Give some examples of everyday vibrdt: ;pxew .qot/ sp .*t/pn3)qwcef,bating objects. Which exhibit SHM, at least appr)qbqpn, tw3/e/*; wpd:osfptc x .et .oximately?

Is the acceleration of a simple harmonic oscillator ever3l0k3x cph.k l zero? If so, where?

Explain why the motion of a piston in an automobile engine is a3 awm p:uqecl6p(pz2p3a ykb(tf2- o:pproximately simple h-z3(p mwakba :feytlu2co6:q (32 ppparmonic.

Real springs have mass. Will the true period and freqm mfz 3da)j(-ruency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Expldr m)-z3j(amf ain.

How could you double the maximum speed of a simple harmonic oscillatori(b j(g 9pd.ti (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scalvaya zq u0eh+ /c:4b-ve, and then is released. Describe the scaa hu va 4ce/+zb-:vqy0le reading as a function of time.

If a pendulum clock is ac: yj: .ztf3f7dhw-g 3 l;vdlbccurate at sea level, will it gain or lose time when taken to high altitude?jhvcl y7ftf3:zd3l: .b; gwd - Why?

A tire swing hanging from a branch reaches neaj4b n,lq/l 5to+ u/kt,euvx 6yrly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatch?kxbve 4yj +,l/uln o,/tuqt56

Why can you make water slosh back and forth in a pan only if you shake therjz 2t8b r y8a()rey2p pan at a certain frequtz2)a r2(8bry jryp8eency?

Give several everydaq xmo2+7/ioc8oy7hdi yol9t6y examples of resonance.

Is a rattle in a car ever a resonance phenomenon?7x(gl.y30gc1q kqw- c dec+hm6oh cpea5 3v b. Explain.

Is the frequency of a simple periodic wave equal to l1/ej* kgm/bj4rbj o 4unq;s+the frequency of its source? Wh/enk mrg1j4/j qbj+*s4b l;o uy or why not?

Explain the difference between the speed of a transverse wave vzyoi9/m0v *8z0q giotraveling down a cord and the speed of g0v *qv9o o m80i/yzzia tiny piece of the cord.

Why do the strings used for the lowest-freques1nn(0 p 7 a0efd8teowqk o;x-ncy notes on a piano normally have wire wr ;a( kpw7 onoet8d-n 0xq10fseapped around them?

What kind of waves do you think will travel down a horizontal metal rod if you d7n t-8nv: 8n:plrtwc4sdxk7strike its end (8c t-lrkv7 wn4t7:n dd8n sxp:a) vertically from above and (b) horizontally parallel to its length?

Since the density of aib mm.-7bafvy i z/8 ip0rt:cx*r decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperatur-ftbrizv/.y cm0 7:mbx8p*aie?

Give two reasons why circular water wavecskf;djw84w 6s decrease in amplitude as they travel away from the 8;w4 d csf6wjksource.

Two linear waves have the same amplitude and speed, b-b h,xjv a437 )wnnb/rrd7rf and otherwise are identical, except one has half the waveleng / ,xfb7r4w3rj)bd-rbav7nhn th of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord yn mutl-cw/ l+l yu,rv4t96* bas in Fig. 11–33, the frequency does not change (althouwnb+l lt,ymlc*t y4 v/u 9ru-6gh the wavelength and velocity do change). Explain why.

If a string is vibrating in three seggh9+sho:p30 jhl5id y ments, are there any places you could touch it with a knife blade without disturb3 sljg+o09p hy: 5dhihing the motion?

When a standing wave exists on a string, the vibrations of incident and rg;j:)c8 nw8f m*zvjeneflected wavescv8ej znw*:8mg;j)f n cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy wmcz65 s,aty3nptmvdq+*hu :.b3 aoi 9as being transmitted from one place to another, how might we den6v*3h ymds,o5btu+qa ct. a3m9: pzitermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, wry uxn*ac2.cj yebhv1+ /-. dghat is the total distance it travels /g.ry*c+ej1.2chn dyx a-ub v in one period?    m

  An elastic cord is 65 cmswl(ugj.m du9hm2, 1n2xod4 nd8jd y6 long when a weight 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 of thisungx.d sd 92u my6m, 2(48 hn1olwjjdd elastic cord?    N/m

  The springs of a 1500-kg car comp4fdnj5 ekx 5)f,n2d qpzq5zk9ress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over4, q dx dj2k9nf55pzenfz5)q k a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretch jq,uxlc 7+yhffe0 w39es 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness co 0,wy 97hjx qfef3+lucnstant $\approx$    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 masssk *.q rn.e(w6upt+y3l 7ahn4k (sjic of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from it tunqiwn4cperks. (jls*+k(a7 .y 36h?    Hz

Construct a Table indicating the p1 ud**habc,1as atj( gosition x of the mass in Fig. 11–2 at times t = 0,t d aut*1 ( gh*bjs1c,aa= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibrates predot fbz ,:qjhxj++2izb4minately with a frequency4z h+qj,z: fb+2 jxtib of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vi6nw+a u ig4epq0rt,pl *bddm9w: 5s9qbrates with a frequency of 0.88 Hz. When an additional 680-g mass is a pqard+sw4e m*,g9i6p5b:n9 q0twulddded to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 timep- :5 dm7ccm:vh gy0o9u8ppkw2r s9t ts per second with an amplitude of 0.13 m.cpo9 g0dk9v:rus 5-t:7hp8 twmm p2cy 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 speed of a SHO half the maximuuv3g+n04mfohl, qm k -m valu0mhg,3nm -4o+f kv qule?$\approx$    A

A mass attached to the end of a spring is stretched a distance) /.xqvsyi v4d $x_0$ 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 ve4fcve(a6z k-u -hpd/srtical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again? z -uhcpe(4 /afsd -k6v   s

  An object with mass 3.0 kg is attached to a sprivyv rvf ))*hh7o etdw *2kpj2y uy6kwc477 1meng with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from itp 7hyv*2ehtkvwc ur )4d2y6yf7m)k7 v w*o1j es 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 to compress the spring of a toy popgun 0xix6myb; t f+v ,pux.c)v9fd*5l*i p d.200 m to “load” a 0.180-kg ball. *im 6, )lf.xdp ipbv* txx+vcu95y; fdWith what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to onem6dtxc1k:.4zc c x1my end of a spring; the om d 14z61kcxtxym:cc.ther 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 the equa byri7n5 92k2u *melrydskan( ( ihx;)tion x = 0.45cos6.4t where x is in meters9s2ny( rky n d 25b*uk;l7aehi )xi(mr and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is t3c jc x s//-9r8r2gzvako0*ye zxk as)he energy of a SHO half KE and half PE? ± rek2*s 0 r v/acy)z3g- 8cz9xjaxo/ks   A

  If one vibration has 7.0 times the energy of a second, but the/+1ctcy. gy:qhq9 al rir frequencies and masses are +tghyqrcycl:q/ 1 a.9the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanginb akt5cggr9;c.z kxoj ;16c -kg light spring once every 0.65 srgo k -1cc5cz9j6abkk;t gx ;..
(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 twoch0i c.xw2u 148tqrsj identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration? chtucixs02r8w q4 j.1

  A 300-g mass vibrates aclqrcci.wr ;//cording to the equation x = 0.38sin6.5t where x is in mewc;l// irq. rcters 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 and 2h*s e,mf lg9g 9us24xeun2mhB. 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 h 8 ipc48i:za,w* swqtssb(t4(k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determinas*8hi,8 pis4wswt4tb(c z q:e
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with an amplitr5nd74e fqx*u0o3qma ude omf0 q 3oq 457nr*xdeuaf 28.0 cm when 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 spriq+4 ;x;r6 rz/phg(o;hxwn lxcngs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg zedb 5 *y3o6iqblock attached to a fixed horizontal spring whose spring stiffness c*qib e56yz3do onstant 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 m4b )t7e olq1wc3gsd8oass 65.0 kg jumps from a high bridge. After reaching his lowest 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. Calcl)d1w 48b gts3q7eooc ulate 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 6yz9 n 6s,xg6(j ua+blm0 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactlm erw7zib(7 7 uyizjh u30:jw.y one swing per second? (That j.e0wzzbmy7 ri(37w:ihu7 uj is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where t:gzf-ob p q*6ghe acceleration of grzq: 6*o-gfgp bavity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lonb-231rm dho) b s4 (img9is2qoqbn dw6g
(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 m)zo(. vsta 9y3fb)j1l 2l c2 xldjuzwf)qa07pendulum bob has a mass of 365 grams, and it is rel2 z.v c)f o)y(0b93tjwalzjx7 ms21)dfql lua eased 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 m+qk7bo o9o/h,,qsjrixet9;a length of 0.9930 m. If the clock loses half a minute per day, howob,ikm he,9/+jqsro;79x toq should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed 0gjy;b /qbny/$v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released from dk,8 - ,d45he rwri kn*cmeo0erk0c4, orr d*ek-8mei , ednhw5est starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every 3.0gg gzou 2 :lkh2:./xrc s. He measures the distance between two crests to be 6.5ulhrg:gxg z2 ok .:/2c m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz ar5(dr mmq )va2nd travels with a speed of 343 m/s How far apart are the wave crests (c mr5r(qd 2)amvompressions)?    m

  (a) AM radio signals have frequencies between v1zrslja;0zd 2rh,5(x . a()l a tlqvc550 kHz and 1600 kHz (kilohertz) and trz clx,;rzd (t0 rj1 l)5sav.2a(hvq laavel 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 longitue0n /ygilo 9ro-,a -kzdinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elasticu ,n6p- n9) 5tnajq j5o.iqmms modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factuao 5)6-mtnj qn5s.i9,jp nqm or?   

  A cord of mass 0.65 kg is stretched betweea;jnlh dhop/z0:mpf h s0(i ;+n two supports 28 m apart. If the tension in the cord is 150 N, how lo00i;aslpd:o mf +pzhh/h(n j; ng 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 6aba--e svci4a steel cable 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 16v64 sbca --iae 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 the surface of the sk6k:7x nv/tz/)c7-cf ptxfss ea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is thecvff-kn z6p/x/ )7 ctxt:ss7k ocean at this point?    m

  P and S waves from an earthquake travel g4 )4mg 0c r.qti( r;sahp3gktat different speeds, and this difference helps in locating the earthquake “epicenter” (where the dis0ggqa3 p c;.ksritm r4h )4(gtturbance 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 b,l0s1dfj gevt(u nb1o;q; : njy a sinusoidal transverse wave. Assuming a fjlnju q;0o t1fvds;e: b(n,1grequency 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 with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, anlcwj,)xqujj 5px2 m 2-d (b) the amplitudes, of an earthquake P wave passing t xm,2ljq)jp j 25xu-wchrough the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an eartt2 *im 8jmabhb-y2sbl1 v2t4uhquake wave passing through the Earth is measured to be i8ljt m s*a-t2 u4bbb2v2ym1h $ 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 :7 iqunk2ntntg.x s67 the same frequency travel through the same portion of the Earth, but one is carrqnt . 6:7ng utikns72xying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but one td.*wfiiw5 ygs. /cop3ransports three times the power of the other. What is the ratio of the amplitudes of the two wavess. 3wdp. *wof gii/yc5?   

  A bug on the surface of a pond is observedgr) f(rkt94/ wirz7hkaubl(, to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If thei)7 r,rzhtf (ka kwbg u(/l9r4 ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in sb7l.oh. xm/vfd7+snFig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of th7o7vx/dns..b+s hmf le 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 Hzxqu*w-9q6 pb zwlip 7d4p;g) v as its fundamental frequency, what are the frequencies of the first four hapl 9z; wux)bp 7qq-*piwv6gd4rmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfuzy) qn /)ndv;ingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vin/n zyq uvd));brates as a standing wave.)    Hz

  A particular string resonatnud7*)d gu / hs63+dhott k.8ec8ekqles in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it willq t s8k3 d*keh7d6t)ou/ hn8e+ gcdu.l 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 standing waves8jv)5 6ajowi)f6y f cggmz 2f* is j ca5)z*f givm) fw6g6j8fy2o 475 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibratcepmre);rw ( ( a1oq qsm8e..cing string are 280 Hz and 350 Hz, what is the frwee. s cqrmr8ca.mq)eo1p((; equency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass o2ek(x tn1y: nsp+w7nw3g8ta jf 3.6 g. The distance from the bridge to the support post is L = 62cm and the strin pn:+gwt 3xk1s w7a8 tne2(jnyg is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but idr+o 9d /f xei9b.4co6qu2 ndit is measured t6r d9duoeiqc 9fx +od 24b.in/o vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to56fdawak0f+c 2 ztmunh y21i1q (/wl h vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be m 5fz 11utw 2dnw0hklyaa6c+2/fiqh (changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude me4focp7d 6 6idnc96zvrchanical 60-Hz vibrator. The string’7d 6io9f cdrv6 4zc6pns mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pul+ir-+w k2 dtx -vzzp2z5gu w*tley. If the hanging mass m is fixed at 0.080 kg, how many dzwtv25pu-i+x*r- tw k2 +gzzd ifferent standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the waw7: fb 53pdrziter back and forth in a tub at just the right frequency, the wbi:rf zd35pw7 ater 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 water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the ;xmwu/vsw1ez:2h iqo9ldp 84 Earth between two kinds of material. If it appro ;uod4x8zslw p9wq/hevm i12: aches 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 vel 7fzbn v6r pc4q:42tksocity changes from 2.8 m/s to 2.1 m/s If the ip 4k 6rqs7v fn2bz:c4tncident 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 of cold, dense air. Ip151k4te1k x13 ;:nlamqxaj qtsz0m s f the sound wave hits the cold air interfaxtq3epm :1qsk 1a ;11atz40jskmx 5nlce 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 typesrjd :i+h 6qe* b/hln3a0uvq3n *aa ogd75qf( d of rock at a ui*7qn0 qb5d3av/3dd6agf:(e ol * jhh+n qa r38 $^{\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 diametexje .9ilm+bso5 vq*o ;r. According to the user’s manual, the dish has to be pointed in the direction of the s m +x9jql;*ebv5o.iso atellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 kmylu0 loph z o3o:n;xdsyj600;/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 h js :y;o 0oudo lp0n63yz0x;lto 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 kN/m Findlfof;peq(o)3pf2 k 6blw2mw; the maximum compression of the bumper if the car, with mass 1500;pb 6f w)(e;ool f2fk2m q3lwp 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 bp ,td 5(u4xbsmelow, which stretches the net 1,b5x(t 4s dmup.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 tncqa6 1 qb5 x,o:g)kxmhe end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the 5o,gqnc61xb: mka )qxfrequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speedjxc 7+w*dde*n of 22 m/s (Fig. 11–54), compressing x ne*d7 w+jdc*the 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 l6l: bpjj)ldvl(; do8(diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves inj;jldd6l)l b(v 8pl: o the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of.1z iu.6.uy7qj ppf v35thr,/cgf dz h a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be c zf5vyuf763q,. . g/prdh1 phztiuj.the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650bw:u+d) ; evqocos7.40t where x is in meters and t in seconds. Determinu ;bdq:w v)eo+e
(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 it accelz a;rec4 b9a8berates at 0.50g (a) ubczr48aaeb ;9 pward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft 7 xnhrvsh8t1u*h* a n*gu,m,v, it sink,xh,ra8un*gmu *vht sv1h*7n s 4.0 cm deeper 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 tunedrwir j3t-s5ma:i8p)q4i,gbh kki, w ( to play at 392 Hz (G) and 440 Hz ( b, 8h5gk )jtw(4wrsarq m:piii3,i-kA).
(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.f4fiu( a)b-vf.leio4 11–33. Determine a formula (a) fu-4f eo)fl4 va.(if ibor the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of u7g ;4y)l,+okh kf ylza))czxeach prong moves 1.8 mmc )kkla)zuxzl )g;f+ 7 hyy4o, 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 oscillac*jv um/tw nd;n /w6t z-u)5getes with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which thwetv ncd/*5 6mt)guj zw /n;u-e 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 “fr ijm:)j 92iwufee” 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 resonant vibrations of such a9ijwm 2u :ifj) string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each on9v)jtob9/ydgkc *9xe e-way swing takes b)c y9v9/xe g*o9kjtd1.000 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 mta 8/md,*/bkmcxij)the vertical direction or can swing as a pendulum od8m,k/ cjm /taib* )mxf small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A p-38qmx- 7/u00j i i8zu0kggyc gebryt(vv 1co ulse is generated at one end, and 20.0 ms later a second pulse is gcierzu/3bq087y-jvigt ux-1vk(g00ocg m8 y enerated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended frot jq y7evj9.-8rwxcu (wi*s -ovkwo.,m 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 maximvq.weusyjrkw oo x (,-w.i7tc- 89jv*um amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 1c jn j :ucv-i)(2ueao22 m long and has a diameter of 6.4 mm. A breeze sta)i a ne-2juuojc:c( 1vrts 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. 11–58 (which also gives1-ctagibcn 8- the dimensions of the block). Y-ic8b ta1c -gnou 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 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz