Give some examples of everyday vibrating objects.67 (gvgg;dx ar Which exhibit SHM, at least approximgg( 6vr7;xdgaately?

Is the acceleration of a simple harmonic oscillator0diia* uy3obslh rkq2)m -v:5 ever zero? If so, where?

Explain why the motion of a piston in an automobile engc)l 7s,m;j/ta ise s+vine is approximately simple tsv,si;sl7me +a/j )charmonic.

Real springs have mass.jipsqsv;x8l 6 v*vw) : Will the true period and frequency be larger or smaller than gi:8xswpj6 * q;i)lvsvvven by the 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 oscillator (SHO)?/n64x lj tp(ir

A 5.0-kg trout is attached to the hook of a vertiobhbq1ka s;1zf57u 6 xcal spring scale, and then is released. Describe the scale reading as a;husbxqa1 z5o1 7kf6b function of time.

If a pendulum clock is accurate at sea level, will it gain ork;w yes 3gy hb(/r)4ek lose time when taken to high altitude? (r)yyh/gek34 bs w;ke Why?

A tire swing hanging from a branch reaches near1gih+5i k1u xop0fxa. ly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatc px+1k5ofxu10i hgi a.h?

Why can you make water slosh back and forth in a pa8c7i0sz0cvguzy n e;0n only if you shake the pan at 80vnuiy0 zc0z scg;7e a certain frequency?

Give several everyday examples of re uuisxia4 r*299mch /vsonance.

Is a rattle in a car ever a resonance phenomenon? Explainj/k+ k mveu*myub;y* -.

Is the frequency of a simple periodic wave equal to the frequencxt :zot -ye*vvn8+de/y of its source? eott8*yd:e vx+ v /n-zWhy or why not?

Explain the difference between th:45h6p e q,96uxq,wm yijom loe speed of a transverse wave traveling down a cord and theopewi,:ql 6hm u4o59jm y,q6x speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes oeayvq n25tc)13)bpzdf rx-5o2 s0i von a piano normally have wire wrapped d-p5t22oeb10 fosv 5 vz)rc 3qai)nx yaround them?

What kind of waves do you think by1 gb -ahe/te.x8or4 will travel down a horizontal metal rod if you strike its end (a) vertically from aboygh84/rbea1e-bx ot.ve and (b) horizontally parallel to its length?

Since the density of air decgjsw 9mas*9 .zvu j2q3reases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary 993.zmjaujvsgs *q2w with temperature?

Give two reasons why circular water waves decreasev zp0fo(t a +sx,,cvh+ in amplitude as they travel awataz,+s+,vfv (hpoxc0y from the source.

Two linear waves have the same amplitude an/+/qm(*cdr yut x,il8dz 7r pthqo+ 2ud speed, and otherwise are identical, except one has half the wavelength of the ot u7,tz/d2qx/ol r+ch * ymiu qt+pr8d(her. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the bh raz-,b jbx-6eb-h +joundary between two sections of cord as in Fig. 11–33, the frequency does not change (although th6b+rzjejb- --hx a, hbe wavelength and velocity do change). Explain why.

If a string is vibrating in three segmeakc3x 20fva4y0n vuu0nts, are there any places you could touch it with a knife bf a300a0 u4vunk y2vcxlade without disturbing the motion?

When a standing wave exists on a string, the vibratil, 5dzih.yfw8 ons of incident and reflected waves cancel at the nodes. Does this mean that enw8zdhy.l5, fiergy was destroyed? Explain.

If we knew that energy was being transmitted from one place tgw0e b4 jr1(t(bghbf1 o another, how might we determine whether the energy was being carried by particles (material bodies) or by1ehg ( b(0t4jw 1bbfrg waves?

  If a particle undergoes SHM with amplitudw*rp;/:4sust k;+g jlbfoz / me 0.18 m, what is the total distance it travels in one *;o l/wtr f/j4skpsgmb: z;+uperiod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85e:-n js.3d4frqhiy * j.hc*mz cm l:im4fh*j -. z e q3rnysdj*.hcong 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 compress 5.0 mm whenf mc )eyb+f.3cekb lm:)5djz) its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what wilm. +)ezklfjcy):m cbd5bfe3 )l be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3. q),vu. /ps)vxvltil8 6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiff/8x ,)luqvvi .v)t lspness 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 when a mass of 0.60 kg is hh d *hkdiq9el neu-;wde)r* 80ung from it. What is its frequency if only 0.38 kg hangshue;)*- dwen i0dkh9q l8*dre from it?    Hz

Construct a Table indicating the p0p: /hmkq i-moosition x of the mass in Fig. 11–2 at times t = 0,/ i-hpk:o q0mmt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibkqn72 e,vz 6vbrates predominately with a freque27 zv kebvqn,6ncy 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 *ze ontw1b,j6 a spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is addetw ,o6*1znjb ed to m, the frequency 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 an ale:kb:r0+ qq* s2vblmmplitude of 0.13 m. Dq *2+l qembs:bvlk0r:etermine
(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 the maximum va+:;kuj hsxq(.jet ja(l e a (q+j;(:tsuk.jjhxue?$\approx$    A

A mass attached to the end of a spring is stretched a di2/wb8nmk) : ccugz+n dstance $x_0$ 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 st6boxiqra u 8 ls0i01*cwr ))ojretches a vertical spring 0.315 m. If the spring is stretched an additional 0.1381oow*q))ris06ib l cxuj ar00 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kgy:/q y e s*4cw d/513rqotvptm is attached to a spring with spring stiffness constant k = 280 N/m and is executing simplq/1s/3 :t5tdo* mqp w4ec vyyre harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress h9xvs1 qnb5c(w: 7 vzethe spring of a toy popgun 0.200 m to “load” a 07:b vnswq1 c zvhx(59e.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end 7qat .au) j (91go6fpf3 oxczpof a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass expeo p 7.u1q(zjoa93tx)fga p fc6riences 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 sy8 v2) dv6cfgwhere x is in met28fygd 6)vs vcers and 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 energy ht1/w3lwbso :wy 5;,hojnir0 of a SHO half KE and half PE? ± ,l13wo hwy5:rw j bsin; 0o/ht   A

  If one vibration has ia,f2.e x9o co7.0 times the energy of a second, but their frequencies and masses are the same, what is the 2f ei9 x,caoo.ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillate(b 7/whocao 28y kp7oss from a vertically hanging light spring once every 0wo (yka /7ohco7b p28s.65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, eac-*/ wdkbv2e lth with bk-v e *2l/wdtspring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation xqde/nyon q- 86 = 0.38sin6.5t where x is in meters eqd6yn q-n/8oand 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 examples of SHM, labeled A and B. For each, what ikjizo1(.x; t ei3u4 o9n f5thus
(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 ho mz5kauxjzq;e4( 6w:ov n2eh-rizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determi;o nqeh2vw6 mza:z-(ek5 xu 4jne
(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 stiffnesseg 8;0f7pe apz constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium poza; eg8e pp70fint (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, wiy (j(8cg/bux vth spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixeded0)bfv9nd asc pdtc3ow ;,tr422ga/ horizontal spring whose spring stiffness consta 0p/attwdcv b4deadg)3 9 ocn2f,2s;rnt 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 ff.d+1z2, 19dmpdh prrys pal9 rom a high bridge. 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 thm 1psd.p+z,d929h dlrp y1 fare 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 exacwva*vof,hl 39 tly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to makng:z j4n0 +rdfe exactly one swing per second? (That is, one complete vibration takes exactly 2.0 f4dnn0 g: jr+zs.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, w5lonnia/spkd (iv13 9here the acceleration of gravity is about 0.37 that on Earth?di9o5/in a3vl s1(kpn    s

  What is the period of a simple pendulujqpxjhl2e;o5:7-v kyh47 oxtm 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 mass of 3 b2 dl h1:pt0by9hvd/jgst,l 065 grams, and it is released at an angle of 12.,0j1y0htptb ld/ lbhd9gs :2v0 $^{\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 clockp 2q:al3/s tddk x6 iaws:-c5o loses half a minute per day, how should youqtwd 6sx c3s2pdl:-ka:i5 / oa adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum f oigez78 )9o5wmr2pqspeed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscilla -*kbkjvfbc12g u u9;gtes at a frequency of 2.5 Hz. At it is released from rest starting at9bgbkjv;fu *u-2 c 1gk an 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 crestsb2exfof a 3e43 pass the bow of his anchored boat every 3.0 s. He measures th f3a 2f4eoex3be 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 of 343 m/*d0em. :itzswebk9l (s How far apart w9l mt0.bz:kis( *de eare the wave crests (compressions)?    m

  (a) AM radio signals have freq6fx),qkh(z li uencies between 550 kHz and 1600 kHz (kilohertz) and travfql) k(xhi z,6el 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 long.h( k:xg,chy4w8 atpm fvb* o(itudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, n o70 ds9pm:gqbut one is twice as dense as the othg0s:oqm9 npd 7er. In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the j uwmt- iw ml 5gs):-2or-:xmxtension in the cord is 150 N, how long will it take a pulse t5 ilw-j)-u -:o wxmmr2tm:gsxo travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620 rvz x5c fbdx2kcq1iv.9.p wtam *40 d)m and diameter 1.5 cm. As the gondola comes to the end of its run, itidrqa)4. 0xp *v5wbmkc.f zxv91d2tc 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 si ,vgiv64 e+u:dhxw kfa;a a9i7de 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 later. How deep is the ocean at thvki : +e4 ig7;aaa9dxvfuh 6w,is point?    m

  P and S waves from an ez.yhvo(a5s )te9dax 7nyzwr168 k u 0p+lr:d farthquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took place). fyvoa rzedtp 59w r suy).xl86dhan+kz70: 1(
(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 approximat(.) wyofeavb 0-vxz+p/wm y a+ed by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually inx0apz m +.w f+-y/wyve)(vbao clude 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 amplitudes, of an 61wykf xg)*dvm+mn gu;fly d, f-/4nnearthquake P wave passing through the Earth and detected at two points 10 km n1n+ k wm,y-)/mg*4fdfdyg ;lfvu n6xand 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through theh 8+bfo0;v1y+j(qgvl/ o qa7 pz*vlaw Earth is measured to be gz/1pj+ o+ov(qha blw*fl ;q8va7yv0$ 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 thro.6x +ck3fuije ugh the same portion of the Earth, but one is carrying twice the energy. W6ukce3j+ xfi.hat is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but o tom7 sxsp;01a u)9ubane transports three times the power of the other.smxuo )a 09tbu7pa1s; What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move c 8z7.xpqepne6k*tv o3g ix21up and down a total vertical distance of 6.0 cm, from the lowestqk1p t exg6v2p87x3c.*e onzi to the highest point, as a wave passes. 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 moving toward eah*zplp 0 ;f +t09z2t:omzkskhs2ne / uch other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch thephup h ;0zo*ztzln/k ssk2+9f02 met: 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 fundamental frequency,t gl pf.gf i+r8)pfx(1t5+m+h bpg*ef what are the f1tbe.higlfm8)r+g( +ft5 p* +xpp f gfrequencies 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 unfingered. At what ngdbo9)o ,w*d 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 vibrad,od*)w gn9botes as a standing wave.)    Hz

  A particular string resonates in four bgrwv3cgan8 kaw.*q x38w ,c* loops at a frequency of 280 Hz. Name at least three ot. w*c 8vx3a8 wa3kgrbwc,qgn *her frequencies 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 gr9ie, 4gx7d-wspd si2r5o a:If the frequency of standing waves is 475 Hz, how far apart are two adjacent node275grr 4ogs xd i,e a-wdps9:is?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whatu4e,lt+e4mlnb(b ,fpd pi ;/z is the frequency of the fundamental?tpp /+dlf ,emn;ub( i,44bzel    Hz

  A guitar string is 90 cm long afpez2n/-ur3 mi b2 :hznd 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 fundamental and first tw hz/:p2b2nzi -fr 3meuo overtones?    Hz

  A particular guitar string is supposes et0 2138sjhkjzh-s+ aplgq (d to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be change0ap82zje(qstgs+1-k hl3 j sh d to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to(x4l f /v z00cswtkbl2 vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tensi/vclk t2zb4w x(0l0f son in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string3- 9azh/aa/(pi+/ t lp bp)qigcc:xww is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass perb3/gx9/ca(a /il cp- thwq )+piz awp: 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 s:u97jp3y j wwj,.wjwk+yed0 string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave pattekjs ww3u9eyp+j:wdj 7 ,w 0yj.rns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tubb7a x7)0r kjka 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 standing77akk b)0axjr 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 withinww)1.*f+gcio2 x k6c, uh wwut the Earth between two kinds of material. If it apprxwf2 w , + ck6tuio.w)hg*ucw1oaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where thm i-8f-1 obnw 9zsz:boe velocity changes from 2.8 m/s toi1o om98z-f:w-bb snz 2.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a la zx*k2/ch,godyer of cold, dense air. If the sound wave hits the cold air intexz, c/g od2*khrface 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 wavfbz4sw4o (u6j:2w7putjotfz4, n0 k spqj, m8 e strikes a boundary between two types of rock at a w:j4u62 tboqzs(ff m, p 4jjn048t,sw7z pkuo38 $^{\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, the s2k jc.*m md(:c)blwo dish has to be pointed in the d.sm2m)o: lc k(wjbdc*irection 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 wavelength 250 km and dw f27ty:n6qx 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 m7xqwn2yt :6df uch 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 spring stiffness constant of 5n-x z95yrpts*jpa7 x250 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, co rtp7jxn-y5a*2xz p9s llides 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 fi(+wpjrq;fl)( 7u md .wnwoa m-re net 18 m below, which stretches the net 1.1 m. Assume thaf+jum q)a d 7.;mn(wpww(lro-t 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 c1 zfdm*:w xwl) shepvr/0u bs 14c1)afreely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequenpbsc*v /l: cu01)1) sawh4wz mfde 1rxcy of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compress;tcp wv2gyyyf.5z3 -ging the spring 5.0 m. (a) What is the spring stiffness congz5y yfpw.3y2 ;tg- cvstant 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(9psgh* j dce2bx:e8y wf2 m7f coffee (diameter 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). Estimate 2e(ed8*hw:2m9 s pf7 jfcbygxthe speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm f.8v4pjc a;6 cp7uoyr)jt1g)gcmnu bu6* a+tbrom the center of a 33-rpm phonograph recor*4caoj8py6gc) 7apv ;jrngt ut6u u1b+m c)b.d have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40eh. kymy 3-.c8; aifcnt where x is in meters and t in seconds. Det -y n8iec3fa .kymh;.cermine
(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 is0h niuh9iz13/ ;ci j9sk ,gfur its frequency if it accelerates at /,i3jnr0ihukug1z99hf ic ;s0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats/l3uy++ f abz8 zt 4r;l0tsexx on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while+extza;rf/lt+84s0z 3yxbu l.
(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 440 Hz (zhnutdzdl ay+ y-*,/;A). ,+*yuazy/d-;zdn ht l
(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 co3cjpua ,j: mt4rd of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavt4,c3m : jjuapier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and cq9 6zd+u;zcn the tip of each prong moves 1.8 mm to either side of centedun z9q +c;c6zr. 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 simple harmonic motiu i2b)+ki+ddf) a 6yl9pxzgv(on of frequency 1.5 cycles per second. What is t)up 6k d9z(ifalid+bv )xyg2+he 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?

A string can have a “free” end if that end is attached to a ring thanxb22h7xh 1hrn,/f r k9esf;kt can slide without friction on a vertical pole (Fig. 11– 1ef h;rk k,r/hxb279sn2hfnx 57). Determine the wavelengths of the 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 xry/ bs:3m1r8z t9dopswing takes 1.000 9tr8/d1 mpo sxbyz3r: 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 or can swijg65t y(l9sopw,*cgv ng 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 o j*w lcp(5ovy,g6t9 gsf the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of)*6is1r d4r-r tmidwc :c vhi9 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulsercmr:1 6 9tcd)rhd*w4iv-iiss first meet?    m

A block of mass M is suspended from a ceiliaib1 himm*:d-ng by a spring with spring stiffness 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 top of dia* m1h-i: bmthe block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cj7dd24 ukx n9zable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is t29 zux 7dnd4jkhe 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 (whiv8 qrcq ,39axfch also gives the dimensions of the block). Y3qcv9xf qar,8ou 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, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz