Give some examples of everyday vibrating objectmnu,g j 3q tx02t3pdks fas.01s. Which exhibit SHM, at least approxima0 tjp.a33dsftgm u01xkn, 2sq tely?

Is the acceleration of a )y.9lwe4 vmjg) tq9uisimple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile /q5 (56zthjvz oodo; yengine is approximately simple harmonictyov z(o6 o/5hzd5; qj.

Real springs have mass. Will the true period and frequencyr;5bi(fp) x4 j+cxyzu( ev s,s be larger or smaller than given by the equations fop( e+c(jfzs i,5br)yvuxs;4 xr a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHOdyj3q i 6;*)rjb zf0lff: 2qbzbw73h e)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is 2e*rjk,.es rgx *0zb hs/3etu released. Describe ,er. r2x /zeeusjgt*h k3 bs*0the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain orun f -c9uxb/p+ lose time when taken t-xu9p nuf c+/bo high altitude? Why?

A tire swing hanging from a branch reaches nearly to the groundpq3 hwi4lp43 h (Fig. 11–48). How could you estimatepi3h 4 wlp43qh the height of the branch using only a stopwatch?

Why can you make water slobag-eaqxj70 )02x ds*,fj ngwsh back and forth in a pan only if you shake the pan at a *s0jxq ngaa-2gxd70e ,wb)jfcertain frequency?

Give several everyday examples olc1gku 3ks3 b+f resonance.

Is a rattle in a car ever a resonance phenomenon? Ew9klc;g q3sb,:m le t5ky1kqx +ff6l/xplain.

Is the frequency of a simple periodic wave equal to the frequency ofmlnnlw :; em.)k5zcm7 its source? Why om.;5:) neclm klzw7mnr why not?

Explain the difference between the speed of a transverse wave travec:p r) i-)t 3n2wuajblling down a cord and the speed )w3:jan - l)ptb2i rcuof a tiny piece of the cord.

Why do the strings used for the lowest-frequencgak4d95k+ veg5 )vsbqy notes on a piano normally have wire wrapped dqev)k5 s+gk94gbv a 5around them?

What kind of waves do you think will travel down a horizontal metal rod if you j lq))t3 2pkknna.on*strike its end (a) vertically from above and t )lnk).a 2njnopq3k *(b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature,cno c+lg5lusoc:*eu 4 sha3*5 but the bulk modulus B is nearly independent of temperature, how would you expect nauc+ 4cecslu* gsh55l:3o*o the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitua1jh. pue4f0h h5ejvh3+040 xrp ukurde as they travel away from h0je10pfj hpu v4+rr 450ux3hu.ak eh the source.

Two linear waves have the same amplitude and speed, and otherwise t-.yq ,v vao0ware identical, except one has t,aw. yvvo0-q half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord f5hw6vx zfh0h7+m: jhpe8al/ as in Figff7 :p/ h hx6hz lw+ae850jhvm. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibratii+xl*uw 1s3f g lxf70y,bckf3 ng in three segments, are there any places you could touch it with a knil*+3 ly ,sf0 x7gxfc3 fukib1wfe blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident an37hnmd z gxjajc 2:d,1e4swt, d reflected waves cancel at the nodes. Does this he347gn ,,2zxw sd jd:jacm 1tmean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mi:.fw)swho s7 )3gfry ight we dgif)w3ro h: 7s.swf)yetermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance 7atyh3(2qw)u k)ejy e7av cy 2it travels in one peau)7h ( ytcw7j kvyea223eq)yriod?    m

  An elastic cord is 65 cm long w,g jm45g3el esrp/g8j hen a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs epj5g4rjslg8g/ e ,3mfrom it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into bxkl;s k x,fu3/ezwqnn2h 0jg ,.d:rn0dny 21the dr .skxbdej k;g22/rn:3h,y z nq1nnxd0ul w 0,fiver’s seat. 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 20rzc7d,7ew1- -s) fs iusqek r.7-kg fish hangs from it. (a) What is the spring u,sz d7-sikr ew7-e0fsc )q1 rstiffness 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 vibraesg:7 lu );lwla +u;eutes with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0 uel+; lugas;e:wul 7).38 kg hangs from it?    Hz

Construct a Table indicating the positf+f3,rykh9bc1l(x ow 3 4 hwbhion x of the mass in Fig. 11–2 at times t = fb rw+xlo1y4hf9h,3(3h wckb0,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 0.25 g is caught in a spider’s web. The web vibrates predomixl 4xpbyf .j3e25qt7 anately with a frequency of yxeqpx2fj3b4 75tl .a 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 sprirnbx+7/oc3k)k bd3pd.5 qc fcu(wfsw;yc 3)qng vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to furcx;7 dw3(wc p3c+3nckd sqkb5).fy/b)o qm, 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 times per secw ke5r5 siayjx7(.xbc y0;.oaond with an amplitude of 0.13 m. Det.wcrab ixo5k5 y0ay7;xs(.j eermine
(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 maximunr hu7+k ovgnp ssu0,:; jns:1m valuhos;gun 1+ srnks0:unvj:,p 7 e?$\approx$    A

A mass attached to the end of a spring is stretcy+oql(c (xhi4b7kpe,hed a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0:ohvdv0 e(/ qj.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium posivdjqe0h/vo:( tion again?    s

  An object with mass 3.0z6 0kjgfdd0j2ki:1k 8n)wg21 fqwpb q kg is attached to a spring with 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 with a ): jwkdk2zw0f1g0pfb iqn6q 8 d gk21jspeed 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 td- d:vh+-cgtzoy popgun 0.200 m to “load” a 0.180dzchv - -g:td+-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horiz/ss s(cm,y; knuxln2p .j9lt 9ontal, frictionless surface is attached to one end of a spring/ cx92p slst(mu9jn sy n,k;.l; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 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 equation x = 0.45cos6.4t wmy 145jj4zdu0 j8h ij ,4egwkjhere x is in jgjh,4u40m1 zjiy 8 k5dwjj4emeters 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 equilibr 5i 79-p umsp*pf;t tv ls9rqoc.8vim0ium is the energy of a SHO half KE and half PE? 0*57p9 .f l8vcp iu; msp -v9titoqsrm±    A

  If one vibration has 7.0 times the energy of a second, but their frequl 04l5uq6gzy5wl mah (encies and masses are the same, what is the ratio of theig5 a 54 ylqlhwmu(z06lr amplitudes?   

  A 2.00-kg pumpkin oscillates fro;3 .uas :ejaq7:5rj 5vdjqbjkm a vertically hanging light spring once every 05; qsqkej.jav 5ru:j: 37djba.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 tw+ wz4d2jv l f6bq5x.om:a5vnto identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency ol5:+ wvt 4x52azmbjn6 qfdov.f vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is ee xk+wttr9,ta3*z l 0hu*i3 iin meters 0 ailkr+9zte*th et,33wi ux*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 B. For each, f j(+wmfsx6u3 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 oufx;wsz 0 1x-hn the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass a 0s xx-z1hwf;un 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 constant 305 Nfxi;w/nv.n697yxy8rk( qh 79bwj1iaa r; obm /m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with po(rqani77 ;wvx6b. bj ;h 9 omynw9x1fa/yirk8sitive 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 spr *3sz+6lynui 8/5 wiwz9qccvoing stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal spring wq *8p-ibnp.ev i 7i u*tae7pp2hose spring stiffness coe*. pbap-8*p ieqivu i77ntp2nstant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After rw2+hbvt6aa(vm w9n0 civzs j: ,hud; ,eaching 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. Calculate the spring stiffness concjahhmwtv b 9d2,v (0u ;wa, +zsvni:6stant 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. W b5tntfqapf5i ./7,alvj - kg0hat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it ibm3 lsv* *e: kdq.2rbds to make exactly one swing per second? (That is, one complete*em3b2s qbvkd.r:*ld vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What 6:o5m k0pmvyu qg:1 nwis its period on Mars, where the wk :nu1 og0pv:mqy65m acceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulu11 i bxqo4o84y xh*bfum 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, (w*u3ev z:afx the pendulum bob has a mass of 365 grams, and it is released at an anglv3fawu z *x(e:e 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. .bzv ;c czndfw.2ef*:9930 m. If the clock loses hc. nzd;c zeb2fw:.*fvalf a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spg0jhpsnn*7rs+g)yy 7k+4 jbbeed $v_{max}$ 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.h ur:h ;vu2ojbiw8/.v5 Hz. At it is released from rest starting at an anglui2 jb :uo/whh.vrv8; e 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 pas:xgyr/t03gr zomz,-w s the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travelingw30mg o ,rr/-ytzx gz:?    m/s

  A sound wave in air has a frequency of 262 Hz and pm u z.f0a+p/4f:r5 d-vx rysgwx* ro2travels with a speed of 343 m/s How far apart are the wave crests (co f/w.zr :+p2rm-y4rxuoxpadg vf 5s*0mpressions)?    m

  (a) AM radio signals have frequenciesr fssx3f* a/;/yzs 7ov between 550 kHz and 1600 kHz (kilohertz) and trss7/ *3 oa;rffy/xzsv avel 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 longitudinal waves in .oh3z /nb ezr0
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modul3:wnxl9in v -7*xf fqn2j4xuius, but one is twice as dense as the other. In which rod wivuq3 jxfn :xx*nnw7-29l4f iill the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between t ck8fkg. cissbd8dq(,6cbq;l b 5)1d nwo supports 28 m apart. If the tension in the cord is)q1 ib. blg c(d8sknc;d8qk5fcsd b,6 150 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 * dkobtu-;-eta steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its rbktt-eu d*-o ;un, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. He hrfskmh) 9;fb;hz8fw b7dz4wapro, ;5ears the echo of the wave reflected from the ocean floor direcbhf4r ;ffhka9 zb)o,;sdmw7 8r;p 5 wztly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at diffeicauklqkb4 4 ) 8*g7*2o hdkvxik(z,rrent speeds, and this difference helps in locating thbx(kva4c,* gzk2 ikkd)r4i*lo 7 8 quhe 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 w+/-kvs z+ )o4hvfxxpxave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frevx/)4 sx zfo+hvx k-p+quencies), 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) nu51 7bvvjz3, d1botzthe amplitudes, of an earthquake P wave passing through the Earth and detected at two points 1zjv7b 11t ub onzd,v350 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth 5jrt 901 hrtv hkcxp9*is measured to be rvt *kth 9 hpx0591rcj$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same poct/ja.n;ra3 ah :gaq kn- *t4wrtion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of tht/gtk.rnhqna;* a34-aa: c jwe two waves?   

  Two waves traveling along a stretched string have the same frequency, r- /s1,w6pgu r(sbdz-o 7okxhbut one transports three times the power of the other. What is the ratio of the amplitudes of hs g-/uzd poxr -,o617b(kwrsthe two waves?   

  A bug on the surface of a pond isgf1g+ksurav8t,s l*1 y( ydt/ observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. Ifrs/yv,s(1g at18dgu yt l *k+f 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 l wu7m19cqrmbzj3(p: x(rn5f each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the en1(rcq9b3 7j5znux l(mrfw mp:ergy at this moment?

  If a violin string vibrates at 44w 36kf )je9-qkpi8g8b uz0c xg0 Hz as its fundamental frequency, what are the frequencies of the first fo3c9bk-wu8)0i kexgp j6f z qg8ur harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. A q/q /udnio( 9,nh;2oz;8dw4omcndrj t 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 vibrates as hz (joun4wodo/rq ;nd2 i/89q ; c,ndma standing wave.)    Hz

  A particular string resonates in four lu/r40v f3l8pd insgt:oops at a frequency of 280 Hz. Name at levl4 /rst 3uip0gf8:nd ast three other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves onukqt. y;6xex)i3 o rn0 a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent n ;.nktrioxue x0yq )63odes?   m

  If two successive overtones 0b+b 0qlrnn7 fof a vibrating string are 280 Hz and 350 Hz, what is the frequency of blb f 00rq+n7nthe fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from tvu;i c)fldl+(he bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequenciel )+uvlc; (fdis of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate a vdh .cx+z/sf4f3s1 xx6 hto)st 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shoulxth.fsf+xss/c xd zh1)4ov 36d 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 stringz)zgl rvpyf q7x/6zr1bs i+/7 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 f+x/ l7zpbrz1siq r/z7g 6yvf )requency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mb1,hoy9 z(xl zechanical 60-Hz vibrao z(9yxzbhl1 ,tor. 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 the string may be adjusted by moving j)wqhvt,2mvral(.atdf / b* 2the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L betw2va/a,*mvf. tqwldr)t hj (b2een 10 cm and 1.5 m?   

  When you slosh the water meha: ci*97b,ckg 0t -pur*)c6b jpym back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at thry:*6 c)9,pci ckbhtme0m*bpu jg a-7e 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 bouiz)e dmodqa u 14-xcup53ah;8ndary within the Earth between two kinds of material. If it approaches the boundary at an 3 hd)x4aa dp;5u8c iqoume-z 1incident 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 1c;w l5+kokyryuz,d(x-xvq 1a ylc 2/5ft ;zh“shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make /2x;yal1f5 +zcd 5yw,k1 trq -yv;lxouc( h zka 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hitsgx q19e lq3q l*kf+w ak2),lja a layer of cold, dense air. If the sound wave hits the cold air intlkl qq9kef)alxajgq1 ,*2+w3erface 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 strion 00 od5vne6tkes a boundary between two types of rock at a 3 60otdnov0 ne58 $^{\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. rjb:6yjk 5id/aj6z. z According to the user’s manual, the .:iy6zr zj a6dbkj/5jdish has to be pointed 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 750 km/h travelsg3 jfgh:n a s(t86bdl z(4as*3ro5bjk across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boab8rj5gsn:(bha k f6gozs*4 l3(t3j dats.)    min

  An energy-absorbing car bumper has a hf;zg6ki + )1mj 07jcwjh6bra4er rw3spring stiffness constant of 550 kN/m Find the maximum compression of the bumper +6kw j1jh0ir;cgba7r6f ehj4m)r wz3if 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 1rnf6o7g )yc v;dz +rk7 tqm1,n8 m below, which stretches the net 1.1 m. Assume that the net ofv71;7d+myrnz6,qr ng )kct behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass09;ocgi ;paq0 qu+ ltv1;gobh then falls 33i;aqc+lqh; tbgv010p ou9 og; cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a h q/i;k1xh q6j bz.2b;cety ew vi,0j5tuge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stkb hq vzj,5exb 6 qi2;j01cytwte./i;iffness 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 ri3 )hf22 qw0qgs/d9 rijemdnv8x -op.eght pace of about 1 step xw)e/fi-qrspd9v 22 hngq. dem o3j 80per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the cjhav (4n*w* unenter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted? *(u *vnw4n ajh   Hz

  A 2.00-kg mass vibrates according to the equati+ltc4o( h,)jf-qi qbi on x=0.650cos7.40t where x is in meters and t in seconi q+(l)hqicj4-ftbo ,ds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its freq4mh vln e711yxwe7/ oiuency if it accelerates at 0.50g (a) upwardv7ei /mw71ylx 4nh oe1,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the rar;g 1x7 ptfbp1z gk+y+ft, it sinks 4.0 cpt 7kg +x1zyf;r1p +gbm 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 musicafix 7bb*u8s* au, vd9 w+:sgmkl instrument are tuned to play at 392 Hz (G) and 440 Hz (A). 7isgbv* +:skum xad8,fwb*9u
(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 downnir)pnz ;,c)a5yhvf 7 the stretched two-part cord of Fig. 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 frei a ry)n;p)v znc,7hf5quency 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 each prong moveyuney-t8q5vcd ,z c 1:s 1.8 mm to either side of center. Calculvt:ecn zy51u,8qdy -cate
(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 hawce -z 6ou(d- wew4;f;hvy*d brmonic motion of frequency 1.5 cycles per dw6ydw-wbvu;;o zf h-ce*(e4second. 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 attacheo55vicu +a:ta d to a ring that can slide without +avico: t55ua friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — .mxc2 c) plqq,)ce-zgeach one-way swing takes 1.00c))cc qe g, m-qpz.2lx0 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 th7p, of(v /8ia utvbcl5e vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swingsc,5upbv 7oa/il ft8v(, 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 /+nlzn :qr )a6gk6cilstretched under a tension of 255 N. A pulse is generatedqna6:g 6czliln )kr/+ at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended f3vc,-+aqg qo arom 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 stay on top of th3a- gqoq+va,ce block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cabl*9nhrsn5rag2frl; ,b4e- inn1k zp r)e is 22 m long and has a diameter of 6.4 mm. A breezernbs*h;zrprakn g-r, 1)iel 42nn59f starts 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:4zw nqg k./7s8unems shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and thezuns/7s :q8km.ewn g 4n 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