Give some examples of everyday vibrating objects. Which exhibin6 m* p/t4z ajqc+3zcft SHM, at least approximateln6qz t 3paz4mccj+*f/y?

Is the acceleration of a simple harmonic oscillator ever zero? I(siy h/ 6t(;dbynizj- f so, where?

Explain why the motion of a piston in an automobile engine isxm0 *gps /5nfd approximately simple hasf*n0g /5xdmprmonic.

Real springs have mass. Will the true period and frequency be larger or smaller 4 5p r1t: ot;/urqvtsdthan given by the equations for a mass oscillating on the end of an idealized massless sprv5/rr4ttqtp: u ;o 1dsing? Explain.

How could you double the maxim5wmtv6 id1;x kdb 4x md2w5,enum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attachn-6 -atk*,wipux 8t i,n2p94sums biked to the hook of a vertical spring scale, and then is released. Describe m4wstutxa98 6 uip2n bisk -np-,*,ikthe scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gaid:m :7oq yb8+;w jpwznn or lose time when taken to high altitud 8nw :odyj:wbm+qp;z 7e? Why?

A tire swing hanging from a branch rec94 a is;7coukaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only oca4uc79 ;s ika stopwatch?

Why can you make water slosh back and fort6r8kvh vlc8(uzo ve6so- c2h7h in a pan only if you shake the pan at a certain frequencs6hvl r ovu8k8 vcohzc-6e 27(y?

Give several everyday examples of resona56hr2cbxjh7b2syb o 0nce.

Is a rattle in a car e) ra1o g 7(y.peqv;ocyyb3h t1ver a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equmh:yzt86di7y al to the frequency of its source? z: 6 di7yythm8Why or why not?

Explain the difference between the speed of a transverse wave travelis0h2q jpp;/yhjhpw7t:/ 2,bt9do wg l ng down a cord and the speed of a tintgwos tb p,/09hhl22d:jp/ ; w7hpyj qy piece of the cord.

Why do the strings used ym0n49kn t r5qmq/u/vfor the lowest-frequency notes on a piano normally have wire wrapped arouq/n m0/nm qt r9v4u5yknd them?

What kind of waves do you think will travel down a horizontal metal)(dnd b;mrhq 8 m9 5juaedo3y2 rod if you strike its end (a) vertically from above mjm;d bdd)oyu nr8qa9 e32h5(and (b) horizontally parallel to its length?

Since the density of air decreases with an increzvt v4wioq 0g- vo7fi5cvp -6*ase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wwv 746v5ozfivv t-gpqo i0*- caves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they 6jtekkn87 0ozlxnbq 7x3s -l5y k9 wq9travel away from thnj 53extyq-z k9nl k0 7q78wolkxb9 6se source.

Two linear waves have the same amplitude anl 1vkjv ztcv:;0t4 laxo,eh 7:d speed, and otherwise are identical, except one has half1 ht o4vcjav:; kexlv07,ltz: the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in a3nv-f r; se7li p;t8cgi0h 3zFig. 11–33, the frequency does not change (although the wavelength and velocity do c3 i-ver03fz nc7hl i;tp 8g;sahange). Explain why.

If a string is vibrating in three segments, are there any placwa:yki ofwfj2; vng/h +7 4.h bij*g0jes you could touch it with a knife blade without disturbing jvo;bak+y 7gg.w0/jw2ij fnh*i: h 4f the motion?

When a standing wave exists on a string, the vibrations of incident sa-s6y fjbq4) and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explaf -)y6j4asqsbin.

If we knew that energy was being transmitted from(zzzmz s-i 1c/ one place to another, how might we determine whether the energ1zs/-ziz cm z(y was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amp0l +l bxfweifm) /k5.ulitude 0.18 m, what is the total distance itbxm )w/0i5k+lufe .fl travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hang3 wnfh*kvaybw6z7l-umwt +: 3 s from it but is 85 cm long when a weight of 180 N hangs from it. What: k+fvww-z3aw6 muy b3l7hn *t 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 int8 a hm-7p6jxpv8okpd7 o the driver’s seat. If the car goes over a bump,vjd8phpo7k p6 xma8- 7 what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Wh f17yk8ugblk, at is the spring stiffness constangu lf,71by8k kt $\approx$    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 frequj;sp26. z c9owgj-nxjency of 3.0 Hz when a mass of 0.60 kg is hung from ij.69nw-p2s j zojxc;gt. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 1yh8, h,bv z8r5u7m rje1–2 at times t =yebv,r858jhmhz 7 ,r u 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 c+-v .vl jv( 3y*rknulnaught in a spider’s web. The web vibrates predominately with .vrjvl( y3nl n* ku+-va 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 wit:larmw5hixp.pb2-( ph a frequency of 0.88 Hz. When an additional 680-g mass is addep.(ahx r:w5m b2p-pil d to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end ok it.t1 00odu;g80u magr2drvf71s nrf a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determine r.0do 0fvti2nur;a r 8 sug11gtkd07m
(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 ha5s2j*zoln af e( lrt**lf the maximum vala f5s*r (ljel*z*2n toue?$\approx$    A

A mass attached to the endwghk,s v rp0 -z6)nd2eh:o kn7 of 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 stretches a verticaojud0i0if:0d3vgvh9 g 2 ki)yl spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium pos yihk0od3v0j2:ii u0g9df) gv ition again?    s

  An object with mass 3.0f9i)iky( jh;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 positi(y)hfkq ;j i9ion, 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 8m2:/ utg*x dul4uoy +x0.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. Witu 2x4+moxu /ul t*y:dgh what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of o/aa,s s p+05xy gsxyyg-yz;ph+/6np 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 ts/xz p6y0h y/ ppos+ 5n,g;a-agyxsy +he 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 vibratelm y 07pe 4wgd8s::fdhs according to the equation x = 0.45cos6.4t where x is in meters 7:hd0sey: w84f dlpmgand t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the hihxc /kyilhrgd ;j859* ;*gyr b7gj/ energy of a SHO half KE and half PE? ± lyii/ xbr r5 c8gh97;d*hhjjgg/yk;*    A

  If one vibration has 7.0 times the energy of a second, bu ujsw3d6(ysfe+ . 1pe7bq jnoop6ob-,t their frequencies and masses are the same, what is the +7joye,1bse3jonpdo bu wp q-(.6f s6 ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring obay lyb:xp,9no3.yl2dt 41 b hnce every 0.65 s. l.t4n hp93: baby2d 1, yloxyb
(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 jsdy+*v 4p( a5bqk60ju( bholparallel vertical springs, each with spring stiffness constant k (Fig. 11–p*4bu6( dj+k0b( qv5o sjy hla49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation xje(i9sndiytts;a6 6qv7i 6o2 = 0.38sin6.5t where x is in meters ai t;yi sns6e6di76v2(ao 9 jqtnd 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 examik) uzy* 9xu))nv,rea8k bhy-ples of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 1247ki(z kz/v ex8tt5m78 axx;wl N/m) is struck by axkkzeix v mz58wl 7 tx7(a/t8; hammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates b8v,d49 ,/lansoe levwith an amplitude of 28.0 cm when 0.260 kg hangs fv vdn4b aes,llo9,8e/rom it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffne,ogo f2b65k 2 ais c2iyxo+j.yxue7(kss 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 strib,ha. :q+wavipi 2jl7 kes a 0.600-kg block attached to a fixed horizontal spring whose spring stiffness conijaw:ih2,lv.7b+ pq astant 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 reachingoe5k9m p.sl0qbe brw5;cbe )7 his lowest point, he oscillates up aw9b 55opek sl7r; ) emb0.qecbnd down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is itsr2) o:ofj ank1sq zh-2(sn,a (lxp hkpsn w8+;
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simp*l5 sw2 )jwvhle pmcn62m a.dlf9c4 3dle pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactl9 hs)m lwnc 23cwpvdm j4e*l2lda6f.5y 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is i *t-/2y myxprkts period on Mars, where the acceleration*pyt -/2mk ryx of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pe8n:pbc .: seco-zj)(b j9z likndulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulumhms)e 77 9j ziij:tiy0 bob has a mass of 365 grams, and it is released at an angle iij0i)j9ye7 zhmt:s 7of 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 penduluzm8 -+1osjxu wm has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of 1xwos8mz- u+ jthe pendulum? shortened by    mm.

Derive a formula for the maximu:xt*wevh0t-+ k a lly*m speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is rele3jnshxq q4e9p ji5,gb2i9gj 1ased from rest starting at aqx,ji 2s93jbqg 14hjineg 95pn angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow oftgpk 0id2bt m4an87z4 his anchored boat every 3.0 s. He measures the distance betweb2kg7dn 8pa04 z ttim4en two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and tr9hm( amc p*wp;avels with a speed of 343 m/s How far apart are thewpm9 cmhp( ;a* wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (ki x x.d, 3nr4rzyr7kn9ilohertz) a9rz xri7.nx,r3ny k4 dnd travel 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 lo . cnwwj-v9w qvzx8ni .qgx9g2-kp 8.ingitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one isch*julm-z8u5 vs ns/ .s 0 rxsxqqu6(5 twice as dense as the other. In which rod will the speed8n j-. zhxsr*xmus5 lc 065/vsqqu(us of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m 2si5v7 .1 jdap39+imcxbqu pdapart. If the tension in the cord is 150 N, how long will it ta i13cuqj pxmsb +adv5i9dp. 72ke a pulse to travel from one support to the other?    s

  A ski gondola is connectedn/-wv -jj808siq jpyq to 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 terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulsev n-q 8j0jsp /q8i-jyw 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 surfs0jm7sfns)t+e w:n s0 ace of the sea. He hears the echo of the wave reflec0)f0stsj snn+ m:wse 7ted 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 speeds, and this differencnf kik4 vk-2/s*( hiepikyq 7al(lk72 e helps in locating the earthquake “epicenter” (where the disturbance took place). vn4k *k((f72l2s7 kh liap/yekqi -k i
(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 sul4 1 8nv9q qnj,.)wevbp1mf hrrface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthqrlhn9) qfn,e.vp411bmv w8jquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplu2zk g jq0;/am7i5eglitudes, of an earthquake P wave passing through the Earth i/l5gmaugk e2j7 ;z q0and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through th,k2iji pi mh1,8p5x 7zoj c0yue Earth is measured to be 258 z1jip7yuo kxi0jp hmic,,$ 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 e7.lbbw 1mh 9qy1gmv8e/g y3nportion of the Earth, but one is.qen1/9vhbweg 7b18mmgly3 y carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched strinln88iip 2,on xg have the same frequency, but one tra,88nnil2 opxinsports three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total verticapu m15,7,z pc6z;w+f sjkaxco l distance of 6.0 cm, from the lowest to the highest point, as a wave pas 67,zp zckcj+u 5owaf; xsp1,mses. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moviicwtvux-65ny 1vv r93 ng toward 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 h5 rvxntiwyc-3vu19v 6appened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamly9rc-b b6d +anpc5 5bental frequency, what are the frequencies of+r9dybc -ba5nc 6lb5p the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibratenwwknq 5/ + tw5 .-j1dgm*ec *n,zbcots at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third o*cnw/-e gwo1.ct*qtj nk+m bndz55, wf the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonatf+*mwr8 fiip;tiq ,mj 8c2(cfes in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will rcm8p ( 8wjfiqmr2 ;ff*ici+t,esonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m(fmlw.sq +2a+n6bvv d/s If the frequency of standing waves is 475 Hz, how far apart are s2+nva fv d .mbqw6l+(two adjacent nodes?   m

  If two successive overtones of a vibry;wnp 6* vgg2mating string are 280 Hz and 350 Hz, what is the frequencvgp2 ;m* n6gwyy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 gfb s809pb ej*u. The distance from the bridge to th b* u9js0bf8pee support 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 is suppnv20 hx ;j+rivqo0s53qm3jqcosed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the sn3s3rv+qi jm0jqq2v cx5 h;0o tring 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 ipad72 ehugx o6os6/ wc;*2pcjs measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequenccs7;poe / 22 6gwjdopuhca6 x*y? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mekt6dm( g +gz1bchanical 60-Hz vibrator. Thgb(t zdk6+gm1e 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 adv4c:e/gw.nkum vf :5r justed 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 mufgc v ve45 k/wmnr:.:?   

  When you slosh the water back and forth in a tub at just the sq+p5f)u:liyip+pi 0 right frequency, the water alternately rises and falls at 0i qiu lp +)fspi5+y:peach 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 wit t0a aysa7+ .rtqly5l(hin the Earth between two kinds of material. If it approaches the boundary at an incident angtl75aqy y+ (tas0r.lale 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 undvkuw- -c6 hae sgj 2,fvxv*)*kerwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests c kfuk 6v- )xhwga*v*se2-,jvmake a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warmiys:vodbq6y ma ji(6h(pf -35 air when it hits a layer of cold, dense air. If the sound wave hit5 j((qy3obsy fipva6h6:m d-i s the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a bounx8cv*eb -9cb4ilj . da*aa6tfdary between two types of rock at a 38aic. ebv8*6aldf*bt-j 4xa9 c $^{\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. vub;l x/c;*4g2vjs hwAccording to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of wlb;jvc *g2 ;hv/x s4uabout 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 Pacila: k(izd74gific 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 durin:(zlda k ii47gg tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 (a*+ qn3wa ss aqibzn,36k/hzkN/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 (approximatelsaaw3isb( 3,an z zh+*/ 6qnkqy 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches o854v.yfc o4*8 mzl)uytz5 *,feeu yvi w krt7the net 1.1 m. Assume that the net behaves like a simple sprif8fw eto,u*v.eiu zm tk4 lcyo4r5 8yz 5y)7v*ng, 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 t mby() v+.94cttj 6: ihif:d*vtlmrtkhen falls 33 cm before it stops and begins .*hvlv)dj b 6( tktt:tfr ii9cmm+ y:4to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compres7pq6na v-s: fssing the spring 5.0 m. (a) Wh-p :fs v67qsnaat 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 (diamfg: bq5yoqreg9 2mu2 4eter 8 cm) at just the right pace of about 1 step per second:4 ue9g2b5gr oqy2 mfq, 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. zlsgw ;9be(ce87. sdom/q bz)8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the freo9)szel/be8 dw7 m. gbzcs( ;qquency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t w-byd87pd gzgx ff3d31here x is in meters and t in seconds. Deter dgb -py3 d1z3gxd87ffmine
(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 /kmqqqude, hq9,9*xm if it accelerq 9 q xe9hq,,u*/kmdqmates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it s/o3v0 2mvm zgu3rdjz ,inks 4.0 cm deeper into the water. When he steps off, the raft vibrates fd3mmvr/ uz3o 02 g,vjzor a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) aer ; q)f7tgqbz0pi(3ard:a- znd 440 Hz (A0ze):t gi q-a(r3zaf 7pbrq;d ).
(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;mb-pihq9v x4c*o,vr 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 (bv;4pbvr*-x ,oh9cq im) 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 j(g sp.tz0im w 30y(dma frequency of 264 Hz, and the tip of each prong moves 1.8 mm to ei0y m igtz((s0jdmp3w.ther side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillatf8pt ;jm*o 2jsjuw5f(b8obc 4es with simple 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 plac fcb2j*f oumo 8jw(;58sjpt4 bed 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 attached to a ring t7zj pb)uc)/r/ahkz yn+ t8a 1bhat 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 huz8n tzj ca)br7/a/b1)+kyp other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing t )6rxzpbin.73 gbpm0o akes 1.000 x3b)r. np izbm706gop s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction fp9u95/b t(2jhok-otnyumh 5 c6 0limor can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the 9hhu t6n2f m9kc0( ly/mo5pjtu-b5oiperiod 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 is9ka d lb:z5f8f stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a secon:9d5f 8lf kbzad 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 )xttx1-8d+w * c -zveyzto.sd 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 o st)-dtw1z .8-v+yztxc*xedtop of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable28wpsxfap8*r l86h +rscd4hk is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. r+f aclwk6288 8 srphdx4sph*What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate asnghpde*;is ebo+jx 6o-*9ed ) 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 of this vibration, giveeo-* ;edoxghipe nd+s)b j*69n that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz