Give some examples of everyday vibratingc/fc)y c-kkx5 objects. Which exhibit SHM, at least approx-k)cc5/kyfc x imately?

Is the acceleration of a simple harmonic oscillator 5a f7kmt,q+j: b (nb x1-wyjhdever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approxr.ooen ;s 2t7nv*xz:kimately simple x ns7oznt*:kr;.2voe harmonic.

Real springs have mass. : ob6p xg 3gb yysjo9c;(4i7fsWill the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized masslesbs7 yo op(f 4jgb9xgis:6 c3y;s spring? Explain.

How could you double the maximum spd l 9p nly )2dx3lty4dl+l9 i38n+riljeed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the g5,f 06q owskamog+a 3hook of a vertical spring scale, and then is released. Describe the scale reading as a funcq osa+6k, 5gmwog 3af0tion of time.

If a pendulum clock is accuratkk6/6 p76xki,tl xd zpe at sea level, will it gain or lose time when taken to high altitude? Why z tlppxd6, xi/k6kk67?

A tire swing hanging from a branch reaches nearly to the grou(ka/hl)idiorxb 0h; , nd (Fig. 11–48). How could you estimate the height of the branch using only a stopwatch?ib)/a r o;,0d( khxihl

Why can you make water slosh back and forth ine0cyj* wxh7 yxv-*xr7 a pan only if you shake the pan at a ce x 0wx-hey*7c*jy7rxv rtain frequency?

Give several everyday examples of resonancl 9 qlm)cq3w-be.

Is a rattle in a car ever a resonance phenomenon? Explaiqa,wi 4 i(sfa3puhk- -n.

Is the frequency of a simple periodic,vh 12ze /;ktid.v 3nx:q*cy smcerbz lx8m4 / wave equal to the frequency of its source? Why or vc3/4zl .si8cmz 2tk/ dexy* hr;x:v mq 1ne,bwhy not?

Explain the difference between the speed of a trpzad* )c bv0kzr lu361ansverse wave traveling down a cord and the speed of a tiny piep a *30kdbczu)rz16lv ce of the cord.

Why do the strings used for the lowest-frequency notes on a pian9 9e vlecjx/n/m:n fy0o normally have wire wrapped around tmn xvyf09: /e n9lecj/hem?

What kind of waves ds12mr+/0rjtc- z p pvzo you think will travel down a horizontal metal rod if you strike its end (a) vezmr-p jvs +/1tz2cpr 0rtically from above and (b) horizontally parallel to its length?

Since the density of air dg vz 5ej.ez*itr 4xy8y1)g k/secreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how 1 /)kxrzyvi.tj*s gze58yg e4 would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water wavefto ;c )oc/;els decrease in amplitude as they travel awayt;;cofl) c/ oe from the source.

Two linear waves have the same amplitude and speed, and otherw)kcmr p7n76b q+ szbzjx 75ls(azoa) wp-c*+wise are identical, except7 j+rbb+(czp q lox-6mwp7wc7z)n5k s zas*a) one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectio 23r 44vqgi+wvsiw. bfns of cord as in Fig. 11–33, the frequency does not change (although the wavelength v 4fw3 vii wrq.+4bs2gand velocity do change). Explain why.

If a string is vibrating in three segments, are there any tozcv( */8n-;nd3oytjdh 3cdplaces you could touch it with a knife blade without distu8n d 3nyv-ctot;c(d*zo/j3dhrbing the motion?

When a standing wave exists on a string, the vibrations owgh-y;; mm su/f incident and reflected waves cancel at the nodes. Does this mean s;g;h-yu /mw mthat energy was destroyed? Explain.

If we knew that energy was beingd ddksr15vh.ls( qv6fi:81ls transmitted from one place to another, how might we determine whether the energy was1d 8v krfs5d.dslivhlqs (1 :6 being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0j +lydsqskqqe re5+)v8.4 ei 4.18 m, what is the total distance it jkyl +s+ d4e8 qqve4)e5si.qr travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75prs ;kw2e0 8fm 0a9tfr N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is mp ;0rka8t0w 9fs2efrthe “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 get,4+ib tuc:bbcw7 7arm)r2 (ytw qb2w gs into the driver’s seat. If the car goes over a bump, what will be the frequency+ c tywraig2 r)2bw:7ub t,wb7m4b q(c of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hs71sb b8rtoq:q* f n:sangs from it. (a) What is thsfqt7srn1 os :b: 8b*qe spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is hit8v k9igt4 ad3u04z 6jsc9giung from it. What is it9 3si4tj gu6a4zd9 c80igikvts frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x m8u:va3nc3l tof the mass in Fig. 11–2 at times t = 0,t mnau tv83cl3: = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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/dsnj0e,rh6bl 6t+vqxlca t9a* s,/v.25 g is caught in a spider’s web. The web vibrates predominately walv, / vecd6 , a+njtblssh*6rxq9t/0ith 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. Wg*o ,osg;6jmn nwcu cm 3a *li3c8zs/,hen an additional 680-g mass is comjmsi zl s,*/gwucc3nn38ao*;6 , gadded 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 a92o iojttjyq p9f 0 -ba.pn/9sn amplitude of pqapj92yst jf/o9n i9t-0b.o0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the spx (sah q5d.7) kz;hcakhaw0rw* ;b1a teed of a SHO half the maximum value 1h *ra (7aawcswa.qxzt;0b dh)5hkk;?$\approx$    A

A mass attached to the end of a spring i 0kq82pnrmbn :s 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 0.315 m. If the s- k)i ussq;9irpring is stretched an addition; u9rq)k-iis sal 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attt+z9gvtd/g ,: m*nc qhached to a spring with spring stiffness constant k = 280 N/m and is e*htd,gg/q9 m +ct nv:zxecuting simple 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/x bqr*a(2qyi *2z ibg.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will bqq ra*ib(2gyz*2x/ithe ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionle5 w2gft/a; v*8c5 a tnjl+xcswss surface is attached to one end of a sptc5l;* at/5 gsjvwc2xaw nf+8 ring; 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 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 = 0.45b*;h3 eol1 axl ku8f0xcos6.4t where x is in meters and t is in seconds. Determine ;8*1u0k ohxflxe3a bl
(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 SHyiz0ueqb)j3j x35p 8gO half KE and half PE? jzx80)3ujge5iq 3pby±    A

  If one vibration has 7.0 times the energy of a second, bcv5xu bb/,oc68k vgje +l 8d5tut their frequencies and masses are the same, what is the ratio of their amplitudeod/c5k 8gvc5 ujx 6lv+8, ebtbs?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprin+ipg 4tp6+m s;aw.d nfor: t xph:/1mug once every 0.65 s. 1t+md;:ih.p ao+ppm n/t4 s ur 6gxfw:
(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 e1 eo:obm hip(+a9c-ssupported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the freqm+1ebah s ie-op:(9 ocuency of vibration?

  A 300-g mass vibrates accordi2k jmg:06jdxz/l;0 q ej5wht j5 bfcw-ng to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Det 5 0f- jl:jk d/t250mjzwgjqwe ;xhcb6ermine
(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 z-shit2h-lr.l r0d, 3:hjv ilSHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the4six.wj8-t e i end of a horizontal spring (k = 124 N/m) is strujw48t- e ixis.ck 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 constant 305 N/m vibrates uf.ey3qrzkq7s,f 32a with an amplitude of 28.0 cm when 0.260 uk.f2y, r7as3qfeqz3 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, wig/n b , krak;gu8,in9hth 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 blockkt67t el1r r:7 p3re/lqj 55gaxeblu+ attached to a fixed horizontal spring whose spring g el3a5p :x rbll7e 1 qttr+u6/ke7j5rstiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching his lcc.y5xa:88 euxc ( myh.fe)e vowest 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 bridge. Calculate the spring stiffness constant and the unstretched 8 y8 hu).ee: ccxyec5m(xa.vflength 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 vj3bd nwhdr2 b/:kn :(nibrations 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 exac0 0pc-tpekuap(p (h9f* t 9iajtly one swing per second? (That is, one complete vibrap-ah c apip*pt 9ut(0ef 9(0kjtion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its periohz 58n0w gtf. ejj6ll1d on Mars, where the acceleration of gravity is about 0.37 z.n5jlf6e0wtgj1l 8hthat on Earth?    s

  What is the period of a sb ,a 6z09potvsimple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum isaktkje*)6v4 r 0.760 m, the pendulum bob has a mass of 365 grams, 6rk)* 4ktev jaand it is 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 clockdenmqt okg3: mrh9. (0’s pendulum has a length of 0.9930 m. If the clock loses half a 93ornqg hm :t0.d( emkminute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxim/) yf( pkzv/tfum 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 atecpw -o yu;w*f6vx jx-xx475i a frequency of 2.5 Hz. At it is released from rest startix v ywpei*5f;xjxw7x-o u6- c4ng 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 cres;pi s5i-j3 gagts pass the bow of his anchored boat every 3.0 s. He measures the distance bet3sgii5gap-j ;ween two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of u2m( a5tykl-jnrt v/+262 Hz and travels with a speed of 343 m/s How far apl 5j-t( +tky/m2a unrvart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and :uo : vngy/av61600 kHz (kilohertz) and travel with o/v6ngavyu: :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 longitudi.(o/ ij8qxh k78jd99gtpigsj/5byd y nal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one m 7i66y-fh6 qplx ;e:qmxwo*l is twice as dense as the other. Il*o qly fm ;hx ix6q6pem6-:w7n 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 asn9d1 u.0x:b 7kjej 4sbimp8zpart. If the tension in 8dmsj1:izsu97 n b 40xb k.epjthe cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a h2f *f xk,bvrl+qi6z+v ill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comvi*qv , f+klx 6zr+f2bes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the 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 sidekaswogqh3+mi*8 m 6 i6 of his ship just below the surface of the sea. He hears the echo of the wave reflected from the mi gks6ai8q*+6w m ho3ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this iv y:o7x/5lov difference helps in locating thevox5 /l oi7v:y 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 apf:zild xt8ra a ;j1e/0a: *ryoproximated by a sinusoidal transverse wave. Assuming a frequency of 0.5: a ro0z* 8xi:; ayeatlrd/f1j0 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensigz*d cerf..7 pties, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected aeprzgc 7f. .d*t two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measqdwydb3zxy c csnn8+0y v,:84ured to be y80y+cv4d nd,q8 nsyc3 zb:xw $ 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 porti0+ -n wqpqwwh,vxq62g6o 5o ls7pkj.lon of the Earth, bu07owg. p5snw +pqqwx,26 l-ov h jqkl6t one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretch dc- 3xhux*nq(ed string have the same frequency, but one transports three times the power of the other. What is the d*x -cnhu (qx3ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is 8cw.a8 nmq5duw2 hw1l rpg6d-observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE changenqwdm 2g- 6 r hcdpw5wu1l88a.?   

The two pulses shown in Fig.ba-7 vz9n ,;oa ffn:wg 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. Whato;v-:,f7naba fznw9g has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as i(7xv,rm e;c ipts fundamental frequency, what are the frequencies of ,im7x v( cpr;ethe first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates ad x a/*w9wkg yho4y.)k.d d*igdoo -:at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only tw ddyk*igdwxo.)o: h 9 k.yag- o4wda/*o-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequenct6vi5;l lo bjvcd64/ny of 280 Hz. Name at least thrb6civldn ;4ot /lj56 vee other 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 2p2 j-o h+ ,z mw;nqyjpmz3*gf92m/s If the frequency of standing waves is 475py2wj*ho nzq3mjz;f- pm +,2g Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 28 ;fdddh-s,fwb(qc,t y18.dz e 0 Hz and 350 Hz, what is the freqd8fd-(f zd,tdy1 s be,.qwch;uency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the .ri4evws6j c (bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of tc6j4.i (swvre he fundamental and first two overtones?    Hz

  A particular guitar string is sup jmxu)k (p8nsgy.9r1 sposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequ.81srjnkg)m p 9y (sxuencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar stri (owgn a*h;)spng is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shou;ohp g(w a*ns)ld the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a swluoo:/ upj:rvd816 u mall-amplitude mechanical 60-Hz vibrator. The string’s m :/u pwjdo8o:l uv16ruass 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 )b7n4e + ndcdymay be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing d)ndyn+e bc74 wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the waeqzsq9q ,jdaek 5mhd*96 n0r,e- ef(hter back and forth 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. r9nedqah*0j6seqe, hkz e9d, (mq5- fWhat is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Ea vjqxx(w h1dl61;h/i irth between two kinds of material. If it app; xdv j i1l6(w/hhq1xiroaches 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 vel1mo tin-m-3ar 2 8dq6ee/4ncn0x yg5rx4s e sqocity changes from 2.8 m/s to 2.1 m/s If the incident wav1xo4 / n8sdqm0ygx4q rnicn2-t3 ees r6m5-eae 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 af+(f7 pgmu iu-. .lkaz layer of cold, dense air. If the sound wave hits the cold air inz.k fmu+ui.( 7fpla-gterface 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 earth,cjv5n)i q vr0)htaxe-d//d n quake wave strikes a boundary between two types of rock at a 3ve cnrj)-thd5/ x)0d, iq/avn8 $^{\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 di 48iyum. 3.ey ur yvoc5du-b:yameter. According to the user’s manual, the diy-uye.byc:34mduro y5.iu v8sh has to be pointed 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 wavelength 250 km and velocity 750 kmwj.dk s(:36pnnwj .xg/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 tsunamis, some of them attracted to the shore to see stranded fishes and xk wgp6n (s3:w.n.djjboats.)    min

  An energy-absorbing car bumper ha(knmnl-r j.v+ 5bfqs;t6) d bgs a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper ift.s (bkvq-f +b ;g)6j5rmnnld the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m beltez+7*lulq ht5esp(t hn,8.row, which stretches the net 1.1 m. Assume.l,zq th5su (ne prhe78lt*+t that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end ofp72 y75omk*;nr bqbrf a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise.; qy 72f p7o*rrkm5bbn What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed oqopny87 v4y1(j:lm e otyd7q 0jg4u*kf 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constan8poy1 eqydyk:v7 mtog7 4* ( qjnjlu04t of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the righrunj0,oe qme 37t t c x;++w;ki*6t75wgzszcut 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 the speed of waves in the c3 mc5w,tjtg;7z7ex+;6+0wzkse ir tqucu n*ooffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm p:xp0.i55 go,m fuit fchonograph record have a wavelength of 1.70 mm,t5 u5:fopiif mc0 x.g. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates acrcn x0lps;(8eozb4j; cording to the equation x=0.650cos7.40t where x is in meters lc0jb;op sn;e x(8z4rand 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 i6u4 s1h4f )rsnapd bc7s its frequency if it accelerates at 0.50g (a4)hp c 47bsrdsu fan16) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raftf*or5nx3-l bj , it sinks 4.0 cm deeper into the water. When he steps off, the raft v3xr*n5l f -jobibrates 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 440 ke7hdm 6.+pdwHz (epwd m7hdk6 +.A).
(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 thj1hi2+dl 1ylb9*5i q4np dy i zpji;7uqrf6 5ve stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter sectioi9 yd71ldr z64*i5ihvpp uf+y1qq bn2l5; i jjn, 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, anspl:k,; r2q tmzez*+od the tip of each prong moves 1.8 mm to either side of center. Calcuko :l+zq,2s*tmr;p e zlate
(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 ha c5gqh 92kj6b5wr86dzx (mblrrmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vw b9xzqkdg5jchrbl5 86r (m26ibrate 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 enhvi (v5vs r72bd is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vs2vhi 7vr(b5vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exacth7oo *c ,h.lysly 2.000 s — each one-way swing takes c *o7sh ,hol.y1.000 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 :;yzob9z3v0f5wrc2 s ers(cy wvs0p8 can oscillate in the vertical direction 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 period orc3ws 5f8sws0p(ve: vzy0r;ozcb 9y 2f 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 w e*ox(fz-jlx+0zln) pulse is generated at one end, and 20.0 ms later a seco-xz0)fje+ zl (wnxol* nd pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceil-(1. 6nolq5q;mq ble) rxapxo ing 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 the block?poqx5xn6 1- ()r.m;llqe qabo (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 22 pdh/ 5v -(fve t+g( fnkc.zwqljf*/b)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 bouqe5( /vw bvcl)zhj-g pdf.k/ tfn(*f+ncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in fzu4zp j;h+9l Fig. 11–58 (which also gives the dimenu f4lzp h+j9z;sions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz