Give some examples of everyday vibrating objects. Whic56jxtz n9b0pto e :6jsh exhibit SHM, at least appr:t 6bo5sp e0 6tznj9jxoximately?

Is the acceleration of -r,t+ vm 5xf51q9xgnv coz6we a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile ek2u yh s;hcuq;j;53o engine is approximately simplc;hsqeou; 5ju;yh32k e harmonic.

Real springs have mass. Will the tr;rsho4y(obqq 1 -iq*eue period and frequency be larger or smaller than given by the equations for a mass oscillating on the endq h1 r(;soi*4q bo-eyq of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (S-agv( .l :bse3njsn +jHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and v-si6j l7+e tkthen is released. Describe the scale reading as a function of time7 i+ktls 6ev-j.

If a pendulum clock is accurate at sea3ji1 nyb 8xck-jt: u,cc(jm 92qhddj: level, will it gain or lose time when taken to high altitude?j8 h19j:jni:2 j xdbcm-tyd, kcqu( c3 Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11 1 j 1z3u. xka(wdvjnv*cve,v5–48). How could you estimate the hevj vze(ca jn1x 5*.1u,vvd3wkight of the branch using only a stopwatch?

Why can you make water slosh back and fort7dhlm1//x y 3vg-pjco h in a pan only if you shake the pan at a certain frequeng3/v1-h o /7 dxylmpcjcy?

Give several everyday examples of 5 sp.5op(y.f c8wv tt(mae r.nresonance.

Is a rattle in a car ever a yh*m28zp.4 ws0trf0d9 ouyi qo/ wu2x resonance phenomenon? Explain.

Is the frequency of a simple periodic wavz3 8oagl*laj o *.-npz2i(x roe equal to the frequency of its source?pa3laolo(rj .2*gx* n-8 ozzi Why or why not?

Explain the difference be1j fqazi6. 8*9rtsf t r(w.oossb*i3htween the speed of a transverse wave traveling down a cord and the speed of a tiny piece ofwjirss6s itahoq**.. 39b8 off(rz t1 the cord.

Why do the strings used for the lowest-frequencp::24uzehqnzpz 3 u9v y notes on a piano normally have wz ez23zhvpu9p:4:q nuire wrapped around them?

What kind of waves do you thinkvury1 2e 40asp will travel down a horizontal metal rod if you strike its end vy1us 2aper40 (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an ihgc d,5eujgwuc 5 118tncrease 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 withghu8 5j ct g1,c5uewd1 temperature?

Give two reasons why circular water waves decrease in amplitude z bnjnwu5r(jc1r7k70t t a-p 5rz/q2nas they travel away from the s1jrt a5cn(jr 2u50pzrzqk7- /wbn7ntource.

Two linear waves have the same amplitude and speed, and otherwise are identical,r1( kdy0sc.;/)0 fvt g;laluxz 8ptgzj/2a rt except one has;afa8d(zu xpt/)c./sv ;rg 0k ljt lytr20 z1g half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary bet0xk,h9w s2juoween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelengthju9s o2k,0 xwh and velocity do change). Explain why.

If a string is vibram )m2rd-n6ijyg 5, :a okbrb6ating in three segments, are there any places you could touch it with a knife blade without disturbing the moti5b6m j aymkbar,-ng)d o26r:ion?

When a standing wave exists on a string, the vibrations of inciden ev 0ds kajf/m fs18rjwm-9a/;t and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Expla eswv/s/mdj 1a;f8 9mf-kjr0ain.

If we knew that energy was being transmitte*ctm+68 ryl 3vi0bvor n13gnud from one place to another, how might we determine whet03 u*n1rl vm8vn6g+ ro tybc3iher the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is thzwb0u rey(u( 1e total distance it trave ru( buye1w(z0ls in one period?    m

  An elastic cord is 65 cm long when a weig rc5ilj)wc,h2 9r ngy(ht of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” consyrh),259cc( rgjwni ltant k of this elastic cord?    N/m

  The springs of a 1500-kg car ngbr;z;l)du72k w2fmoacos* ffkh6 2kr47* icompress 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 freque nlim o)s 2f2kb6fru z;k;**7c2owfh dg7ka4rncy of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg b7gbx/, vxrba/dmn*7ity 6 *c fish hangs from it. (a) What is the spring6*ixy v 7m/b7, d*rbgbnxta /c stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 H4qf f ,js9-h2 pai se/)8yy6awnrqm,cz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs fro/8pqa ,4ans,)r y i 96fjmqhy2-w csfem it?    Hz

Construct a Table indicating the pe8 dx.:mc t2feosition x of the mass in Fig. 11–2 at times t = 0,tfct8:e.ed2 xm = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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’en-r rp7ch)2 yrjo 5+ws web. The web vibrates predominately with a frequency of 4.0 Hz. c)e+p5h yj2 rrrw-7no
(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 k kf8 44t7ed0 -y oubo/wfgtd1b ;yr*xwith a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the valueydbd/7 1o*k uobtwkyxe rt04f8 ;g4-f of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an ampl -dfcgw3*j5(wglt (hl itude of 0.13 m. Determineww(flhlj5t - cg(* 3gd
(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 fr; z+ t ou5hiwyfq+4gde mn5ews9 lp:2-om equilibrium is the speed of a SHO half the maximum valu wqzn-:9p+y;s e h5 +glmu5f4et2oidwe?$\approx$    A

A mass attached to the end of a spring is stretched a dihojqp/0j1pnid z 1tjsj33)1 kstance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 mhr iq6-puf6 yj+v/nj,. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equili/qu6 jfj yi6npr,-v+ hbrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffxlamkek0cr9n:/3 i k. ness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020rl nakk9 xc3/0mkei. : m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m to:cphvox 48 o0 tm6bq(d “load” a 0.180-kg ball. With what sx(m84copoq dv6t0:bhpeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfa- d.axnzu 0ztl674k hkce 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 massk6dz.7l z 0an thux4k- 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 c jux e;5u5euj 2t,1f zkeb/e7to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determ/k15 7ef2j,uce;5te x uu zbjeine
(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 fhw syp90+px6 half PE? ±0spfw9p6y+ hx    A

  If one vibration has 7.0 times the energy of a secontus;e p)wbh-yyp *bx66)v 8n:o+ ywhpwf p ,7bd, but their frequencies and masses are the same, what is the ratio of their amplitudes?-s);8twbhp yy :7 ep+fvhb*uxy6p)6 pnob w,w   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprindc8ekjl/q2 3ei bh5 a9 p7,ivkg once every 0.6bvp/e7 d835akh k2cqji el,i95 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical paral(4)dzep* uxf zlel vertical springs, each with spring stiffness constant k (Fig. 11–49). Whatzz u4(e pxd*f) will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in i)gnt.3f db-pgry8,dh:x b8 ometers and t is in seconds. Determine p o.nx-8:g)d,tbd8 figryh3b
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what wzgxp0o*2 h+z is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) ex e,a7acjyclvl 9 082is struck by a hammer, which gives the ma lv ayx70e2, cc98aljess an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibratesl--z, 3tqblprx x/*wx with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with pos/x,xltzp xb-3l w -r*qitive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness const1pils74sm9 r* vv2z,t-pugupants $k_1$ 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 smyf kf;15-qyp pring whose sp-yfmkfp ;qy15 ring stiffness 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 withxky4t 9vb 6put ;mvu;xh+,nn8 e*c(xa mass 65.0 kg jumps from a high bridge. After reaching his lowest;x,xceuk86+;t4b v*ax v ny tm9n(puh point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 l8-( pzi p rnv*7s:pcsvibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactlywf763j6xsn a3ey 6 njs one swing per second? (That is, one complete vibrajw7ya6 s3s6n6 fj en3xtion takes exactly 2.0 s.)    m

  A pendulum has a period of.(:qyq/blr rz w53hn j 0.80 s on Earth. What is its period on Mars, where the acceleration of gra5q hn lyw3r(/:z.rjqbvity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 c78c)r8 *uexi zvzt o8om long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pn;fzrz 07xej 6endulum bob has a mass of 365 grams, and ij7f nre6z;z0x t is released 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 hohomngt tpa.. /o w438as a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length ofa.pth /oog.8on3wt4 m the pendulum? shortened by    mm.

Derive a formula for the maximu 5cv p3y0q )8q)f9v oj.psmbdnj m(-dvm speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2a0 forb ., yx,5fkkasn+y td.5.5 Hz. At it is released from rest starting at an angle t 5b,y a xrk0df.fo +a5.sy,knof 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 thegh(.iyjq08k jv5yt*l 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 wav0.*v l8ty(i5j hkjqg yes traveling?    m/s

  A sound wave in air has a frequency of 262 Hzfj 3+66dw mr tyo2ft)r5o q d06xv2bfk and travels with a speed of 343 m/s How far23yd+x 0foo 6 mbtt6 dvfk6r q52)fwrj apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz tq9 jx+ku-4ate q(ov,(kilohertz) and txq-v+9 uet4jq a(k ot,ravel 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 suq7q,cxr:5b) u7nsxis0wjd44 v0tywaves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastiue7-*lz;y /az9iyryp ur vu 3(c modulus, but one is twice as dense as the other. In which rod will y p/r;3r9y l u*7e uziavz(uy-the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supportsm3xjagd+a:8z qy( d3x 28 m apart. If the tensi8+aqj zdm(a:x3xy 3d gon in the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of lengt nfc,wz)q.de0 / wio+uc4x/kd h 620 m and diameter 1.5 cm. As d0nc4 kdzce q ,xw/ /+i.u)fwothe 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 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 bpsiw.9i 7e vn-elow the surface of the sea. He hears the echo ofs7e.p 9 iv-inw the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speedsd0xmr ;-c : ;jsr,vze5rcb 3ut, and this difference helps in locating the earth:z0 ;scet bjrv u;r cxm5,d-3rquake “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-producedi4t f* aepw9um jn.tx:ebj35+ surface wave can be approximated 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 objectx.nj: p5+i3ue tw* 9bf4metja s begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the 9n5julp 9g jt)amplitudes, of an earthquake P wave passing through the Earth a5l9p)j j9 gtnund detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquzof.8 4 folcy04fn yy2ake wave passing through the Earth is measured to be 4 fyz o28ln 4cyyoff0.$ 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 9vn/r73ura :rpkwk 3ethe same frequency travel through the same portion of the Earth, but one is carr/ kr73 :rrpn vku39eawying 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 trf:j4lz1z0po e,zqh )nansports three times the power of the other. What is the ratio of the amplitudes of t 1hej zp:o)z0n,flqz 4he two waves?   

  A bug on the surface of a 0dc w0onsl)2jpond is 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. If the ripples decrease to 4.5 cm, by what factor does th2ndw0js)o0l ce bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (krlja 5 2uuye. x5+sn(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 t5e5lu2jxsankr.y (+ uhe energy at this moment?

  If a violin string vibrates at -a+5 xq*erdvj440 Hz as its fundamental frequency, what are the frequencies of the first foura+ 5vxj*r -qde harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hzsg+nhlo0 8* woxso( n0 when 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 as a standin0* hw+ooxgssol( 8n0ng wave.)    Hz

  A particular string resonates in d;-m,xi349du, rtsmhcl0fvypn h9m9four loops at a frequency of 280 Hz. Name at least three other frequenr,h 4s-9m yn,lm;d9hm dup 39xv tifc0cies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing wa0lgu :axq1e,n ves is 475 Hz, how fal,x0 :aqne1 ugr apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what 4l qd+vk iy5m;is the freq kv;d4mq +lyi5uency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6we77z7 pctdve6 a88yo g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies y c68p7odzw8e7et av7of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 20i5nhg-8l*ib mn* 9 nr 5rbyb6x0 Hz, but it is measured to vibrate at 205 Hz. By what peri r8igb-*6ybnr hn mx595n*lbcent 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 to vibrate at 200 Hz, but it is mexhb0eyiu+t/v , r(t9 0m vbia*asured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decrh,9 y*t t/0bi x+ vveai0r(mbueased by    %

  One end of a horizontal string is attached to a small-ampk+ /)ztg qos-8vl:4m(:pzdpkro ov*z litude mechanical 60-Hz vibrator. The string’s mass perz z szm/+:kvk8*lo gov-rd):opq4 pt( 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 adju.nuq9 *hj s0mj.d0dev sted 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 m? u h0.q.n*v edjjsmd90  

  When you slosh the water back and forth in a tudwda7m n/xd s w3bz8o r+zm(*+b at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose t+s83dbwzd w*/or7dmzax(+ mn he 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 Esc5/-ejvs bi7 u2a q):g,w 3cvd. epdfarth between two kinds of matejuv:i, -d3 e apf. /sdegwb57sqv2)ccrial. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where te +gvacxu6e:h*4pu2i 2xpf f *he velocity changes from 2.8 m/s to 2.1 m/s If the incident wave 4p :c x+ v2a efuuf*6*2ipgxhecrests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travele bnll/1p9 9v+psdg2 kha/ 5hdbo e2r(ing in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of l2hdo p2bd +/pel1ae vgsk5 9nr hb9(/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 al-2kz lc)lsu.dst0k; boundary between two types of rock at a l -0uk .slkt)s c2l;dz38 $^{\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. According to the use8b dv1bmvp5iy-h +k.vfl:x7 jk6n8yr r’s manual, the dish has to be pointed in the direction of the satellite, but an errokl bv8+1j.r kf5 8v7m:ypxiv dby6-nh r 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 vel8q;d.zu :tej u;o4zmm ocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual;zuu 8 4;od qmzmtej.: decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a sprikj*t p(t3x.,5 kvf z xm3h86rfo+c gkxng stiffness constant of 550 kN/m Find the 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 3rx,ffm xpgot3ktv*k5 6 chj.8xk+ (z5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a f inp l3*c2y*zyire net 18 m below, which stretches the net 1.1 m. Assume that the netc*yy nz*3 p2il 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 mass the/ 9a.dsf 6d:i 8jzaawnn falls 33 cmz:n/s dafda8aj9i 6.w before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (F8;lgnjxqgt jv8vjp274i b )z5 ig. 11–54), compressing the spring 5.0 m. (a) What is the spri)2zv8l;4g qtp ji8x75j vbngj ng 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 ck2.z 9 -2j-a l0ym g)jbnkob(zq pmbe5up of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until e.lm- 5 zj29ka m(bpq2zgb)-ykbjne0 oventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certa,-zqa(h c6hckin groove 10.8 cm from the center of a 33-rpm phonograph record have h6 (aqhk-,czc a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equatjcyr , yuqq;5:ion x=0.650cos7.40t where x is in meters and t in seconds. Det,5; yqc:uqr yjermine
(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 freq;hyctsy bkinawy9 g5zxn3:2 ,l /r, qtj+z+e7uency if it accelerates at 2h,xasc 3 /z5:in7y+bkqy yejgl+,rn t;tz9 w0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg me -y1q-+yo drjan stands on the raft, it sinks 4.0 cm deeper into the water. When he st-- joyr+1eqdy eps 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 musicb/+d/lrjhe )7 ,k dkwzal instrument are tuned to play at 392 Hz (G) and 440 Hz (A)r)h 7k //bk,+d wezjdl.
(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. 11–33.( 7ba1pe omla pk73a.u Determine a formullbm7k .p31u ao(7 epaaa (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of e-l;8rm5u0i6u g uykc vach prong moves 1.8 mm to either side ofu ucygv k-l;5ui068r m 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 simpl./kkrl8fv*7s2a zm lve harmonic motion of frequency 1.5 cycles per second. What is the mlslk./7r vmv8f2ak * zaximum 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 “free8nz6 e3pc-,ovemy .s71ryoh c” 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 a string with one end fixed and the other freccr-sveh7z6o, 8m.3ne p1 oyye.

  A “seconds” pendulum has a period of exactlyowwzrb p.o:mz 8v(b9 -2ofpf1jabq 91 2.000 s — each one-way swing takes 1.000 :9qmr (a1wbp9 b12wfo poz j-v .bozf8s.
(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 oscil1yip;7+ v(bdfna*wyyqu-or0 2s,yb a late in the vertical direction or can swing as a pendulum of small amplitb(f adb o; iyw0- +yu,71*spq2yr aynvude, 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 pupdhc, lqeml0z( y/ lh 5n4/e xsj*t45qlse is generated at one end, and 20d 5lh*t c5 qy/nh4exp0s ml,(/e4qzjl.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 s *9jo7ve-glzzi5 qa lju 4h i3d-81fpnuspended from a ceiling by a spring with spring stiffness constant k. A penny oi7hlq3z8* n5j pevoadil-- jzfug941 f 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 block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the jugx9m004 /3 +hhhn qymf cwmbvdv p92s6nkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouv9c39+nxwmyp qs0h/62 v mb0hfmgd4h ncing 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 pla 0i-d0/a zwhoqte as shown 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 analogy to a mass vibrating on a spring, estimate the frequency ofqzho0d0 /wi-a 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