Give some examples of everyday vibrati;n8patm h8tt6ng objects. Which exhibit SHM, at least approximat68nmtt;a pt8hely?

Is the acceleration of a simple harmonic oscillatoit4;cu0) m uuwr 6d,vir ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approxi8r1 znjtv-nhyn 7wbo; ll-0)fmately simpon10wjf hlnnzlyt-87 )- vbr;le harmonic.

Real springs have mass. Will the true period and frequency be larger jy .b -c1rqf bo(8z(qeor smaller than given by the equations for a mass oscillating on the end of an idealiyqfq zbcb8oj( -1. r(ezed massless spring? Explain.

How could you double the maximum speed of a simple harmzk:elnun0u+ uhd l7nwuu4 +: 9onic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, andnj wqth)u, a,((*vrs7hbpf5m then is released. Describe the scale reading as a function osf)p ,mh7v*b,hn a( j5(wruqtf time.

If a pendulum clock is acct96ceavf;c4 6w0/o0 jjvdk jp :kt4kkurate at sea level, will it gain or lose time when taken to hige4c ajk 6jt/0kjv;kov0:t49 ckpd 6wfh altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–4862c b*e 1xlfjc8v)v pcx8mg*)lwijc*). How could you estimlcpmvcl bj*xg 2) )cf8i wvc6x*j *1e8ate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pfseq83nk/l z6e:. bkuan only if you shake the pan atnl6 /eskef q .kz8:3bu a certain frequency?

Give several everyday examples0 f:nx wwtxce2,9oy1x of resonance.

Is a rattle in a car ever a resonance phenomenon? Expddhreo(*rc19:8 r*: yla k0 zu 6xzw8cggwov4lain.

Is the frequency of a simple periodic wave equal to the frequency opq ny/g4xvn6;no d+3 hf its source? Why or wx;vp qhng/3 +4dny o6nhy not?

Explain the difference bem4ine- (j pb- jod0k2xtween the speed of a transverse wave traveling down a cord and the speed ofj-njki( p e mb02od-x4 a tiny piece of the cord.

Why do the strings usjn(:v )7y wf z4 ppcvwa0,8sxaed for the lowest-frequency notes on a piano normally have wire wrapped arounc40(v 7 :s8vpjzwyp,nfw ax)ad them?

What kind of waves do you think wixm x0vicba;) bq zt7/b32b,th-n9v hmll travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paralleib2h /3,h-;x0nv bv)txa 9c btmb7mzql to its length?

Since the density of air decreases with an increase in temperature, but the bw f-qkhz7 h k ; rur)f;mq*b57ra37lymulk modulus B is nearly ib77kf5aur*q- r l qwhh;7k3mfyr;m z) ndependent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease innm4gn*( b6kmy h)2wte amplitude as they travel away from the s 24nmy hwm)6g*bek (tnource.

Two linear waves have the same amplitude and speed, and otherwise are ident7b bhv5nnki0 k4woc+ :ical, except one has half the wavelength o h5ik w:b4 n0+cbvnko7f the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between twaq8il* 5p +v6/nzcxml ndi3dm36j a4 so sections of cord as in Fig. 11–33, the frequency vqn3jpiz/8mm4lcx6a i+d3 *sl56nad does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any placexi i,u+2l;r)k0/xbxj pxhws/s you could touch itx+w xsux/xkli);0/ j,rhip2 b with a knife blade without disturbing the motion?

When a standing wave existhsq)v jlujwl+ bj 9gkm*eiy374 .q7xb 3(*knf s on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? k x7j7)hn9i* * vjbsu+jkl. ef33lgqb(ywqm 4Explain.

If we knew that energy was being tran3/wsf-j5f0xoow f z7p, th+kt* gpgp 9smitted from one place to another, how might we determine whether the energy was being carried by particl7x90pp pfwhwft,otkj5g*o sgz/+ - 3f es (material bodies) or by waves?

  If a particle undergoes SHM w014lmi oysy) ( dc9evaith amplitude 0.18 m, what is the total distance it travlei 1a4o9md() yy0csvels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from ousvlc 8 ipz.g h0h3(mx86pl2it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” consm8h p 6ouig (c20zl83hlvxp.stant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into thtq90 .usdn 6mae driver’s seat. If the car goes over a bump, whn96u.sdt qam0 at will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-knut70 etn 6l)jg fish hangs from it. (a) What isju7nnt06t)e l the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequent)lwsq8y :be9 j40rnxcy of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from it? r9ybl4:xs 0tqnw 8)ej   Hz

Construct a Table indicating the position x of the mass in Fimd*msit8 jyn 6 /addx+y)2 h6og. 11–2 at times t = dmtdsm6o2j)di y8* /a+n yh6x0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. +7/ii6sw nhzt;il + dfThe web vibrates predominately with a frequency o+/fznhs ;t76 ilw di+if 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. When ,a hr l+6c9m:fu xo8ayan additional 680-g mass is added to m, the frequency is 0.60 Hz. What isor:,ay +cax f9l6mh u8 the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second witu by;r: zi):nwk97werh an amplitude7uewi)bn :r:y z;w9kr of 0.13 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 speed of a SHO half the maximumq ;6u2+hnbty. qlhfe)q0yl ,jy k)7ze value?qe7qu.)y zf e6byq hyl2tk 0l+j;n,h)$\approx$    A

A mass attached to the end of a sprilzd x8y.3e, leng is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg st : iavdcy7ur-/retches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m an ui-7ay d/vcr:d released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a sprim wxgm.g78 v3l uba or(oh-a;/ng with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its eqb 3.;ru-hox(g/m 78aaowlvm guilibrium 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 m tb.ac7ihc5-s co “load” a 0.18-acshb.57 c ci0-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to rv99 yu*vivcwh x/+ n8u5sw1aone end of a spring; the other end is fixed to a wau 19csr5 9vhn8wyw x/vviu*+ all. 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 = +ej1n56 l dhmz0.45cos6.4t where x is in meters and t is in seconds. Determ+j zln6h med15ine
(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 shf c4(e6kjz0and half PE? ± z( 6s 0fc4kjhe   A

  If one vibration has 7.0 times the energy of a second, but their hw/l di k,;tt-9egb 5sfrequencies and masses are the same, wh5-tb9di; glt,sw /ekh at is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates e42 owupl; xv0from a vertically hanging light spring once every 0.65 sw4 ulp0xvo;2e .
(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 v.rzuhijv+,k h.xh7 f1ertical springs, each with spring stiffness constant k (Fig. 11–49). What wil7h1 ,ix fuzrh+..hvkj l be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x isekabka wy ,h(c,.y,q1 in meters and t(1ky wa,b e,chykq. ,a 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 oy5 *dyo1:k nvymv w3(/dq if+j.v.tz;. byrlef SHM, 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 the end of a hori4b4q5bs5yc xgo2 hqx6zontal spring (k = 124 N/m) is struck by a hammer, whiyc 5qx 5 6h2goxq4bsb4ch 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 wit *clk:ek9eur nzlfhc ,-jj/r3olm862 h an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=kl ,rez:nu r *8 l9/co6-hejkl3jc f2m0) 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 xzo ++/ j .hbaad /i3(umaqbn(two springs, with 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 bl6t:p fpnx:ac,aote.4xcx/ qh3pm c+ :ock attached to a fixed horizontal spring whose spring stiffness constanxhf:c tnp,o/e:a pac+3 .xcxp m:tq6 4t 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. ba0wfhnd p));After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finallywpd)ha0 ;b fn) 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 vibrations in exactly 60 s. What is-t j 0pprpvri9a/r t3) its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per secoqxi q/np9 42 sr2y:ws:vwx1e ond? (That i42 svpq no9e1q:2s:xx w/rw yis, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its periotqdwvmx5p n 3qj 00p r-+vs+t0d on Mars, where the acceleration of gravity is avj30msw +-v+5xn0d0 trq qp ptbout 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm aml1 bf68kn8ulong
(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 haaiz/:2j e2a qq nt2xejfqp,)k6i.* vhs a mass of 365 grams, and it is released at an angle of jqfte2/zpake)vjan.i2 hq *:i q2 x6,12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a lenrbocn d-x; /ljejw0 x47l k+l9gth of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length jxno9l xd7;ckj0-/w4 lr+ bleof the pendulum? shortened by    mm.

Derive a formula for t,fx g ;x,s qosx(z:o8qhe maximum 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 oscill;+fuo1shbg; 6pcso9q ates at a frequency of 2.5 Hz. At it is released from rest starting at anq9p;oh gb16 s;ou +sfc 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 anchored boat everb0 tflg+h1+2hla1a t jy 3.0 s. He meb+ahj l0h gtat2+l11fasures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 e )xughpccxg ovjq.y 1r3430/m/s How far apart are the w pr vqg1 x0u.3xhc3c /4gje)oyave crests (compressions)?    m

  (a) AM radio signals have fre v59(vew,(5c j 2y,mu vcvy9mskhh jd9quencies between 550 kHz and 1600 kHz (kilohertz) and traved5 yv(9,(m mvjs2wvykhcc5e9 vhj ,9ul 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 longitudhumj41lp-0d dinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the samey- /jvuxd g/ie)9oyt( elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinalteo9)xu/y / d(yigj-v waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. uxt;tj o ,5t chk3o0g8If the tension in the cord h83 ;5c0uk jogxttt,o 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 ,ka,64onpj 8enipqi i1 -ifj/the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its rn,o8i/i1fp4ej 6 j,iq i anp-kun, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of 1-+ tku*d ajem3qs+vc 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 oceuvj-q+sk d +c3t a*em1an at this point?    m

  P and S waves from an earthquake travel at dxpl+((3h m q3r p2rscqo 4eaftli;:u* ifferent speeds, and this difference hqmlx3r (e hp2t*ocq;:l +air(s 4f u3pelps in locating 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 sur.jgjz. . *wld9mhxklo/ggn5 *face wave can be approximated 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 lk d.w*ln/9z5jgox .hmg g*j.ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudews,23 0w4ic kr7*vmmm8 on rscxd9ctpns7 c),s, of an earthquake P wave passing through the Eartsm8vcc,mcr3o)x7sr,* k m i2 w st9wcn7p0dn4 h and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthqf9:2k zc3 b bqyj* 8daeus*,cnuake wave passing through the Earth is measured to be *qau 32 c zbnd8yk:jf,*s9ebc$ 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 traaox6zx8a ywguc /f.*8 vel through the same portion of the Earth, but one is carrying twice the energy. What is the ratiofoa*xza8 / u .x6wy8cg of the amplitudes of the two waves?   

  Two waves traveling along a stretched strindyrti w)k+y,ay d4 dy. z6fd7gz+ix.6g have the same frequency, but one transports three times the power of the other. What is thidz. 6wdk. yi,+ zfdyy)r7 46 ya+gtxde ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is oqjq zhkf3q3( ch*e8; zbserved to move up and down a total vertical distance of 6hqefzq* ; (qj8h3k3zc .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 apjec (f3q12dk* p i)vmoving toward each other. (a) Sketch the shape of the string at the moment they direidacf )1*p 3kp2je vq(ctly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibraln6x 4*-uhef; q/; rol+ea goites at 440 Hz as its fundamental frequency, what are the frequenc +*ro/-;linl6eq uh go;eaxf4ies 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 wil,kmu)o w1l dfjl-,xu5l it vibrate if it is fingered one-third of the way down from the end? (That is, only two-th,,ux1l-muf wd lo5) kjirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 21 uwocstq yn43h)l)g8 80 Hz. Name at least three other frequenc)c)s 1 lguq3own4yh8ties at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of 98wp uv3uln f47* x u**lhhwvrstanding waves is 475 Hz, how far apart are two ad v**ulufp7nxvl98*4h3 uh wrwjacent nodes?   m

  If two successive overtox tg w7f/2wne/o .4xutb9m )gknes of a vibrating string are 280 Hz and 350 Hz, what is the frequency of tun xtf4o9 /gx 7bwkt/2 .w)mgehe fundamental?    Hz

  A guitar string is 90 c2b(;qmmwg ntn(.yjo/ m long and has a mass of 3.6 g. The distance from the bridge to the support post jw n;my.go(nb/t2( mqis 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 to vibrate at 200 Hz, br6ng5xl cc20e fs 6tl;ut it is measured to vibrate alg tlsfne6;0r2 x5c 6ct 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string mojly; wf-t6 :is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should t:;mf ojwtl -y6he tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attachedsbg-lrkv08 s g32myj7 to a small-amplitude mechanical 60-Hz0 s 2l 3gbkymr-8vs7jg vibrator. 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 moving the pul6.1x,espxem:5a piv bley. 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 and 1i,e.b xm e:pv5a1p sx6.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency, (4yv3tk k inpoxz)n7:the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speedzk4viy3knt(xo p n:)7 of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary xni+ jr: ax3z;within the Earth between two kinds of material. If it approaches the boundary ja :+;i3xnzrxat 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 velocity changes from auwu 2ksd:i + -,ofsa,2.8 m/s to 2.1 m/s If the incident swfi:ua +, ao2-ukds,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 lp:zwxnt;:bnsb24 x f ll 50e:mayer of cold, dense air. If the sound wave hits the colf0:znl 5x b:4bt;nxe2slw:pm d air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary ; *(ppfwhm 9ycbetween two types of rock at a 3pf ;p9mc* yh(w8 $^{\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 usek8 r:62s fxrfup5+aahr’s manual, the dish has to be pois+uhfp : rxf6ar2k 8a5nted 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 km/h travels )d1se sk9ga*f( bt :rphd7lf 2across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrea* f bdg( rl1atse:pd2k)f9sh 7se 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 bump4x(+d q5r qmt-fj7niper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides withq5 f 7d+j(-qrx4n pmit 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 below, e0 c+vdgs04cc which stretches the net 1.1 m. Assume that the net behaves like a simple sprcg0s e0dc4 v+cing, 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 springgfs:a5px /,nxtbq0 w* -c 6wvq. The mass then falls 33 cm :0wbf s-xqgx c5t vp/6,n qw*abefore 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 (Fig. 11–54), copr3 aj 4h :a*zarbg)npnk9t5 )mpressing the spring 5.0 m. (a) What is the spring stiffness constant of knppaza*3 nr:rt9a gj4 )5)hbthe 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 (diamete 2r(lauo0r-l5c *dxthr 8 cm) at just the right pace of about 1 st ud0lr52rt*hao(-xclep 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 coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of)ipn).j(abwv a 33-rpm phonograph record have a wavelength of 1.70 mbp wnj( .))ivam. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates acc2g kc*131j1ds pdra hxording to the equation x=0.650cos7.40t where x is in meters and t in secoj1d a gdp1s 13r*x2chknds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is inu3g2 d k7d;fyts frequency if it accelerates at 0.50gd 7kf3ng2 u;dy (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the rafjvnzgsgip08-e i;l *+3tehh3 rah82 ot, it sinks 4.0 cm deep *-noh heir83spgt lz2gv+ae8i hj;30er into the water. When he steps off, the raft vibrates 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 instrumerh w 5b (qa*vfdgfky+( )b*o.fnt are tuned to play at 392 Hz (G) and 440 Hz (A).fhw y )v(*fb(r*doa+f.5 gbqk
(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 n-9r +q7)r,et kxfnvs down the 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 section, and (b) for the ratio of the wavelengths in the two sections. (The frequency issr evqnrf+nt9x ,) -7k 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 lq):j jnj8: a o7hrp.uof each prong moves 1o .nj:uq :8)7harljjp .8 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cycles sq y/h7c tms/5per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with th5qh7/ m c/tysse board during the oscillation?

A string can have a “free” end if that end is akeiktz5b)a5i )zt 5*l ttached to a ring that can slide without friction on a verk 5* tbai5)kli t)z5zetical 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 — ea zc8.e 8fusi-t,cqyv 9b 90rpech one-way swing takes 1.0trez,c9-08fqycip8 s.b v u e900 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:zrz2au3 i v,w oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longr wz,2v :uza3ier, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretche+g ta5) wrg ds7,wviw*d under a tension of 255 N. A pulse is generated at one w5*),ras7gwvdg t+ iw 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 9y:8derg dg m4suspended from 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 amplitu4m g:degdr y89de of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car adm47*v8 :mdxrm8r jx zt the junkyard. The steel 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 v8j7 r8x*mmzxmd4r: d9–1.]    s

  A block of jello rests on a plate as shown 9 9sca8*t*dr;vniv kjin Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given iv8*djav9 ks* nc rt9;that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz