Give some examples of everyday vibrating objects.tnoux(y6 el/ . Which exhibit SHM, at least approxyot.6el u nx/(imately?

Is the acceleration of a simple harmonic oscillat)x4hbvm(mi: : c zhcf) mbtn3wki l*6;or ever zero? If so, where?

Explain why the motion of a piston in an (tye7y5ryok47/*xp,bg oxdd automobile engine is approximately simple harmon577(tgxkoxyry dy b /4*e pdo,ic.

Real springs have mass. Will the true period and frequency be larger or smaller 5 :mv;(oh nr u6e6kmrjthv5: r(66umm krjhon; ean given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscilnxloq/0(-gcr9 l)mw bn v6) qnlator (SHO)?

A 5.0-kg trout is attact yexed3 4sw a7mto+-7hed to the hook of a vertical spring scale, and then is released. Descrme7+dtay- 4 3sx wote7ibe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose tign (p1 .ts)howme when taken to h (1os h.gnp)wtigh altitude? Why?

A tire swing hanging from a branch reaches nearly to th fty)b:zv5jbd x; -c*je ground (Fig. 11–48). How could you estimate the height of the branch uszfb)b;:t*c v 5yd jx-jing only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake t *yr+1*zl iv1d:w wuej:xygu*gsa 2b7he pan at a certain frequencx7: wu*a 12dsgel1jbuzvg:yiw +*ry*y?

Give several everyday example5-enn+jw b4 djs of resonance.

Is a rattle in a car ever a resonance phenomenon? Explain.xq(34z h oel;(a9v f9t+g hcbq

Is the frequency of a simple periodic wave equaluwx9fuq*zt( - to the frequency of its source? Why or why nou-t9zqfx *w u(t?

Explain the difference between the speed of a transverse wave trz7cflc .,q -lieq9 z3mau*o(gay1m p1aveling down a cord andceyilq7f,*a uq( m1z3m-.cao 9zp 1lg the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequen4(j(m (g:afdj5cfm w (x4 nfpfcy notes on a piano normally have wire wrapped aroundcff((f5p4x((ja4mfm g :w njd them?

What kind of waves do you think will travel down a horizoq wyg*g, 6yxx4ntal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its lengt*xqyxg6,wg y 4h?

Since the density of air decreases with an increase inm)t 8j) :g1kuuwewq5 k temperature, but the bulk modulus B is nearly independent om51jg ku))keuq ww: 8tf temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in am vf5lmdv d 0-iu7v/x1bplitude as they travel away from t f5i 1u-bdl0vmdxvv7/he source.

Two linear waves have the same amplitude and speed, and otherwise arewfm3nfl/ n(e( identical, except one has half the wavelength of the efl n(w/m(3nf other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary becb+2. 0da /md)tmiodop ov 44ttween two sections of cord as in Fig. 11–33, the frequency does not change (although the /omm 4t dabdod)vp0 o.4i+ct2wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any+fqmg zdeo) g.d- cs5fv9z6 ch5rq:7g places you could touch it with a knife blade without disturbing the m5sf)eqz : g 9q-+ggh d.z7dco c56mrvfotion?

When a standing wave exists7 cvcvl6b.7 *na(ivlg on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed?bn.v *vgl 76 caic7(lv Explain.

If we knew that energy was being transmitted from one place to juvlsma42 ebi.. 85shanother, how might we determine whether the energy was being. 5v8jh s4amube2si .l carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m,vz2:h7ao .)kphy0a+by pk)z m what is the total distance it travels)aaphb: m.2vkk0oyhyz7 +p ) z in one period?    m

  An elastic cord is 65 cm long whfw+df2g(v- xpuo jl8*en a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of thpf lj g-(fw+x2duv*o 8is elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when itxjb) jo3g x,67 u-dnr,rmmzc.s 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequ. )j,om r6bd-m73xjz g unxrc,ency of vibrations?$\approx$    Hz

  A fisherman’s scale sf0bat7(3.istopqpmv0u49 w ptretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is thp q07o.3i4s9 tva0uwppmt( bfe 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 ofp6dghqz u r4ic;8;vpkr 5xx 80y3s:xa,b 5aq a 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs fr8:85sg,rzxdcykix ap6;p;05 qb3u rvax h a4q om it?    Hz

Construct a Table indicatiz a,zd tf;mp(/ng the position x of the mass in Fig. 11–2 at times t = t/;md(z zap f,0,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 .)st n )(dg5y jn6cgtlg is caught in a spider’s web. The web vibrates predominatelyn)td)c6l gt(yn j 5sg. 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 vibrat9 6;bm1klsi;xvcqts -es with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value ;imc tl 9xks1- 6bs;vqof m?    kg

  A 0.60-kg mass at the a/ a.;cjdggen89fgi2 end of a spring vibrates 3.0 times per second with an amplitude of 0.1a9e2ga;.cn j g/dfgi8 3 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 hal(dys(u2: + lothg d5vff the maximum valuh 2 s +(fdy5(:dovgutle?$\approx$    A

A mass attached to the end of a spring is stretched a distanct6tt1 ou )qa/ wf,;owue $x_0$ 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 adv cw4k(0 xq-il- oe6e vertical spring 0.315 m. If the spring is stretched an additional 0.1c-6o( x klwe-04ieqdv30 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg ifh jzawppi6p4 ()r f;w 2+s8ius attached to a spring with spring stiffness constant k = 280 N/m an+i6w ffu;w8r () jh42p apipszd is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/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 tokp0 o d+*xv,cx “load” a 0.180-kg ball. W,0vdkpc* xo x+ith what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface 9(jcw6 t bpahx1z;mo at,329rm k)ezris attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required tphxa ( z,oa)mtwt3rj 9k612m e9c;z bro 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 = 0.45cos6.4t wh qrhezx;7 ibobis1 s;(9m/y 3vere x is in mev;iz;y9me( 1hsb/37bsiro xq ters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and6qrc6z elqn*h(9 od7zx2caa, half PE? ±( ch2,dz * 9qarl6z7cxane6o q    A

  If one vibration has 7.0 times the e03movw q 9a(4fwzc h2unergy of a second, but their frequencies and masses are the same, what is theo 3( 0vahw9f4m2cwquz ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every 089zg6i . vxycc8ixvgy96zc c ..65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, each :,p7n ke/ubr99njvqmw6 p 0 bywith spring stiffner7puj9,q n k:b6e pmw/0 vnyb9ss constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation xti) z(evff(4r,*pvok = 0.38sin6.5t where x is in meters and t is in secont i4f*zo pv(efrkv( ,)ds. 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 ofl90n 7tla, fpx 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 r.i),et ppl o*s0orv.gest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, veprog.*i .lo )st0 ,pwhich 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 5l3d ydq p sg:fy4.0il,xlfl3with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) wg, ydls d:f3i.ql0 4px5fyl3 lith positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with a lrxkr(i .2)cspring 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 0.60 beu-h *fulk* cac10fupcgej 859f e;-0-kg block attached to a fixed horizontal spring whose spring stiffnessbckj- -*fgu;fu05ep e 1c*u cea9flh8 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 l9: :f0ek m;+ yqcxoqdm,*raw1i6rw a d(u)ewnowest point, he oscillates up and down, hitting a low point eight more times in :mww e*oufe190q; ma kcd (:dr6qrixwy,)+ an38.0 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 vibrations in exactlptgg 1xze2 jq-:z4c/ry 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is (zanp*3+0rsic8 sv r09 juqaz to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 s.)+ izvpr rn z008aa3jcus9(q s*    m

  A pendulum has a period of +i b s 9xu75i7qt/(j4gu:v:vlgaroot 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 t7ioug(l/ 59ojgvb7s+ :vr tua:q tx 4ihat on Earth?    s

  What is the period of iwqn3i e6rgi+ju;,9e)c oh j;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 pendulumbwifso6d4nsmi- to *n ns0 -18 is 0.760 m, the pendulum bob has a mass of 365 grams, and it is rele6o w s1f0mnits - oin4s*-8dnbased at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 u)+aku yi6 xg5yd+98g+gsdd vm. If the clock loses half a minute per dxgudygv5d d)g siu6y9+ + 8ka+ay, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the *r mmw wzxr -9.chlz +2765hv-c s xs,kc9vdnqmaximum 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 oscillyws*5 :fkzo /e1bc5ivates at a frequency of 2.5 Hz. At it is released from rest st:/5zv fko*eci 5swy 1barting 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 m:m bm *t19dwfuqg 9ebdvls a-t9x* :,crests pass the bow of his anchored boat every 3.0 s. He measures the dis,t-:xgsmu vl9:1m d9 *qwdtba 9b fm*etance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air hsv/iv 4l1gg a8lm +1qlas a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressions)?l +i1mg8v gq la4vl1s/    m

  (a) AM radio signals have frequencies 3c. rqt1 q6pt2ndk br:o(kn :abetween 550 kHz and 1600 kHz (kilohertz) and travel with a speed ofkndat:ct:6 r 1 3rnoq(k.2qp b $ 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 wavda*z qbiy(b qj91bx,p 7gv64mes in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulusg; r2 r 3ezt3zc3ele1s, but one is twice as dense as the other. In which rod will zc3re ge;3rlte s123zthe speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between)hmihw d9 e 4ua(7bx*v two supports 28 m apart. If the tension in the cord is 150 N, how longh x4imh 9a(ud7 e)vbw* will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of lengt;+wxljw6t-zu h 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and seljz-w +x6 ;wtunds 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 his ship just below tk 3d 5f3okoxm:he surface of the sea. He hears the echo of t:d3mf 3k5ko oxhe wave reflected from the ocean 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 di3-3 vkpl c-yimfference helps in locating the earthquake “epicenter” (where the disturbance took plv- p-i3mkl 3ycace).
(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 ;rpw.hicaow7hyg/,p9/ a ih/ 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 s7;wy/oa9. hah/ r/hiwc pi,pgo that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensitief/m a ts x+h 45 y8o0g6p4dwgm*1ykbuws, and (b) the amplitudes, of an earthquake P wave passing through tkwbpm/4s86dx f 1 auy+gw* 0tm5ogh4yhe Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave p:eoo -x1 yt:vaassing through the Earth is measured to be o1oe xvt:a: y-$ 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 sa7j7 q:p x9;ehljs bcf8me portion of the Earth, but one is carrying twice the energy. What is the ratc7b9l :ehp q8jjx7fs;io of the amplitudes of the two waves?   

  Two waves traveling wr(ud rs *lc 70gb pv*0mj/7u3 qe8qayalong a stretched string have the same frequency, but one transports7lra08vbqqyc(*7 0 jgepd3 sm/uwu*r three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of 0h6wcv 0ea9-hx:xp6ci)szv ea pond is 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 mah-exv sz)6pha0:vex6 w cic9 0ximum KE change?   

The two pulses shown - t yql(t+u (phzlreq .9ifa,q5pbs3v*o0c 0o in Fig. 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 9h+-0qcbs l5(oav.rf*iq p te0p 3(to q,yul zthe string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequencng 6s 7cim5incr+ 2,hty, what are the frequencies of the first n +mhg7nc r2icts5i6 ,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 wi-zg w) ub-n w/ +tfyv-.zs dxzk:xg6+nll it vibrate if itkyt-.wzbs6 gf-+:z -zvxxgundwn+ ) / is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency3 1a fov:4p0qt gsht..p03mw tgcm b:x of 280 Hz. Name at least three other frequencies at which it will0c:vxt:.gmfqptsm14o 3b3h.g tw a0p resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string i0, uju uurf+9as 92m/s If the frequency of standing waves is 475 Hz, how far apuu 0uu+,r9fajart are two adjacent nodes?   m

  If two successive overtogqh4m8 /)xwtu nes of a vibrating string are 280 Hz and 350 Hz, what is the freq4m8whgut) /xquency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distanceton(yu+0a cq yqqkj(12 ub.y) from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental a+q)ka1tbyuycjuq0 on. 2 y( (qnd first two overtones?    Hz

  A particular guitar string is supposed to vi7fco e5l8ggso 440i mabrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed t4f 75a4 lsoogei0gc 8mo correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it i4ugq ul5+g+:+f+i v7 x 4ygn mcfcgo-ms measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frg+ i-m+xf7uq yvcugo:+gmcg4l5f4n+ equency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60-Hz r*kuqr,h;;y1f cc wu7 vibrator. The string’s1 kuyuq*wr hr;7,;fcc 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 pulles0g 5mkj ar (vtg i,va-w 3bnz c5,lfi(4b4aa/y. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may,ga3ni 5i,mg4jztk4-a w v/lr(av b a 0bfs5c( be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water bac5sd-x 0+bwtcokwh*b7 k 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. Whaw 05ostxdkbcb-* w 7+ht is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strwlmua(2i j( n8p4 )nujgvqu-: ikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident2 -pg:)n u4luiw qajnjuv8(m( 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 ux12mcf 9v8ofy nderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident w1c82mf 9ovfyxave 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 b-uvya3( (+/c erkj,+hkvgzaof cold, dense air. If the sound wave hits the cold air interface at an anglej,(a/(k-b he 3 +czvvaykr +gu 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 ah; (hv/*cly2e p yqh)4s5 tfqy boundary between two types of rock at ap5(hvsq ly /; y*4 e)fq2tchyh 38 $^{\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. Accordi dt2;w.ha k;xqng to the user’s manual, the dish has to be poi.x;aq h; kdt2wnted 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 across the Pacif.fmh t;fntsm,*f 1b.u9vh 7d0.lram tic Ocean. As it approaches Hawaii, people observe an unusual decrease of*0u. tmn mdafmfl,b. 1v;t 7shtfhr.9 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 consta*z 5ain816oh z tt /il2dcrkl4nt of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collidest*2hik 5 4ldlzzn8ac/o6t ri1 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 below, wha-s d1fe qqufc6 9:zo5n +v.idq+c(ofwmx,) rich stretches the net 1.1 m. Assume that the net behaves like a simple spring, and 9 cce(,qi+nfr wqmfo)d xu5+- s 1:6.qfdoavz
(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 pbzg(8 aw*qhu58 4buzulaced on the end of a freely hanging spring. The mass then falls 33 cm before it stops and uubza 8qhzbugw8 *(45 begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sj2.ucva z.e)vv ypq16pring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) 16jvpcz.qu vye a)2. vWhat is the spring stiffness constant 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 (dia-h-5/ 0h+fm1 zb pxj:ehlfs1pesnb 72twa uu2meter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until j/x17:l 2ef 1 m hwb s- upnebf2za-pu0h5s+hteventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certaif8ysk .ai8 c;cn groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.c8a 8.iyk;cf s70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t wher jg23tfn2x h53k-wsiwe x is in meters and t inwhfg 32jw-nx 532tk si seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if it nb n /ms940bkvaccelerates at 0.50g (a)9v0ks/4bm nb n upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on5 r:mgie**4orbh .t fm a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper inim*h b t g.mo*er4f5:rto 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 instrument are tuned to play at 392 Hz (G):hqf/e h8iickj 4a+x4 and 440 Hz (A)c iqak/xe4if8 +4 j:hh.
(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 traveli2yy(h/ * sif7nrug2*pn, fsvdng 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 is the same in both sections. Why?) (c) Ihyuidn* 7r2f y,s*2 vpg/s nf(s the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates atdbiy;8n8u i:uio7 urc m;)pk. a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to eithcmi r.uuidk78pon )u8by:i; ;er 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 gvhv.svp:d 07hna )mjj04 ot :of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board :d0h4tp 7 0svjmvn.g):jhv aocan vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end y.00kkcbq0 f6rkl**fg ek1 yj is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibration0c*kfj0 ekkbgq k6l*1 f0y yr.s of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-wa : r;fx:0ii1ohcnzl x3y swing takes 1.000 szlxir:3no:0 hcx i ;f1.
(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 oscillat(1rq yousy7 tvls+ tx:8)j gxw,wpo;7 e in the vertical direction or can swing as a pendulum of small amplitude,y s7+ vw7jrq)o;lx put:w8to g, sy1(x but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ 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 N5erdle-sff65xndr ;m ,ii9)q. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at th nd)fle qs95dr ;f5i-6m,xreie opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a 8419m/j zl fw d0ss 5dqpgw:mzceiling by a spring with spring stiffness co9s jfwmzm8gpsq 1z4/0w ld:d5nstant 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? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steerv;s-1 o0ec(w yd v9as3o wjumkct9(5l crane cable is 22 m longmetrks 0s;o-o((9v3yd aw5c w1u jv9c 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 9–1.]    s

  A block of jello rests on a plate as shown in Ft*)/nzlkbq 1cg hpt30u 8bj3 qhh3 os3ig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then yo 3q t*qto gl/u3j8bhhpb)h13 ck0nz3su 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