Give some examples of everyday vibrating objects. Which 20yatji hs:ij(zl : + mvc2fu+exhibit SHM, at least approxi (v+js a2c :z+:hf uiitmj02lymately?

Is the acceleration of a sivg* x0)dopz9omple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an2h 6f:efoj n5k automobile engine is approximately simple:ehk2ff o 5nj6 harmonic.

Real springs have mass. Will the true period and frequency be lt l+ah; xxs)v.uo :2qmarger or smaller than given by thes2 +)xuhx:am ;ltqvo. equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic o whuc z6id5vhn+f w/-7 rskgzcbz;f-l1b 6l0(scillator (SHO)?

A 5.0-kg trout is atta /ykbiitfth4v46 d ef/h s080pched to the hook of a vertical spring scale, and then is released. Describe 0b6t4v/hfh 40fysd e ptiik/8the scale reading as a function of time.

If a pendulum clock is accurate e56uuk+8rsl uat sea level, will it gain or lose time when taken to high altitl8ksu5+ru 6ueude? Why?

A tire swing hanging from a branch reaches nearly toy 3;o qqwze4tl)mw(gw)ahok9j (3(rz the ground (Fig. 11–48). How(39w 4;qe(k zom jqgytwa zr)3ow()hl could you estimate the height of the branch using only a stopwatch?

Why can you make wat5y gbr/ *e+v ;1;h1osx72yzymgiv 5hyausj9ber slosh back and forth in a pan only if you shake the pan at a certain frequ7z;s* 511u/ 9shoy+yxib5aej2gbyrv y gmv; h ency?

Give several everyday examples of rebpcr o5;5e0 qasonance.

Is a rattle in a car ever a resonance phenomenon? Explain./gz(( j mrcsa1uf 0 wzef;0jo;

Is the frequency of a simpleto yv1h,0wpb9 periodic wave equal to the frequency of its source? Wyhvt, 1 9b0wpohy or why not?

Explain the difference between the speed of a transverse wave traveling down ,xypt0j:h+ pwc:ava/a cord and the speed of a tiny piece of the c wxc,a j /0+:pptva:yhord.

Why do the strings used for the lowest-frequency notes on a piano normally have 7o2uj uzl5:asoj54my wire wrapped ao ay5j 7mz:42lsjouu5 round them?

What kind of waves do you think will travel down a horizontal metal rod if yoeyzkf2p y*ki s1a e:3-u strike its end (a) vertically from above and (b)f e-2p:zk iesk3 ya1y* horizontally parallel to its length?

Since the density of air decreases with anqh2vl8ydfg:r;g)f w (p -eih0 increase in temperature, but the bulk modulus B is nearly independent of temperature, how dr0h8 lgvff i-py) h;ewg2q:( would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they trav/7i;d.g hwbz3h9zyif el away from the sourc/7i;bz z wihh9yg d.3fe.

Two linear waves have the same amplitude and speed, anftmd*pqw 4q3 n :w+tz0d otherwise are identical, except one has half the wavelength of the other. Which transmits m 3:qtn0pmt +q4 d*zfwwore energy? By what factor?

When a sinusoidal wave nu w-7t yq+csa0bu 5hfs b6a08crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do changu0ah bc- 6tf+wu0qsy7sb 8an5e). Explain why.

If a string is vibrating in three segmentswjvl-grc o7 *4, are there any places you could touch it with a knife blade without disturb7jr goc *vw4l-ing the motion?

When a standing wave exi,(pq id,8 ig kiu4uv0,k1gong sts on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean ggq(0u ,, gd,ivipnku i48ok1that energy was destroyed? Explain.

If we knew that energy was being transmitted from one p x t* al/u+wx*eue;x wdgs3u4(lace to another, how might we determine whether the energy was being carried by particles x*eu;l+da */gxw es uut (4w3x(material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what 5 ; qkx8/u(,asopv9t7nmym2j 8ltx+w-cyeln is the total distance it travels nxm u(7 e+q85vyyt,29aw k m;-xoctsl/jp n8l in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs frov6cy1uf1zh : bm it but is 85 cm long fz16:vhy1cbu when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car complkdd,+ :os pag3gt8r:2t tkyon :/2hlress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, w t22os:8o /lg tlpk:r,ngt+aydd:h3k hat will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale sm,c 4 pl otix3i(ag*l/tretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constaami xlpilg4t,3/(*co nt $\approx$    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 ( l7ovgav k,ju6e5nn2when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg han,n2va7n u6k5o velj(g gs from it?    Hz

Construct a Table indicating the position )x8c33j- 41yrehlcedad 2sda x of the mass in Fig. 11–2 at times t = xdcrsjy4d138-ldh e2)ceaa30,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 0.5d4,odd 5c zhqvss)9j25 g is caught in a spider’s web. The web vibrates predominately svd5h 9o)4q5dc j,szdwith a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrat9i: buvdz)sm2fu(bu *z0gp0d es with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the m :biugvsz0 zpd f()u 2u09*dbfrequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the w-5yelm 4wwh9end of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. yehlmw w 4-9w5Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half 9(ot6c.dp)4x wycct6zzjl)6* qjrlxthe maximum valzo(xj ycp96cdcx ljt.6rz q6l4w )* )tue?$\approx$    A

A mass attached to the end of a sprin d6rid1;.bbdyg 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 vertical spring wx.1f fkuxx ne,(3bd7 o*ixh ,0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) ef. kh( *fx7,3x uodn1 ebwix,xquilibrium position again?    s

  An object with mass 3.0 kg is attached to a o 4jk* dlnmg.m-4ayi3spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/a mmg.4i nd3l-4kyo* js
(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 80.0k( leumfj1kv q dkea b4/c+w:(n,6 t.d N to compress the spring of a toy popgun 0.200 m to “loadcnddm .j,fe:6aqe+(k ( 4vl/1w k tbuk” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface u axrj./,twqc nc.8. sis 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 spriun.tqj/ar,.8cs.c x w ng by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to th7iex nwvosh-1+dxp-: e equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determi:hpids+x-nxv7eo-1w ne
(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 t8a sm4g txz8;d:slp1ehe energy of a SHO half KE and half PE? ± m; 4ds zp88aseltx 1g:   A

  If one vibration has 7.0 times the energy of a second, but th hkwp.o2i0 w*lk.rqs7eir frequencies and masslkhw qp.72*0.rwkioses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every- ba*y(a6 egex 0.6xgey e(b*6a -a5 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 twp.x7(ri; q(jm7 .dcln*u fr jio identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?j* (7dmurrn.7lci;(qif . jx p

  A 300-g mass vibrates according ef8ihslw 3b ,/wt7rxpz;xq5iqd 1)9 qto the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determine z xipwwbth;7ef)xi,s5 q3 qq 9/rld81
(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, laphpwx-ag+7cqtkdgzy::1tlj( 3al .0beled 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 enefnx:onx)/s t/34-h trqk kmo ,33 brcd of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial mr-e4hn3 bs3t /oc)q:f kx 3/t,onkxrspeed 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 a6b;y:wj5gqjwcol 3i7mplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through thw7i:b65y;jq 3 j oclwge 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 sti;y+0-fp d zxsqffness 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 horiz e48(c;rcewg;m tgxa+ ontal spring wh ; 8mgw(gce;x4eac tr+ose 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 b yqvf)fqec4 ;d ttqk5z( / f*twu5xc*2ridge. After 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 25.0 m below the level of the )tf wq54q/d x( vtf*c5qc*utez yfk;2bridge. 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/ ruq/m-)liil,4wp rg 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to0pocn-t ejr dwu ,,,8(y f7zpd make exactly one swing per second? (That is, one complete vibration o8 nu,d( rjwe f0,t,p dp-yc7ztakes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wherdyxa. jk:9- zre the acceleration of gravity is about 0.37 tha z9xyr.kd-: ajt on Earth?    s

  What is the period of a simple pendulum 3y8f9.q nfvdw80 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 qmqt19 x*vz-:k 1prafhas a mass of 365 grams, and it isqaxpvzt *kf r19mq-:1 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 has a length of 0.9930 m. If the clock loses81 2lhnyqphw*(f 1rlr half a minute per day, how should you adjust thehn p( qrlh*yfrlw1812 length of the pendulum? shortened by    mm.

Derive a formula for the ,hacxn ob 6 uv(;nc51er)d co1maximum 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 released fn mx(l 2ii2ts)j.lv4 trom rest starting at an anglelmli sn2tx42.v (t )ij 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 thatu2.m0 zqryw/ p wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests tqyup02z/ w r.mo be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and 2llb kn;l 0b0 ,w2pefrsdo 38ytravels with a speed of 343 m/s How far apart are the wave crests (compressionsle nlfl22,r yp0o 3bw s;bd80k)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) .4dcz xm;f2 kgp:op4 qand travel with a: f2pokzpxc44gqd.; m 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 longa:7xo 4x;drvj 9g,0aouitr f )itudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is t2aj 22-u1hawfoac t/dwice as dense as the other. In which rod will the speed of longo2uwa/-c1afjht d 22aitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suje 9i+dhy,j5(du3s vpy z8k;npports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel ,s39 jjpn8 (hzevd ; yu5+idkyfrom one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length w4i; imugt-d 5ja4h -j620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bum-tjia u4wh4m-j 5;g idps 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 simn ra,af 1)s2d7 +a6fllfhzr g9;( de.yna5gide of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s lan)a zh6(gd,g rff 9a7+s e l .r1mnif;yala2d5ter. How deep is the ocean at this point?    m

  P and S waves from an earthquake9g( el(ye ds.n55be qyp-oy7 f travel at different speeds, and this difference helps in locating the earthquake “epicentde o .7sy5y pge-leqf(59b ny(er” (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 approxisp5 c yp1*nbcj wtk138mated 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 neetcc1w8 1y3j 5pknp sb*ded 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 amplitudes, of an earof7na ) tt62egthquake P wave passing through the Ear)eo7t6fan 2 tgth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measq (b -zdl,x6mlmsm 6:mured to be 6 qmz ,mls:b6l-md(xm$ 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 tmqc u,q uuchqtbmr*+/uv-x19+ c /op0he same frequency travel through the same portion of the Earth, but one is carrying twice theq/ mc+/9 uh+1cuu,qmu brx0-oqv cp*t energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequenccxk( *kg 7 6p.ijbpre,y, but one transr7p(jpg i 6kb.xcke *,ports 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 upa3t5;qcx j013 m z0fzi vo0roa and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decreas3;r jmozox0 i qf0zat5c3v10ae to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving towzbbi*rw17jgo 9;: crw ard each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at thi i9b woz7;: *1jrwrbcgs moment?

  If a violin string vibrates atisc5vjr tqls *-1og6p+y40wm 440 Hz as its fundamental frequency, what are the frequencies of the first four haopc01i6vqjw4*r- s5 m +tgslyrmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At whats )3x ptz hk7o.ox*2ox 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 standinh2o.ts)3 kxo* x zox7pg wave.)    Hz

  A particular string resonates in four loops at a frequency of 2 in-3ktu x1d4f80 Hz. Name at least three other frequencies at wh-fidn31 ku 4xtich 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 fre,cbs a :luek0 .c1wxnb6jt76oquency of standing waves is 475 c0etnbo w su:jx6 b1k7 a,6.clHz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating stripl 5qm 2 oqhs6x8pk*r+lq1q9lng are 280 Hz and 350 Hz, what is th9 lp2l6olqqkhr8q q5m+1*psx e frequency of the fundamental?    Hz

  A guitar string is 90 cm loe3c+ opvknl;+del4. bw.,c fw ng and has a mass of 3.6 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 of the fundamf,lc.3ed . w+4 ;w+plcekobn vental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measurq/2pz zgy9vx ;c 51hrved to vibrate at 205 Hz. By what percent should the tension in the /9vpyv 51q hc r2zxgz;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 q,16dxu;fami at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be ci6q;,1d afmu xhanged to correct the frequency? decreased by    %

  One end of a horizontal string is att2r-w ajr iy5/aached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit2wyajr- ia 5r/ 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 adjuste gn8es0yu a63hzfjrc,0u ta.4 z+ 8epfd by moving the pulley. If the hanging mass m it34+anauys0 8j 86 rg.f, zzucefhe 0ps fixed at 0.080 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: mz-ukpg 1tx:gz;:p( 0bsolu (fur(m in a tub at just the right frequency, 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 upro :tg ;1lg-: f 0(p:uzms(bk(zmuxspeed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s stric pqupe;k8/sif r2q/5kes a boundary within the Earth between two kinds of material. If it approaches the boundarye;p 82/uqsrc /kif5q p 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 “shelfz v7uqu+p cr,hzq f:)f.hv m+/” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave cresv,p.)qr+cvq :7uz+ fh z f/muhts make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a la.b iyx/l cr222fwd ;p 8negss8ky(3,a kvfr 2vyer of cold, dense air. If the sound wave hits the colk,rl;e2a. i bgx rfcns/(yks f8v222vwd8p3y d 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 boundary be(ld +-y7f8 8v1gupaxh;dxea(xf o8 pntween two types of rock at a 3u- x8fd pxa8 (8 a+yfend1hpol7xg(v;8 $^{\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. Accovf3v7e00ncj )o 3jnd p(rpyf:rding to the user’s manual, the dish has to be pointndvjj )p p3oy:f0vf(0 3 nerc7ed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of waveleneeapy;epn 1do jftf*9 5jq9 +7gth 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunami9 *eepn7 f;5fpjq9t+ay 1jeods, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing carewnm: k+j c5/d2aa8qx bumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall aa c: x+qwda km2jn/58et 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 f v be4htd4.wah )uw/swfal;: *ire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spr;uw ta4s) /bvlf*eh 4:.wd whaing, 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 placep(heya;dp( 3jmuy)z2 d on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to risey( ) a(mz hd3yep2j;pu. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 1( zuv5xzj (4:4ofzpnp1–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the sp4( zz: ujo(x4v5f pzpnring?    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 x9a/6e5z(wcjnjez9 (6iq td ecup of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee slosh56qez/tez a 9jdc(96w n(exij es more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the hqq7z6jj7q:6icc 1 oucenter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What 67jch juo 1q6q c:7iqzwill be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibra5(o0k c78s2jlpdn pm otes according to the equation x=0.650cos7.40t where x is in meters a7n2m0odsp k( 5 o8jpclnd t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency ifvug v71y- okpc(qm3cfi .59 tdz*l xy4 it accelerates at 0.50g (a) upward, 1v . f-y5qp(79ciyovkuzgdtm3 *x4 cl   f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on thet7zsjxy/k * g e-d1wk: v(we6vhmu+3j raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vib(wu t v7d+e6jyw 1ejxk:s3hkzg m*- /vrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 44q4uf*+rym ;eh +kuje 40 Hz (A).j*eu u +k4yf4m;ehq r+
(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-p+0wrn 3rmx fk7art cord of Fig. 11–33. Determine a formulawfxm3r0r k+n 7 (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 eachw,r( g *ned hp-h2imp68coq3u prong moves 1.8 mm to eithe8dhhp ognupqr,w m6*23e- c( ir 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 k47bp c2 awfd1with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplipa1kb7c2 wd4ftude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if th7nse,60l9xmysd s b. sgsx*w7 at end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of thdg w0s7l xme.xs,7ss9s6y bn* e resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takes dwf 7e(ew u+g5eyw2 3sh+o, oi1.000 ew+eu (+sw,ofgw35 27 oediyhs.
(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 or cy/ rig+xloq:c,, ,jksan swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let ,,r sk :,j+lqyigox/c$l_0$ 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 strrtw;1/osgxpr73 v4t6jx+d ys etched under a tension of 255 N. A pulse ps4j;/wtx1 36sv+r ty7gx odris generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from ay.h cwwzgdcc wo-*/45 ceiling by a spring with spring stiffness constant k. A peny-ohwccw.5g 4/zw cd*ny 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 a 1200-kg car at th;cywzii(5) g pz p1wt0e junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts;5pwwzt1 ci0p)yz ( ig the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives the 8x famj*1 1noxc;iiz 3dimensions 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 vibratizaxx;n c3m1jf 1*o8i ing on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz