Give some examples of everyday vibral2v7;qf f*pccting objects. Which exhibit SHM, at least ap flv7p;qf*2c cproximately?

Is the acceleration of a simple harmonic oscillator ever3d d; nmg,3l8yo,de nt4cjw0c zero? If so, where?

Explain why the motion of a piston in ak tj6 r p;rxqf43soj02n automobile engine is approximately simple harmoo30sk;p4jr tx j2q6 rfnic.

Real springs have mass. Will the true period and frequency be larger or sms0z xt ) 5. 5.xdcj(glolvoe3ualler than given by the equations for a mass s.53oc0g zj(vl) oetux5.xldoscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed or h txq,c+yiw/3 ,rxj/f a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached t)dajecm1m dh,.v n- 97rib/foo the hook of a vertical spring scale, and then is released. Describe thefd19 noj.-h /v) cmabi7d,rm e scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain ojs)vq(h.qow. ryb+,i r lose time when taken to high r w.)s,q+obij(yh.q valtitude? Why?

A tire swing hanging from a b ( cixa14aszv7ranch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of v7 izxc( 1aa4sthe branch using only a stopwatch?

Why can you make water slosh back andxl cv 1:g d;8kpg-)7 citnwh*h/my0oq forth in a pan only if you shake the pan at a certain frequency-dqk)tphloc nx wyg/0 7c *vih8m1;:g ?

Give several everyday exampl54eeh 0mqk4n kes of resonance.

Is a rattle in a car ever a i/p /kswi zn626mjue :hf70h uresonance phenomenon? Explain.

Is the frequency of a simplb4-q5.. eebdiytq0oue periodic wave equal to the frequency of its source? Wid05beqy u -.e4obt.q hy or why not?

Explain the difference between the speed y ac9ux)we7w/1 ok . ig5hm 7j+dz:ivxof a transverse wave traveling down a cord and the speed of ag 1wiz eui7d+h a.79v/xx5)ky :owcjm tiny piece of the cord.

Why do the strings use t n9wg0w abf39l2(rcfa4gohz aap --*d for the lowest-frequency notes on a piano normally have wire wwl(--t3waag0g af 24nb hr9o czf*pa 9rapped around them?

What kind of waves do you think will travel dogg q hlz*da(e;*b6du6 pvxv* 5wn a horizontal metal rod if you strike its end (a*gelv( azg;xpd 6q6* b *5dhvu) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature8 (3ck (vegpvf99eopq/1h2opa xwun -, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to- /ec(8xgk oq h9 po2vw9epup(3 na1vf vary with temperature?

Give two reasons why circular water waves decrease in amo m gu7/3fcec+plitude as they travel away from the sour+g3cofuc/7 me ce.

Two linear waves have the same a g3d+e tbq6y1hz0. ofamplitude and speed, and otherwise are identical, e.f0q+ 6bz ogty3ha1 dexcept one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses tc w6s9 ze6om)l7j +agv+ti g2hhe boundary between two sections of cord as in Fig. 11–33, the frequenc+2ezi 6 )+t6ocm 7ghlwj9vsgay does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, p-ip 0 /kli5kq3q.day are there any places you could touch it with a knife blade without disturbin-idkila5kq/3 pq0 p.y g the motion?

When a standing wave exists on a string, the vibrations ia 9 ao m37t6bxb2t2ybof incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Ex b96bt mi2boax27a3y tplain.

If we knew that energy was being transxa : vd(i5rgcoi ;e;u)mitted from one place to another, how might we determine whether the e:)i; rg5iavo;xu cd (energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amgzi,.y)+ ytrg plitude 0.18 m, what is the total distance it travzygt)+.ry,g iels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N h 0: le0tivszadvbnh7:md55 q9angs from it but is 85 cm long when a weight of 180 N hanb0l7v:q 0:a55e9 dtzmsdn ihvgs 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 when its 68-kg driver gyq9 yw0nq1i0 nets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibrati yw0q9n qy1n0ions?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish e8hgj *djt5.dc 5sh+xgomb;* hangs from it. (a) What is the spring stifg+5mo.x5jct gsh j he*;d8d*b fness 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 vibrv3 viv) y.;xewrzr6 ca-a+h;fates with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. Wa;+z 6vrfi;ve-x h).w3avcr yhat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. (lutxut)fyg 8lw 4, p3w+p4a k11–2 at times t = 0,t =(u+wtt 83ypfal p ,4)l uwxkg4 $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 tqg4-bn8 nn6k g is caught in a spider’s web. The web vibrates predominatelybnkn6g8 n-4 tq with 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 vibrates with a frequency of 0.88 Hz.(: ct- 8fn9ze ;fljo etg79xz4do2wnj When an additional 680-g mass is added to m, the frgjz 4ezx f ;-j7t lf28tn:ncwode(99oequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the endx+, s;km m73wgled (ct of a spring vibrates 3.0 times per second with an amplitude of 0.13 (xl+memg tk c,sw73 ;dm. 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 displacementsj p8(4fd8nkx from equilibrium is the speed of a SHO half the maximum valdk 4fx(ps8 8jnue?$\approx$    A

A mass attached to the end of a spring is stretched a distance 1 a ,z6 m86hswghn2usj$x_0$ 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 verti8l xi 3zl;b4ujcal spring 0.315 m. If the spring is stretched an additional 0.13u3l;8xzb l 4ij0 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.5m cs93/.hb xv;pnzeq 0 kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the objec; 3c xb95 vzh./penqsmt 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 the spring of a toy popgun 0.200 9pfp w- 4 qbu9/9d.raiv2wkrd m to “loa qiw kabrvwpd r94u./99fp d2-d” a 0.180-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 tz2 m ho.cqo55 grc7w0end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released fqom57 t .goc0h w2rcz5rom 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 isa0fvirz1b)knqz fz05* p 5ch, in meters and t is in seconds rz,k*pzi1z5 cbv hf00)anf5q . 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 of a SHO half KE and halfuph 9g2qp*w/ 14*c5qsfhgu id PE? ±12h5gqu pw udsfc *g 49h*pi/q    A

  If one vibration has 7.0 times the energy of a second, but their frequenxk7pbj+9mm ary )p18 ocies and masses are the same, what is thexjkor y+m pm7 )b18pa9 ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once ednigc.u y(a()qe9 3pwel3 -o xvery 0.65 s. dxa3n-o(cp( w9l gyiu.) 3e qe
(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 is7khc b0kkw)jr +z7e g/ supported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibratio g/7)k+wb rz0 kj7cekhn?

  A 300-g mass vibrates according to x*( azp9.z wse;l-6zs 2whmtt the equation x = 0.38sin6.5t where x is in meters and t is in setszzh ;*x9plam6sz tw2. ew- (conds. 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, d qv6vp0l,v 13 l;jfpa(aa. qawhat is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) is st7d yr:j bhhsz1fejk0 ooj:)29 rucybk1oj s de0jfz2 r7hjh:) 9:ok by 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 ykx,kz-87j 2o u7:tlssqei00 yg;y no 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 pointuyxsok0k8qizl-g 20yse, t y:n7o; 7j (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, w2g co7ga*i w029wqmyiith 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 blop. f arjj()b1bck attached to a fixed horizontal spring whose spr 1. a)pbj(fjbring 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 x+sq 20 sgu9fdjumps from a high bridge. After reaching his lowest point, he oscillates upu g+9sdqxs0f2 and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 mgu)*iokt18 2s1kq 5erus *ai bol7.kvibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly owb pusele j,1po6mj f(6z(j3e1tm a *-ne swing per second? (That is, one complete vip61( jtmo(j1ajpfmwu6*lsez ,eb- 3 ebration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where v5el*6 x1x - 1(vkx xtc1rjxlodv(z g+the acceleration of gravity is about 0.37 that on E vvrj+(c51 *xt- xx6lgv(z leo1dkx1x arth?    s

  What is the period oq-q3 3od6gbaetk5czv3m2o m,f a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pend 0hwftt6 en+ cdhehp:/b1i1x1ulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is nhw/1d 1e0tf6 p1bhhct x:ei+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 ha5 ntpcq 9, j /x+f1-gev0vnfqis a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortenpc1/vj 0vg-tnx +f9if5en,q qed by    mm.

Derive a formula for the maximum speed:w0i hva oob 11/bjq-6q q4ixx5jza6h $v_{max}$ 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. At5gt b / ngds:y3zd-ua, it is released from r t gzsy,g-na:5bdud/3est starting at 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 crests pass the bow of his busdx4pgu**,c af2yzz bs9,5 anchored boat every 3.0 s. He measures the distance betwedyxgau5p9*2b*c z ss , 4u,fbzen two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has -2gq59pds 721dicz,v.ol ig, nqt jgg a frequency of 262 Hz and travels with a speed of 343 m/s Ho2s92qj5z,gp,gvg i g dq1-li 7dtonc.w far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kin3g nbg5y v3q7lohertz) and travel with a speed ovg3 35nby7qgn f $ 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 wav*a o(+rbzgxukvynf/i3fy klx 5 .7)h0 es in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as 0uiz :ft8sc0gthe other. In which rod will the speed of longitudinal waves be greater, ancig:s0tf 8z u0d by what factor?   

  A cord of mass 0.65 kg is stretched bead -;x u0,4o)g8t h fwzzk.ozstween two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel 4 dash; uozog-t.,z80zwk)x f from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 6wa*rih 1*1 rjo20 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cableiao11hrr *w *j. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. 41k pywy s8wnw1g: 6plj pb64nHe hears the echo of the wave reflected from the ocean floor directly below 3.0 wgypj y4pn w41 wnk8b:1lsp66s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different spej+mzqq/+kri 9 eds, and this difference helps in lqkr j/9zq+mi +ocating 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 appnr : p6znhhn :5v5ebg4 7m5fkjroximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set 7:km4zfe:5h nh5v n r 6gbpj5nthe acceleration a>g]    m

  What is the ratio of (a) the intensities, an 6ii kbq;:h9,powyiz *d (b) the amplitudes, of an earthquake P wave passing thrzk i:qy ;hip6b,o w9i*ough the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake waonxo5 ulc5m8xc 68x.pve passing through the Earth is measured to be 8cn po xlc.m6xu 55xo8$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portizs5vdzm;:twl 8iim nr)c9 3 .ion of the Earth, but one is carrying twice the energy. What is the ratio of th 5 mvsmd8li.cw;9 zn3t)zi:r ie amplitudes of the two waves?   

  Two waves traveling along a stretahdm47k nc:u1)y8:ot :1u abgfhu.cgched string have the same frequency, but one transports three times the power of the other. What is the ratio of the ampm:kct:1 n.gbcg17ufy4hu :o8d) uh a alitudes of the two waves?   

  A bug on the surface of a phd1a. 481;kx s)joqgkml kxc1ond is observed to move up and down a total vertical distance oxk hx )kq;11j8losdcak4gm 1.f 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 maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch the;p i ck3/makp0 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 eac3 ipmpa0k;/kch other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamenta09o eul,ghdq1l frequency, what are theu d09ohleg1q , frequencies 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 frequency will it v.+2nu6hs fidx eo/ 16qh :ebxlibrate if it is fingered one-third of the way down from the end? (That 6. dsub2fi n oq:/e6+xlhhex1is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonate/ k)1ema:nr z5x1eap wpy sfi, :gbu2;s in four loops at a frequency of 280 Hz. Name at least three other frequencies at wwp;yxfui :nbm ask5,2e : ge11/r) apzhich 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 stanuu; l(n2 q5xuicq(o 9r00usikding waves is 475 Hz, how far apaku0q0 ui q925 oucu;xrs (i(lnrt are two adjacent nodes?   m

  If two successive overtones of a vibrating string ,ng5vdqp c jma+ry ,2/are 280 Hz and 350 Hz, what is the frequenmpcva ng /d5rq+j,,2ycy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mgqw *v t red+zmrpb,;q; 3ca0-ass of 3.6 g. The distance from the bridge to the support posp te m*rb drg-w +;0aq;3c,zvqt is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed torkoee o1z; rczdy*:7 bk:29id 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 thodyz:2ok*kc;ze:d7b 1rr9 e i e frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at ezq8-05o+ms2p zai7u 7dkqgd200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be chana0mduze8 i dksq+zo 25p7- gq7ged to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 4 yglql zg:j w-,bn3+x/vs2 mr60-Hz -qg mly+xsn2r/3gwvb : jl,z4vibrator. 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 the string may be adjusted by moving94 xi 0o*y(g 0txrqk yemih1a* the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm anyi0e4 xmir9aox**0y1khtqg(d 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency, )zdlr )pl2bjpa2jg-/ 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 -lapjj z gdl2)/ )2pbra 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earth byb ,dx bfc5+)xetween two kinds of material. If it dbx5+c bxf,y) approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the ;.r o diiw-i3rh;lpu m95c,c svelocity changes from 2.8 m/s to 2.1 ; .rps 3hi9ouliwmdrcic-5;, 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 layer of cold, /susli.3hn5kd / zhii17hea*vr30im dense air. If the sou s.z5l na0/hiih *hi3eu1/3 v dirksm7nd wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundar7 /n,eu z9a5tm*fh kmby between two types of rock at a 38 hk/mub*t,f9a z7 5enm$^{\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’sklre5v9 7;k lypri+k9 manual, the dish has to be pointed in the direction of the satellite, but an error9 yk+;ek 75rvir9 kpll 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 velocity ax/t6ovt b8n51 r+avp750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual tx658artpb 1+vvon a/decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness :m/ ruhmivo n5ve9gc9h z4x14 constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: mn/ohh r:x14c5u9v9egv m4 izUse conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 8-e9okn.jc(ad7 gs z sm below, which stretches the net 1.1 m. Assume that the net behaves like a si . kosd7zn9 ca8g(ej-smple 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 mas* g0+m/-ze :hjzyx yzbs then falls 33 cm beformz:-z0 by*/gejx hy+ze it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s ()27t x5cd npxuFig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the sx un2)5 c7xptdpring?    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 csjvi8 m5fp e9/offee (diameter 8 cm) at just the right pace of about 1 step per second, the co/epi5 msvj9f 8ffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of )dm +qc ok+mni,sfqzz68hp3 0a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be 3q+mhci06+ ,kz8qmpfsonz d) the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accq c(6p6/wqbo p(hr xhc )ojsvc06;; syording to the equation x=0.650cos7.40t where x is in meters and t in ss;6qcbppq/x0)vochyj( ( h wors;c6 6econds. 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 f8irk z rd71c+lyz4 :i8d ztq,7v+hvdvuktp;6requency f. What is its frequency if it accelerates at 0.50g (a) upwa : uvd6dl4+rkc z7q;tz yvzkdi, tip8+rv h178rd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it sc )b:6lvy t;4rocj .abinks 4.0 cm deeper into the water. When he steps off, the raft vibrat:bytv6r4c)clb ; .o ajes 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 music9yqd csa c:+ies1i5+x al instrument are tuned to play at 392 Hz (G) and 440 Hz (A)s:s+5 a1eix y iccqd9+.
(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 cor. 9csfj+tage0 lql).v uqpk9 3d of Fig. 11–33. Determine a formula (a) for the ratice93kqlp+.lt.sg u )v 0q fa9jo 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 each prong7benh8 ;3s hnu/f-uft moves 1.8 ; /sn-7 n38fhutbfu hemm 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 oscill g)jv 3yejvd 19tki luun240o4ates with simple harmonic motion of frequency 1.5 cycles per seco tuonkldg 2i9403ej 4vyvj)u1nd. 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?

A string can have a “free” end if v2rt qp9 *yocm(o5q,d that end is attached to a ring that can slide without friction on a ver( o mr2qcq ,p95y*tdvotical pole (Fig. 11–57). 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 — eqr w/ pu1jst2(ach one-way swing takes 1.000 sj/u2(r wtp sq1.
(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 dfe0.:qx9-b yzd.i.ex1ru) onf2v vl virection or can 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 period1-.2xf .odv :vu.e r l x9qe)ifbyvz0n of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pul; kf8 w nb-jqaty/yz/;6tm6qcse is gen/yaqtqwj6y/ c-z; fb 6 n8t;mkerated 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 fromr3r vwpb jcm.3 3erp+q2rzn*) a ceiling 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 oscillationsjbmrzq3pv.w2r+ crrep *n3 )3 that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steelqcxfu-)0;tx7 d hv (v:1 bslvx crane cable 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 the period of the bouncing? [Hint: Refer to Table huqxs (0 xb:v- ;l v1dvx)ctf79–1.]    s

  A block of jello rests on /+yw8 hli,qi:yvwgo,-9 j evy a plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You vwjygw8e+- l/qiy , :y,o9vih 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