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m :6y,m xs ixx r60qwgkc/cz:tx k0/v.tapart. If the tensiow:cgsz6m0/6.tit,x: xxr y 0q/ckxv k n in the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620 am.irny.up30;khk * w;uokv ) 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 thy3wpo).u;*0rhm;av k. iunkkat 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 y s11akxwytv n76:bd8below the surface of the sea. He hears the echo of the wave reflected from the ocean flobvyswdy1k7 t:16 8anxor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake trapa35v)q/.pp hw ptsm7fngs9cfh/m6 ; c n3q /cvel at different speeds, and this difference helps in locatcf nc.7mv/p3nmtq6gp; s)hfc9hs/ 53/ qp pawing the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approxima, qglz-u ;+jvoz.ld u6q.p bgcj1 ,k3yted 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 +p-b6q,u3gdl1 gzjyjzuk l,. .vqoc; leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, lp,dci qsyjum+rp/i)q8 )k-:, ,w1ql wpt7lg and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km m, 7itqw, )8,u+glcw:k)qyp i-ql1dpspj rl/and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured j7 onv*b t6z0bto be 6zvb70tb jon *$ 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 thkrv4(j yhmu )a9ioi9r--slek 7j4)me e same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes o9ar9iuhv (m 7k44ks-)ol-rmejy ej)i f the two waves?   

  Two waves traveling along a stretched string have the same freq ubp2 yh: lofc,5f9i(0wp+kqzuency, but one trk2 by9oczpl,f5u: (0 h+pwifqansports three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a tota5+ tcfzlilro 4w6bl +rbz3-8 yl vertical distance of 6.0 cm, from the lowest to the highest point, rc6lrtozy 5flbibz-l48 w++3 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)zq,rjwb2 j1i ; Sketch the shape of the string at the moment th1j,bzi2q; jwrey 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 frequencyzsf,k+w tw:-d :ejzw0 , what are the frequencies of the fij+ftws :we0k,:zw zd-rst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what fr3w1avy*a8*oua w: 3;pzhip ktf0+psiequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string 8pwyi0owia zp sptu*+haf3k: 3; a1*vvibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name atf2en* ds7 4ld:uv hop3- 1etab least three other frequencies at which i2v 7pua ef:*-s tdlh4oebn1d 3t will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing6j 8 b,tueg(yd )uawo3 waves is 475 Hz, how far apart areja,oe 6( uu8dw3b )gty two adjacent nodes?   m

  If two successive overtones of cq3 cx /b)1h3ssur5uzn/3z h no9e1ora vibrating string are 280 Hz and 350 Hz, what is the frequencyhz/z3/1r1e) oqn3cuc35hous 9rn xb s of the fundamental?    Hz

  A guitar string is 90 cm long andtta ttxk 8q2t/1p-6ue has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequ kt6-e2a8/tx1tq tpu tencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz,yr:wped 3zw 5k2+xh o) but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies h3w:)pw +yexo5rd zk2 are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar s x8 v)5l5iofrd;h/f/jjwha (ftring 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 changed to correct the frequenca ow/(ihldf5x/ ) vr8h5jfj f;y? decreased by    %

  One end of a horizontal string is atzolbvd gga )32 /r5wi1tached to a small-amplitude mechanical 60-Hz ra l)523vdb/g gwz1oi vibrator. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of thwf vgq1iijw +loo--5 5e string may be adjusted by moving the pulley. If the qgi1 +wf--jiol 5wvo 5hanging mass 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 frequenfc+7 sbs)8i oxij ezia8fh657cy, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frbi67ihax+ 78jsfe c ifzs)5o8equency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes 0;tsgjh nei)f( +ktzzq b;v5;a boundary within the Earth between two kindstghqnkz(b tzvf;+;5sj;e)0i of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changesp qcz+-6 vwkze6p7 kd 0 )ojnmxxx(j43 from 2.8 m/s to dn)0+v w mkexx4cjq zo(6zjp6 k-7x3p2.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer o/kcc2, 6 0tvaw)v(nmrqtxed4f cold, dense air. If the sound wave hits the cold air xekv,(26v t4 dna)mw/ qctc 0rinterface 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 q*4mpt t20 yfhph+r tdd2p5;x rock at a 38 5t yprd mpx+qh d0f t422;thp*$^{\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 he(*sn g+3qyp. According to the user’s manual, the dish has to be pointed in the direction of the satese(ph n +3*ygqllite, 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 wavelengthx+v)7o, ff jxn 250 km and 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 nf7o+fx )v,jxto 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 g j69ve wvl ng-q7p7,aye9v4wkN/m Find the maximuwp967qve je 7 w9 4-vgnl,gavym compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which9nk8u9titc4 e stretches the net 1.1 m. Assume that the net behaves like a 994ui8 tketcn 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 qq 10/ ed:uxo,hz g*w,bwx7ov bg3-jgt b.+riend of a freely hanging spring. The mass then faxrhto 71/:e* dq-w3xug wbbov,i0+.z ,gq gjb lls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a spe qi 73yc5kw;znhex/t 4ed of 22 m/s (Fig. 11–54), compressing the spring 5.0 me4tx7 /q3hw y c;ik5zn. (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 just the right pace ofl 0ck7z2mapk7 mwq92t about 1 step per second, the coffee sloshes more and more until eventually i 7m q lc2ta92m0kpkw7zt starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain grxw2/cl 9 aca,myc0 3vpoove 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 ey93ccl/ pc aa2vwx0 ,mmitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t whbkt.( uw5 xon*ere x is in meters and t in seconds. Determin5 t x(obnwu*.ke
(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 osciltl120vw)f h fmlates with frequency f. What is its frequency if it accelerat v)w0fh ft2lm1es at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake.d8)9zml- kaqrf-,ais; f zv:v When a 75-kg man stands on the raft, it sinks 4.0 cm deeper i -f8;-,d msa:rlkq v9z va)izfnto 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 9 a*(x1jrnvywz+v3q iplay at 392 Hz (G) and 440 Hz (A). j vnrw+9x3(v*z y1aqi
(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. 11qk k/ 4wqv.:gkax w0r5–33. Determine a formula (a) for twaxq: 4gw/kqrk5k0 v. he ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip oj.-jdke pb9c4q;/n9dh tab v0 f each prong moves 1.8 mm to either side of q/djh jt-9bavdk90pc. eb 4;ncenter. 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 ocpo. o+/4glbi7 eefc 1f frequency 1.5 cycles per second. What is the maximum amplitude with ecb ei /o1lfog7+cp. 4which 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 “fqqgtn8 +u.y n1n4l:fcree” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonantq1nn cfn:u 84lg qt.+y vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — eac/v:*y *cz iskeh one-way swing takes / *zei ck:*vys1.000 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 ca9q5 70oyxcro0c9h4:wh a/n 2 iselwkhn swing as a pendulum of small amplitude, but not both at the same time. Which on 5a /k9cyeo04 7so2wl0h9nq w:crihxhe is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stre 2)-.br2mu(yfbl a q(ie fejg9tched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meetbul(imje22gy (.fq )9r fab e-?    m

A block of mass M is su6xum b6r0 ,xw (khoi vxy(9f5bspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just v uf90 bh(krxxyo b ,6(ixm56wstay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the md m3ukpus2w 1kqo71sp4 i*1 fjunkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze star3*s up7 dow4ipku1 11m2q msfkts the car bouncing 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. iw eq: h one+-r3you69m,0e94mq*2clzxycv r 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section meehrw,lo360-qvzmy4o+nrq i 99*ce cxu2y:9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz