Give some examples of everyday vibratc(2 u(a+edps /mo4 s.0xjd h7de.xz nming objects. Which exhibit SHM, at least appros/7 mh( e dx ax4+0.djuzd(e m.2npocsximately?

Is the acceleration of a simple ha)bd-v)+db *(z lgj8ybvy ys(srmonic oscillator ever zero? If so, where?

Explain why the motion of ajmgb:),jta1 p piston in an automobile engine is approximately simple harmont,pjb m :ga1j)ic.

Real springs have mass. Will the true pedi4m .vv0w**l96hvtf f0vtxu riod and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an ideal fw0l d*i hm.x*v0f6u4tvv9t vized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscill: po6fbe;j px2eo4s;pator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical sprc 2d f*n9; m5:vfmpsi5i/*bi0klg qsking scale, and then is released. Describe the scale reading as a function of ti i:cm5v;/9gi5bs qi2n fp *s klm0kdf*me.

If a pendulum clock is accu n)pz:+e+ cdkdrate at sea level, will it gain or lose time when taken to high alt+p:ne dd)zc+k itude? Why?

A tire swing hanging from an-z 4kt6cgza6th(qu s9k-s btkw:q42 branch reaches nearly to the ground (Fig. 11–48). How could you estimate thew hkbn (atq46-64q- c:kts9st2zg kzu height of the branch using only a stopwatch?

Why can you make water slosh back ak;gep tp 03;dmnd forth in a pan only if you shake the pan at appk 3e;gm0t ;d certain frequency?

Give several everyday examples of resonanceesx/i v*(3x8l c4upecc3 jdv7.

Is a rattle in a car ever a resonance phenomenon? nmsi0wss;93zi 5i9ufExplain.

Is the frequency of a simple periodic wave equal to the frequency of its sourcebx9xo/*ii mqtn0l q0 (s2b ia;? Why or why not?n9*0o qx2 i;(/ mxqbs aitbil0

Explain the difference between th e.)t/v *wx;cd-ojhingux 1k9e speed of a transverse wave traveling down a cord and the speed of a tiny piece of the9xc/djt e*g) ;vwh-ixu1on.k cord.

Why do the strings used for the lowest-frequency notes on a piano normall-ck irf+hg 53xy have wire wrapped aroundxg r5-ck+3hfi them?

What kind of waves do you thints pv ;8d5g1fpjlfq89 9hfpn(k will travel down a horizontal metal rod if you strike its8ph;9p 9ffd5flgnp (v j1ts 8q end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature88ucjcdajt *7 , but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound jcu tj8d* 7ac8waves in air to vary with temperature?

Give two reasons why circular watewvb)gxjhb5r8h kw 1 nh,0fv . ;bhj4z.r waves decrease in amplitude as they travel awayxr,h hfvzv8. b)4.1n jghbkb j5ww;0h from the source.

Two linear waves have the same amplitude and speed, avok2k c ll-/v6nd otherwise are identical, except one h-vkkco ll 62v/as half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the bounv)/ kjy;q ,z+smh:dvjdary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do changdsh)qjvm jv,:k y/+ ;ze). Explain why.

If a string is vibrating in three segments, are there any places you coul j,kwb 0rj,6a:iywv*n1rq l-c ew2 c(fd touch it with a ,vw:1,ky2*-wjjw qri(br0l ecf 6canknife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflewp2pi.5i dc)b cted waves cancel at the nodes. Doeiw. pc2)bdp5 is this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another,/v) ox6 vk1hp m)f(y2znvmb y5 how might w 51z6) bm(yh)k/vvfm2op xynve determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, whatgzk/+;v, bz *ltp pqb/ is the total distance it travels ibzqv* pg / p/zkb+;t,ln one period?    m

  An elastic cord is 65 cm long when a weight osd8ri(n v0xn4 f 75 N hangs from it but is 85 cm long when a weight of 180 N hangs 08(dvnn i4srxfrom it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg dri3g pebajbsc1aj0 9z* q.x3o j1ver gets into the driver’s sea931jaoe0qjbjax c*1.ps3z bg t. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a .giyh;kzxz z f;w-c i+xvl7(; 2.7-kg fish hangs from it. (a) What v(ii.x z ;w;c yzk+g- lzfh;x7is the spring 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 Hz w*i y*7un g0;mgs lh1uehen a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs umliy;gg*01u n*e 7hs from it?    Hz

Construct a Table indicating the pos ;p2(hq)wagpaition x of the mass in Fig. 11–2 at times t = p a2ap)(qhw g;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’s web. The web vibrates prmn0 itqs1f; y21 d aogsun9u23edominately with a ;sg sfumq10n21ya 32uti dn9ofrequency 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 frequency1-4pg5 io1 mfoqaf4d n of 0.88 Hz. When an additional 680-g mass is added to m, the freq-gna544mioff 11 oqd puency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with 06dx*phxt, ,m1 i2opxk -3ycymk mpn+an amplitude of 0.1 c-ho xi,xk3my* p6m,1+n2y mp xpktd03 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 equilibr)ihh kk1q:mk/etp/p4e )yp*kium is the speed of a SHO half the maximum value?kq1ek p)k pk)yih *h:4/t/emp$\approx$    A

A mass attached to the end of a spring is stretched a distanch93- rl,)1/ekprrofd53c jrdes e t9nsm 3rs0e $x_0$ 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 m. If the spring is stretcx+ba:) bkf4 y5 yd0mqwhed an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?kqb:m dyfx54 0y w+b)a    s

  An object with mass 3.0 kg is attach izf9hh-c0:tied 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 ic:thfhiz-0 9on, 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 k +t9+1i* :rzqk ziscwvv3av-to “load” a 0.180-kg ball. With what speed will tiw +9 cs:i1t +vvkr*zq-kv3zahe ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of cd( yd, :ywaiiu.5nphuac,30yv. -ul 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. If0la,.hy 5 a(n.uvduydc :u wpiy c3-i, the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x i0mnugdbqz9 7lvit8al 2-*b/ un w0mi7s in meters and t is in seconds. Determine -int7*2mq8 0bgzbv uuill/70a d9m wn
(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 SHOv9ca p p4m)l3a half KE and half PE? v93mclaa 4)pp ±    A

  If one vibration has 7.0 times the en r8n 0f1d0r3byihkma 2ergy of a second, but their frequencies and masses are the same, what is the rati312r8dybi0m k h 0fnrao of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprinim yew8 m mut,ons4p-ui5 6g-mx7kt4 ,g once every 0.65 s,iwg4 sy, tt- 5 x4mnuop-m6e8mmk7ui.
(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 parallel vertical springs, e :kqm +r:dxos s sqh-,495czxeach with spring stiffness constant k (Fig. 11–49). What will be the frequency of vib9 s- m5c: zxk+r4,hoqdsq:s exration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is qaxwxv/ogp6r;gqa76 7ol2* b in meters and t is in secq /qg6lw x72*o axgapv;7or6 bonds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what i9g-fpo 6sjg4k hkd 0f4s
(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) yhgqzn57plvpq 824f/ )bgd. cis struck bv2z/y7pf n8g5qc ).qlgbh4pdy a 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 with an pf:wwz4 wc8:q amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point 8c4zpfw qw:w:(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 stif6 pyyb11 vs,ekfness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed dls2c 8czq/c9 horizontal spring whose2qz9 l8dsc/c c spring 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 with mass 65.0 kg jumps from a high bridge. f3 y1 atxk s5f4s:lrb:k ,anr7After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 2r :bf15nx37,tkfaks4l:ya s r5.0 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 isd 85;i0sfzd xz its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly rl6mup7v ap;,one swing per second? (That is,v6m, pap lu;r7 one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where 3ws4 xq c,tm3bthe acceleration of gravity is about 0.37 thb4,t qxms3wc3 at on Earth?    s

  What is the period of a sc: *2b;wwxpkjm r b*l/imple 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 0.760 m, the pendulum bob has a masa we uz:j+i01xs of 365 grams, and it is releas0iue1+: j xwzaed 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’she ,luzx0 8hd1d)b ra. pendulum has a length of 0.9930 m. If the clock loses half a minute per day, howh 0).z dr8ba1hxe uld, should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum ltt1 -o9 bsfc;y0g q:fspeed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released from s+vog:tpzx q-su 55ojiii1 .1t e7rt0rest starting at an angle of 15gte7trso0ju p.i5 q1 :x5i -s+voi1t z $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored bo1i ogy3/(y5tvz2lyero 1 wzk/at every 3.0 s. He measute2/wko 5vy/ yo(z1 31lyrzgires the distance between 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 travels with a speed pvic6 u*8eqyipmc4) v9,tgq s:d vl*3 of 343 m/s How far apart are themcie 9: u)qvs, *3vlcvpid* 6pqg4t y8 wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiloheffveg9ywa- brk7v: er(1a 44 dh r:tj8rtz) and tre4f 14rj vhyvarr7w kab:8t-g9d(e f: avel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves cxl4/ 8gxa2wqg 0av34km t/ biin
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic mo40wa 2qrbw 3urh;m ld0dulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factor3rbuwl0hr0a q 4w2 ;dm?   

  A cord of mass 0.65 kg is stretched between two suppo7m3n+yf vy4f orts 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the3yo4f+fn 7mvy other?    s

  A ski gondola is connected to the top of a hill by a steel cablets5q0(*qc3lt hobxq ( of length 620 m and diameter 1.5 cm. As the gondola comes to the qsqqol 3hx5t*tc(0(bend 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 se4z9qg/i62w frqv )*i x5kvgr hip just below the surface of the sea. He hears/zq6vgr 95i)wi2gfeq v*kx r4 the echo of 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 speeds, and this di1k h*0bmyr)* mdvc0y zvtr v4q+h:q.efference helps in y vy*hm rvm1+04c bz0qedhv:)*. rkqtlocating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal trf hc 32cq(yjq/e ie-4yansverse 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: Set the acceleration jf2c3 -yi ehe4( qqyc/a>g]    m

  What is the ratio of (a) the intensitiu0 zh0qt0s3q- jjle0les, and (b) the amplitudes, of an earthquake Phs0u- 0j jtll0zqq0 e3 wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave paoxu zo 9:pe: 4jr9 q8alsd+-azssing through the Earth is measured to be aoqx:9jr9 e-u4lz: p soa8+zd$ 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 lx* xeuf( xd02travel through the same portion of the Earth, but one is cad f x(le2xxu0*rrying 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 oner./ kx8 c31q2(ujzqjq+vxmf w-oux8 i transports three times the power of the other. What is the ratio of the am/w+xm-f ( icq2kouxz1u8 .j3qrq jx8v plitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down.0b kpyk8qp nuc zt5-, 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 the bug’s maxi,nzp t .upbq c-8y5k0kmum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch thej 94 vko(fmgs epw)z59 shape of the string at the moment they directly overlap.45pgjksm(f woev9 9) z (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fuzgeiop k*- ozydd ;oq(ai; )(/ndamental frequency, what are the freqpodq;/o az iydk;z*)(g (eoi-uencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when u )dvp; vk iv0n,*i4qfqnfingered. At what frequency will it vibrate if k qi*0 v;,f)qvid vn4pit is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four lhq xx8o ,.q7ll,9d1yp rhaz)ioops at a frequency of 280 Hz. Name at least three other frequenc)proiq y9x1lqx7,dha8l .z,h ies 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 wah 5b+em6lv1c lves is 47be lmlh1+v65 c5 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whaoyoip/b .ns(l.h.u) d t is the frequency of the yld ho.bu)o/i(.psn .fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from thstuhq e n c-)wi6zh8/rn95p9we bridge to the support post is L = 62cm and the string is under a tension of 520 N. Wh9e 5qts 8zwhr )in/wc-9 unh6pat are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is su u3)az5lz 5*s3bby kpkpposed 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 frequenczap5 3su3 )*k5 zlbbyky?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppmeh+ x l7qd:-b rj3a3tosed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in : 3a h73jdexbrl-t+ mqthe string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is a7y8u k4, apt/;urpt i)t.ly oattached to a small-amplitude mechanical 60-Hz vibrrp8lya i u ,.)/tpo;t4u7kaytator. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of til :4(9czfqyq b; ;qsh 4ymz6phe string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.04hzq f:clq b6imys( ;;yzp4q9 80 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right f(*ryr4, 0iyxf )smammt.tpa6aa ,q w +requency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the spp.m ws( 6ra,y )qxyfm0r+ t4taim a,*aeed of the water wave?    m/s

  An earthquake P wave a4y3 ku9g/clgx(p6b s traveling at k.0 km/s strikes a boundary within the Earth between two kind46klx3a9 (g u/pbgcsy s 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 “shedo; nxjr2o y/ 4jl)uz4lf” where the velocity changes from 2.8 m/s to 2.1 m/s If the2y4j;/ jxo)dr4nuo zl incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is trav2dl5 bb7j rdbm lf/59ueling in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold 7dmf 59rb/2bllbdu5 jair 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 boundary between two types of rock at a jdd :shyhnu;*- 2kyun)l,/ng d2uk yj;/nl -d*nu:)hsg, hny 38 $^{\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 user’s manual, twpw (ek.ak7,r he dish has to be pointed in the direction ofr,kw7p aek(.w the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and veloc9ldi8p*k 83dmx: ic sj szvd)1ity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level *zdsl81sddc 3i9mpiv)k:x8j 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 sp.g.)alq9ug ak0 :x obdring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with ma .uog09lx.) aq: dbagkss 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire netwvm;a9( nf9(xem pmo5y a,*zz 18 m below, which stretches the net 1o*a99en (5vw(zm fz;ma,y mpx.1 m. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass theniv suiy(hn5957x w4ic falls 33 cm before it stops and begins to9i 4nhii7xcuv5y5s(w rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at .gq;ew)ulc s0mk 1bz16zou c/a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 mgm.01 kz1ul)ecsc wu;6 zoq/b . (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 (diam+-8 82gx704m- cm/cdnudof;rreviqfh 5 d mwi eter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estima+uigc q m/8-d or07-e fdmhd2wmf; r548inxvcte the speed of waves in the coffee.    cm/s

  The ripples in a certain groom;d9jqwlhwq .kki* pa3y;+,r ve 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be thkrwq+qmjwp3y i;. k,9ha ;ld*e frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according mge)j-.8 z: u3gkxly l u/*ncoto the equation x=0.650cos7.40t where x is in mete .youl*nj -lgcme :g8)z ku3/xrs 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 oo 0 6jsrqrj89with frequency f. What is its frequency if it accelerates at 0.50g (a)sj8o90o6j r rq upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft,a2rcgt1z .kh(j,mt9 gdx )bd , it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for jg , d12(m,tbxdcark. 9thg)za 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) andlvioo36sl 8d 7 440 Hz (A).8odv6l ilos73
(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)xss. io lau8q1 ;6xlx. Determine a formula (a) for the ratio of the;8u.ai )xlsq6l1s oxx 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, andfgtj7o33 wl,ch0+ jks;nt.c f the tip of each prong moves 1.8 mm n3c;ls tj+tojfkg0w,ch 3.7f to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simpjt5na;a z0 yoce t7x05le 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 with the board during the oscillation yn a50z;o et0axtcj57?

A string can have a “free” end if that end is attached to a ring t5;-x.noijb:ze5 hhr shat can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with-jh. 5:r;s5 hon xezbi one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-w 6sh+v2( e ea+p+eensyay swing takes 1.000 n6ys2+(a+e +v hsee eps.
(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 directs69wg1f0at ynion or can swing as a pendulum of small amplitude, but not both at the same time. W60ws a n91tgfyhich 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 12c/v uyl b4q;gs,doj /o58;ecx3 g is stretched under a tension of 255 N. A pulse is generated at 8;;lscgv/5odq jc o,x eb4 /uyone 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 sp7eqs,k( nz/c l9t1f0sa:hnq( b 7idmtdg ji41ring with spring stiffness czsk/0ls7jd(g:qeaf(b,n19mtq ch 41i ndit 7 onstant 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 block? (Assume $m \ll M$)

  A crane has hoisted rvf 4cjw8(/gbj4os 8ka 1200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A bg848fj r 4s/vob( kwcjreeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests+rj 9jg) kq1mu on a plate 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 freq9jg jkm)1+q ruuency 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