Give some examples of everyday vibrating objects. Which exhibit So2n7xb(z kml6u:x.kn HM, at least approximatel(kbm6n kuo7. zxx 2ln:y?

Is the acceleration of a simple harmonic oscillator ever zerwi,4ji yui3doh0i t(7 o? If so, where?

Explain why the motion of a piston in an automobile engine is approxi/a6sn. 1l pvp6u)b1j 8dzy )tsxx2sakmately simple harmonic.kynx1jub pdx/a8la.zv 6 ))ss6tp1 2s

Real springs have mass. Wik2e be;v*d6i x5/q :afz;z cp:y9o mudll the true period and frequency be larger or smaller than given by the eq:5u d 6* kvq ;dpeieyxcmoz: ;z/ab92fuations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simp.b fo8afz n8/sle harmonic oscillator (SHO)?

A 5.0-kg trout is attachegto0y /7p:2r( a2wp8rdcdbs id to the hook of a vertical spring scale, and then is released. Describe the scale reading8 sdr7c/ dp2p(g02yrw:aio tb as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time wp/gm nb9-)*h am b*gzehen taken to high altitug bmz*bpag/e -*m)9h nde? Why?

A tire swing hanging from a branch reaches nearly to t5 /dz *le *nl 82smbuwevub)a;he ground (Fig. 11–48). How could you estima; 5a8nl 2bmelwuuds)z / vb**ete the height of the branch using only a stopwatch?

Why can you make water slosh back r 3h5 anyn bcd xwg9)m9izfegrc,u0/,j08j-g and forth in a pan only if you shake the pan at a cer9d gr0xc,r9n/wg0 y3)5ng8 jah ie-jmcbufz, tain frequency?

Give several everydafi-qvc(l* 9 * ihhx;f)-zpmkj y examples of resonance.

Is a rattle in a car ever a resona, a -id(an(p zd) jb3u07 kyt9dcbmoc)nce phenomenon? Explain.

Is the frequency of a simple periodif it; )ybr*y)vc wave equal to the frequency of its source? Why or ytbf) ;yi*v)r why not?

Explain the difference between the speed of a transverse wave traveling de7gbv. ), zej l.hexj rozff3;3j/:wuown a cord and the speed of a tiny piece / zjrf)bu :;.wxl3h foe 3.,egjezv7j of the cord.

Why do the strings used for the lowest-frequency notes on a piano novynxw0 3imboza2/z2 8hhpc4o85vh 9 yrmally have 82 cvhywbo ih /5z0ap2hyo x39zn84vmwire wrapped around them?

What kind of waves do you think will travel down a horizontal metal rod 56 k) slx7ebugl dp,b)if you strike its end (a) vertical6l eg xd,bulsp5 7)bk)ly from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the bu f:2ia303d ul7m;byk;he+yhlat1w oulk modulus B is na03dla f2; ;1k bhmeyotw:+u7i 3hylu early independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease4ibh 6h;to tn, in amplitude as they travel away from the souh6t; n4 obi,htrce.

Two linear waves have the same amplitude and speed, and otherwise are idr :wxz/ajpxkfznt)s/81 0 c*uentical, except one has half the wavelength of the other. Which tf npwt/s *k)8xczu/j01 az:xrransmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two secemfm:yoh2dq-p4 z qjp .rn20 .tions of cord as in Figqfr2 .qo md z-pje.y 42h0pmn:. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you c0biuqwwr6l v c6xi3rp4s1-g2ould touch it with a knife bladgs cpi6r vri1 w6 04w-q3ux2lbe without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident 0h.wviu6shv gvuxs; 2 jp)d88and reflected waves cancel at the nodes. Does this meux2s8 8.g)vw d6huvj ivp0;sh an that energy was destroyed? Explain.

If we knew that eneruo 7,m9eopqe5aq if9.c9jyu1 gy was being transmitted from one place to another, how might we determine whether the energyy.j c9u9q7o eumfoae,qi 5p1 9 was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the totuz qa6m* (p+qhz-rm*wz1 bo ;sal distance it travels s-w +b*16mz ;mo zuaqh(*rpqz in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N han kf( w8ibhb:i)gs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic coiibkw) 8fb:( hrd?    N/m

  The springs of a 1500-kg car cby si lftp:+ze/ff30b 1ksg2dd:.b 5oompress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibratiop d2:+:fi 3fbt sb0/s.kdog1be 5zfylns?$\approx$    Hz

  A fisherman’s scale st9)eri4c f q:nnretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness n9r qn )4:icfeconstant $\approx$    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 ctj2ple2d (;b with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it(;eb2ljcdt p2 . What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table ind to+1+ttc v+f)8d tiigicating the position x of the mass in Fig. 11–2 at times t )c ovt+i tt+tfgd+8i1= 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 0.25 g is caught in a spider’py4sn2x)0nw)l hmal a/c ov0uyh )y2 8s web. The web vibrates predominately wiv8sahp4lnowy chl)y2/2))0xny 0m uath a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency q; fh7rmso..s9dze x c9mu718v2dqg w of 0.88 Hz. When an additional 680-g mass is added to m, the f.mrx779q eo qg 81z2fvmchdws.u;sd9requency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a s7 s k1zeguyg nz-z8x22pring vibrates 3.0 times per second with an amplitude of 1 2zyu8xe gzsn7gk2 -z0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equian ec04t9 (hralibrium is the speed of a SHO half the maximum value?(aceh94ar n t0$\approx$    A

A mass attached to the end ou0yk4b : eor8pf a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretchm19c;l d d(ulyes a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and rele mld(ydu19cl; ased, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attli po tyve 2d.gp*6d..ached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m foti. .ep6 dv yd.g2lp*rom its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a t vu*+*w7mr ./ ltqqmn x*9yohboy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave ttxm9m*yr7oqn*vlqhw/ bu.* + he gun?    m/s

  A mass sitting on a horizontal, frictionless surface6vt39wl1eo2f4 kyg jw is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spvjl32w ow 1yt6ge4fk9ring 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 az 6f-,hgljvd9ccording to the equation x = 0.45cos6.4t where x is in meters and t is in sh6z g9, fdl-vjeconds. 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 the energy of a SHO half KE and hal bd+.d3:pd6p a e 6yf.yzm;hrof PE? ey3rdfh 6:moy d6bdp. pz+ a.;±    A

  If one vibration has 7.0 times theyq8g54s 5pkzj 4ew5cu energy of a second, but their frequencies and masses are the same, what is 5eszwy pcgjq 5454k u8the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates fromf)naqg ;2.tl o a vertically hanging light spring once every 0.65 s.natq 2 )f.;log
(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 s2 euwyo 7;hvs53nivr, 2 kfvj+upported by two identical parallel vertical springs, each with spring stiffnenoy r vw2 f7v2,h;5 jv3+ukisess constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t whex p/)(e1ze;wa m) 5aalsu je:hre x is in meters and t is in seconds. Determinlau:5axea 1/h ez spe; ))w(mje
(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 ixw-a lp 4hxh4-lo,r24:egy0 lk0np b z;+cui 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 o(oz6xqau .;n spring (k = 124 N/m) is struck by a hammer, which gives the mass an n(;6aozuxoq . 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 N/m vibrate w/g/k /x;-xuh5ru 6oyasorfn ;(8 ysbs with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with poy8-gws5bhono; fs(ur u kx/r6yx//a;sitive 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, wimf+zncn rfc ny:od ( 7i(z90a *jw6pqyv;)ty6th 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 q2urpen.;w,95 wr kivei;6gys) lj6y 0.600-kg block attached to a fixed horizontal spring whose spring stivwey;. 5enkwp s;i9,2qg 6jlru6ir )yffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reac0fe m(.vsr k((bg1nrf hing his lowest point, he oscillates up and down, hitting a low point eigm1s rf(b0g (nke rf(v.ht 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 wwpo 19 o5r(vys. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simpl67qrgt(4 kjq7sn-ig0ls +na ve pendulum be if it is to make exactly one swing per second? (That is, one complete vibqvlnni t7s-k4j sga rg+(670q ration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s mkspwwpys/ij372;2 z on Earth. What is its period on Mars, where the acceleration of gravi3/m7 ww;s z2s jp2ikpyty is about 0.37 that on Earth?    s

  What is the period of a simplvo3m- 5hsx9() udw kszbb80q*q zciu,e 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 0.76 q* tvja-k yh x)m6zjj9.lq1y4b9rzc*0 m, the pendulum bob has a mass of 365 grams, and it is 1q .q9yzhjk* * cb-t)mrlxjvya9z6j4released 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 pe)1*ejrjt5ufz.cg * upndulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the p)zef1ju tp*.ujr 5*cg endulum? shortened by    mm.

Derive a formula for the maximum speed 7.7o.gkw,h ;atylatdz oi t85$v_{max}$ 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 ,t:,gufu5a .kptstz0 2.5 Hz. At it is released from rest starting at an angle of .pzuutak5t,,g ft:s0 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 b2 7rv u)6axuje,b.yryfkd)k2u2 cv ib y//y;iow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast adkix.a )u)yrb;,2j2kvr /buu iy/7 yvf6y c2ere the waves traveling?    m/s

  A sound wave in air has a frequency of 262mu 9kl k67om;v Hz and travels with a speed of 343 m/s How far apart are the wave creskm;67 omkv u9lts (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kaw b(hk( e,q-g wfp-j,ilohertz) and travel with a-akq(,hbg ,(-wj efpw 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,9uehc4p,bh avn:l 5f 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 twice as dege75 a jcce *sj6ucx,8nse as the other. Inejce jc678*ca5 xu,sg which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 eguoku-(2 )z i tpi.u0kg is stretched between two supports 28 m apart. If the tension in kiugu(i 02.utoep)- zthe 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 thdv*z6,;j7j ftt w)x co the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the;j6 )j7 zwf,tdvtx hc* 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 f2y c57otn3h wqg*7oz5;tf gdhis ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean aqo2gz cf y7 n5;3gdow7tt5hf*t this point?    m

  P and S waves from an earthquake t6k)x,(-m yrewb1t vyl ravel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the dist w6r ,kytx- yb1v(e)lmurbance 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 kxdyd) fkr425 x-nml(by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Se5dry d)xxk(n24m- lkft the acceleration a>g]    m

  What is the ratio of (a) th/*k mhtm3ue0he intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detect 0/ u*hhmkme3ted at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured tgic3+ u 3s8jyoo be soigc3 3j u8+y$ 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 y e: psftv3m k/m;*oul,8-cm.uwk9 t ufrequency travel through the same portion of the Earth, but one is carrying twice th f.umwve*otu8 pm9- /k: ;klutc3,msye energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequenc5*pyz o,m gsj--ucp)dy, but one transports three times the power of the -jp s*,gomcd 5-)zpuyother. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is obkpgfc77 (u s)gserved 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 the ripples dec 7fpgc(usk7) grease 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)ji4eb(5jj l9; rptoz, 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 ,i4zel j9 pbtro 5j;(jFig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, whatb ;r5;1 7qv0iqkmt lw l33huhm are the frequencies of the first four ha3b k0lt qh7m1r 3;5lwh;ivmuq rmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz w6hr6j*:mfc 7sh jft y9hen unfingered. 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 vibrates*hsjf9 6 c:mj y7h6rtf as a standing wave.)    Hz

  A particular string resonates in four loops at a rfunv4e )2py)kekf9 b/llw:: frequency of 280 Hz. Name at least three other frequencies at which it will res )p kkwr92nb:fluf: y/ee4lv)onate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a stringtc(i+bo/j m (p is 92m/s If the frequency of standing waves is 47ojb (p/+tim( c5 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating stringa;j)5vzkf0 acly; ; rr are 280 Hz and 350 Hz, what is the frequency ofra5zrljfa;v0; )k ; cy the fundamental?    Hz

  A guitar string is 90 cm long axns / skgf+;ube5nrd5- b.aw( nd has a mass of 3.6 g. The distance from the bridge to the supporbwx ae g+fks /r(n nb.5d;s5u-t post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string 4g//xv bld- hjis 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 frequend-vjlb /g4xh/cy?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposedc7y3w 0b qz ozfjl-v.1 to vibrate at 200 Hz, but it is measured to vibrate at fzbj-1. 7vc qywzl0o3 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attache45 zs0dxiju-u,jtvre x) l42 td to a small-amplitude mechanical 60-Hz vibvlt-ej5 0x2uj x,r 4uds)z4t irator. 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 lee e0ec:vt0m.xwgy ; ,syd*bk 0ngth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 eyxts0. e;wmeg:,0*vb0k yc dm?   

  When you slosh the water back and forth in a tub at just1aec z q8y3 yg*ng(ry9 the right frequency, the water alternately rise(r*yggy any39c1q 8zes 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 th u1rqw, witb2e1k5:kt *zwd 6pe Earth between twkwbt :zw1k u 15 2ditrq,w6*peo kinds 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” )q1q 0w3.)xl 4nka+llvk;seq au 2skn where the velocity changes from 2.8 m/s to 2.1 mqkxvn +w3)nq;k ule0lqslk ).1asa4 2/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 h/ d59ar;c azu(fw+tv4xa)woit hits a layer of cold, dense air. If the sound wave hits the cold air intera()duv+x4;wt 59z r/ ahfawc oface 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 k7ul em 2+e7cfa boundary between two types of rock at a 38 2 fme7ecl7+ uk$^{\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 dcivqzy 40 k;yq iv3 r,7bo-sb*iameter. According to the user’s manual, the dish has to be pointed in the direction of the satellitesby-3y i0*iq vbrv7,4oqkc; z, 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 travels across the Pacifv xv:6w-jlo9zic 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 boats.)-6wvz9 voj:xl    min

  An energy-absorbing car bumper has a sbn9ahgz )/,jewp bq0,t*2 i mepring stiffness constant of 550 kN/m Find t hmeet/jz,0a9)n* wg2qp, ib bhe maximum 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 )/ gn)mee mz kgi )7:h 0hi(rdgkju6k/from a window to a fire net 18 m below, which stretches the net 1.kun7kg06j )/m:z(me rg) dhk)ii he/g1 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 q6xmx 8cunk 1+cle*fhg cfl ,);3ys+son the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscill), 3;f*ncxyxkqsflc +us6c+ m 8g1hleation?    Hz

  A 950-kg car strikes a huge spring ats fhz; :gnvg 0ss-.tk,3uc8 tk a speed of 22 m/s (Fig. 11–54), compressing the spring;-8 . fzknst0uhgsg,vk 3s:tc 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at 0+pbfmz*z4ncu*gz* ojust 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 i*zc* m +uopgnzzb 4*0fn the coffee.    cm/s

  The ripples in a certain s,l)b t 2fcs(/.ut-qpkts rz9groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm.ts2 t.9zcbr/-spk t()l,su q f What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650 -dpfy 116pgglcos7.40t where x is in meters1pgyp1- glf6 d and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if g5c+dom0 ; dr dq:jeb)it accelerates at 0.50g (jme rc05 )d+g;dq:db oa) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake80xs. oifz gv6g8kc8z . When a 75-kg man stands on the raft, it sinks zfxok.86g8sgi0 z 8 cv4.0 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 tuw,d-gm/i1ie irvmxw-ul+ : e; ned to play at 392 Hz (G) and 440 Hz (vimugie x;+/em, d-- rw1: wilA).
(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; enl/s2c8s b5(mv6qv8 gmp xsnvk0) h-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 frequency is the same i cshmgq ;0xv 8)lkm5n6snvb8(e 2p/ vsn 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 ofhpkc ( e0/d atmq57x-c each prong moves 1.8 mm to either side ot0 7( -adhx pccq5k/emf center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with szo6zmmd o-80uimple harmonic motion of frequency 1.5 cycles per second. 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 with6 muz8ozm0o -d the board during the oscillation?

A string can have a “free” end if that end is attached to a rinr uimd380lfw fc/go0/ *k1bztg that can slide without friction on a vertical pole (Fig. 11–57). Determine the wabkf0rd 801/mc */uol f3i twgzvelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum h87o pzk hms:+sa:gvjf)gq s+,as a period of exactly 2.000 s — each one-way swing takes 1.0s8:hsv7kj) ag,p+: qofsz+ gm00 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 sprmj4tl8i*i 1n p0b6a xsing can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer xit8s1a*plnmj0 i6 b4, 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 tensionj- dzt (ufpe--dd;pdn8h;9q d of 255 N. A pulse is generatez-pd(9 n ddp;e8 fj ddu--;qthd 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 from a ceiling by a spring with spring stiffness .:h*. phk szan-p3m ph6.c kkyconstant 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 the ..ykh3sp phn.mh:z6 -pac*kkblock? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg+6 5, f gxh+;;ffiwfsyxx ;npy car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Re5 ; snpyxxfff +;xywfhg 6+;i,fer to Table 9–1.]    s

  A block of jello rests on a plate as shomjkw1;a5zh: 3y;uo ex- wg 3wiwn in Fig. 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 h 5:e muj3x w1wka-og3iz;yw;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