Give some examples of everyday yl qip9 yv87v.3pg f mngyc).b1b +b6tvibrating objects. Which exhibit SHM, at least appr. p1ib.+yyl63p v8v gct )7byfqnmg9boximately?

Is the acceleration of a simple harmonicf: l43rc3 kbf wo8waxbv1j;/d oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobil:ywlo-i/oql:g:x2 j( q v lp)yv2yc 5ye engine is approximately simple hawy:go:cly/lx:yqi)25( qlp j-v yo 2vrmonic.

Real springs have mass. We/k ,+1b2bi gb4niro will the true period and frequency be larger or smaller than given by the equations for a mass oscillating on 1+ i,w 2r4en/big bbokthe end of an idealized massless spring? Explain.

How could you double the maximum speed of a simpw8e0yw wnid43:n r;6 ekqby9i 0-tia nle harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical springc)*pl6 s115v bvwod 82 wpzc.vy .nwhh scale, and then is relea.c.spl156)w1 8 c *wh 2vwnzbvvpoy hdsed. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it vmzbs+pn (tzqw7q6)8uc9z 1jgain or lose time when taken79pjtv8 61bqucsz) z nz+q w(m to high altitude? Why?

A tire swing hanging from a branch reachesaedf n;0d1cf 3(p+to g.h5kj m nearly to the ground (Fig. 11–48). How could you estimate the height of the br1tf(mak .de3dp j5 fh;o +gcn0anch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if youa9gtao3o 75m8 k2wc ju shake the pan at a certain frequencgcajoka u3957 2o m8twy?

Give several everyday ex;wrnb+wd 4d;z mq/z2 vamples of resonance.

Is a rattle in a car ever a r. .3brn;h69shmp bu)mxap l aw3l42noesonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of (dwn8*yme3k 3pfy *odits source? Why or why n pm**fow3n 3yd(8d keyot?

Explain the difference between the speed of a 5 x*u/qoegsuyt1r7p kn5c)2 c transverse wave traveling down a cord and the spe5oxpytu1u )/2gncr7qe5* s k ced of a tiny piece of the cord.

Why do the strings used for am) skk5e*yc ,the lowest-frequency notes on a piano normally have wire wrapped ar5ymca)* e,s kkound them?

What kind of waves do iwff.+auqmk64: o xkiku./5x you think will travel down a horizontal metal rod if you strike its end (a) vertically from above an .w/xk:kfiuaqx 65m+f4ko.ui d (b) horizontally parallel to its length?

Since the density of air decreases with ark yk-r-e *;mzn increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you ee z-y-krmkr; *xpect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease r0rt 9j+5 v tdl0wkhn4in amplitude as they travel away from dh+l4 kv tr9tr0jwn05 the source.

Two linear waves have the same amplitude and speed, and otherwise are identicab-z pxp,hv d(9l, except one has half the wavelength of the other. Which transmits mp,xh9v(zbp d -ore energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of b-1qa5w s-4zd6 b8 rvkc/xo p0kz j3dxcord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Expl5o/6c4r0dxsd -8 bzjq -1xvkz w3akbpain why.

If a string is vibrating in three segments, t zoc-0l obpd,6vhb2u)z 5ch)are there any places you could touch it with a knife blade without dis2 tpc u c0,ob bz)d6hozlv-h5)turbing the motion?

When a standing wave exists on a string, the je1 ;-ogwp hxky9v3b3vibrations of incident and reflected waves cancel at the nodes. Does this mo j3-hk;9xg wype1bv3ean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mpl2o h ez-r0;(w 7mipxight we determine whether the energy was being carried by partm; (pz-xr ihl70eowp2icles (material bodies) or by waves?

  If a particle undergoes SHM w 3i:4l 4l/k3h hnl5iee4j9rh 7xnkiwpith amplitude 0.18 m, what is the total distance it travels in one periodw4i :ex/4ekhk7ni 4jln3lh5h9 r3li p ?    m

  An elastic cord is 65 cm long when a weight o )rr i p09*g,7+ahpoi,8oe-anx17hsr fcl t twf 75 N hangs from it but is 85 cm long when a weight of 180 N t+raiag 0c7ps9tr h, wrool*h7n )pife -,18x hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kx7 il1f g,,qows.e ko)g driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency ofqxkfe.sio, ,lwog)71 vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it.p pkxq6: bb:xh qz,z+v2:oy4 n (a) What is the spring s:obpyn6bxk4 ,q:z2x z q+ v:hptiffness 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 sub1m/n8 8t ;g*i(y gded 9o,*fvhare with a frequency 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 1 /io;d9 btu g8yf8(*r v,mhegaesdn*it?    Hz

Construct a Table indicating the pok,5 ef9lw+hw oth dia,, mq28rsition x of the mass in Fig. 11–2 at times t = 0,t = d+r,qloh,e59 tk 2wmw 8h a,if$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 i mztuio+4w- q8n a spider’s web. The web vibrates predominately with a frequency of 4mitz4-o +uqw8.0 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 vibratese:2 u:)0gf(lsrieli g qxii9/ with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. Whatx0:g (:fe)/ 29grulsil eiq ii is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per secoo) sxny -u ux,ejbnq:4bjq 1/7nd with an amplitude of 0.13 m. Deterquu/bj,n n ejy 1:-sq4)x7obxmine
(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 maxi1to u27jq -yhwdt3v* lmum valuewh3 y ju-dtt27*lvoq1?$\approx$    A

A mass attached to thebpc.8 xv/; )lcbyqvb/zk 1uq: end of a spring 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 stretches a vertical spring 0.315 m. If the spring isn )6 dw7v)lwn; r ml4z6bm6akx stretchedm)664 nxzm7rll w aw6n )bd;kv an additional 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 attached to a spring with s0ha3s ci2z.3 e kg h7wiyj7n/ypring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium positi0jk. /i7agn 23h7ehswi zc3y yon, 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 80t5yxt w-c(f4zaebx/6 aq:y :nxzd)c/rwqt( -.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With whad/ -wca4c(/ynz xf:azxx6-w b5qre:)t q ( tytt speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is atta( vv kg(9g 7ayaj2ah1jched to one end of a spria7vajk (j2 v(y 9ghga1ng; 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 = 0.45cos6.4t where x is in .t2ui4lcvvp 3lu,nh: meters ltv2l:u.nhuvc , 43i pand 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 equiy - wu817)usigo.pbdm librium is the energy of a SHO half KE and half PE? ±8).sp17wy- mogub idu    A

  If one vibration hassvte5s x2aey 9sif:5- 7.0 times the energy of a second, but their frequencies and masses are the same, what is the ratio of their amplitudes?e t:xisesfs-v y59a25   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every 0r::ytj y*y.pt.65 s. pjyt . *:tyr:y
(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(,4h9s j4r:ta 4x p4qfw mrqtx by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will x ,q4t 4:4 (mtsrqaf 4rx9pjhwbe the frequency of vibration?

  A 300-g mass vibratesff:gh1z +.k wazq:fca i.6v-j according to the equation x = 0.38sin6.5t where x is in meagfz:.ch w jvq1-ik+ :6az ff.ters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, whav v.;tdoq tv0:t is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m)rs *0ppp /jes/.rhud ( is struck by a hammer, which gives the mass an initial speed of 2.96m/s De/jspp(r*du0 h/ reps .termine
(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 con-kz y8c3 f(odjstant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs -z8o3jyc kf(d 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, with spring sti) i k0h;o1mnshef2n4nffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontalp8db7x;a)3zyv (sx jd spring whb(; z jyv x)7ap3xdsd8ose spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a h nlrq 2::m4jriigh bridge. After reaching his lowest point, he oscillates u:jq 4: lnrir2mp and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibration9 nx+se 3nt7ijx(s8cw s in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if i.kzlk2 8 cu+xrt is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 s.) xk.8rz+ 2uck l   m

  A pendulum has a period of 0.80 s on Earth. What is s-b-cmq qe1 -xm6p 9ypits period on Mars, where the accelercm e y-bpp9-6q q-sm1xation of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm longs73 k z;3)bu) b wikrrhk1k(ky
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of 365kz) ,)inim vd4l-y7lq grams, ad4q 7 iil-mv,)l zkyn)nd 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 clock’s pendeswgm4yuft/,7 z 5b6dulum has a length of 0.9930 m. If the clock loses hte bd/mzy 5g4 7sw,uf6alf a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum s)w(u.:hr e spypd: tj3peed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscil/0so1v ki0f*/lvbp . 0 vqbewtlates at a frequency of 2.5 Hz. At it is released from rew1be* /0sf iv/o0 .q tkvplvb0st starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anch*zxtgpqta ko1::qysxb ,-f : ,ored boat every 3.0 s. He measures the distance between two crests tos,k,tzf pa -xb:g: xy:oqt1* q be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frecj4zq/ 1*qpdm 2srsn:g 3e2tsquency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave cr*4cq/1 ns:m3zrpt qjg d2 sse2ests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiloh*v k4(bo+q lk,srphx: s s(e-q/ 9kpnjertz) and travel witk,x(sr j(blvk* s-q9 4qn+hpop: s e/kh 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 longitudz,ho tr.;h-uxd;,secii5j f 3 inal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have t6jsfmh 3:ui,s szo3k:he same elastic modulus, but one is twice as dense as the other. In which rod will:k, s um:33sf6jsh izo the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppoo38nc umg8tsk- 0ekx0rts 28 m apart. If the tension in the cord is 150 N, how long will it take a pulokm 0 nkc3xu88-e0gs tse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill bydx; gn68/bc nb a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the c68nb/;xnbdg 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 his ship just below the surfa tdf+u y85fe8rce of the sea. He hears tfu8 5dey8+tf rhe echo of the 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 thiizmdirbc;.b, ) gh7k4s difference helps in locating the earthzg .4); ichk7m ,dbbriquake “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 approximated by a sinusoidal transvem:z /68rl;t ez v:wvv)gzfsp:rse wave. Assuming a fre f /zw r8:e tslpvzvzm6);gv::quency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplits2j3cgntk z9gn;d 5,ludes, of an earthquake P wavesg,; 3gdnzc 59tknj2l passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquaerl78,mq k fk g)ep.9lke wave passing through the Earth is measured to be r.8e 7l e lpgfqk),k9m$ 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/ g dcsj52,4p0vt f7niddzs2p y e:a;z same portion of the Earth, but one is carrying twice the energy. What is the ratio of the5f sd7 cgapj/t2z in40dzpd2ve:, ys; amplitudes of the two waves?   

  Two waves traveling along a stretched stringx:5 zkxu6 w.m bxp1fo) have the same frequency, but one transports three times the power of the other. What is the ratio of the ox x1w :xpmz6k5.ufb) amplitudes of the two waves?   

  A bug on the surface of a pond is*eglw ;nptt6cgex. 45 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 th*p.5xte4;ge cg w6nt le ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. bfw3j;e4ti2 r(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. What has happened to 2r3ji;w b4etf the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental freq 45cpeu s6ikr/uency, what are the frequencies of the first fours /rep 4ukic56 harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates attuvzwv4 xe( fxa45g( : 294 Hz when unfingered. At what frequency will it vibrate if it is fi v 4(v(xw4a5 utxgzef:ngered 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 lo/5 wc(v13f;nly z+ pwrqgxe 9np)trb 8ops at a frequency of 280 Hz. Name at least three other frequencierl 8 e1f5(wq9bcpy +n;tpgvnwz /3x)rs 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 stah285 xektpsl cs7m +tet 4p;m8nding waves is 475 Hz, how h57pt 8tss lktx8+ mcee2pm; 4far apart are two adjacent nodes?   m

  If two successive overtones 85p:(vn48d ue ta 2 efmspe:bgi4o /iiof a vibrating string are 280 Hz and 350 Hz, what is the frequen8/t e4 gdnp i2:fsm :v4i5(eu8ia ebpocy of the fundamental?    Hz

  A guitar string is 90 cm long andvi:fz/;* vyld has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental a; v* ifdl:v/zynd first two overtones?    Hz

  A particular guitar string is supposed tmbs-i3dyeff.e;;+ ug/bek :mo;z / h 4sfnz 2wo 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 corro+;eeyfn 4.e3-uzi/g fw/h fdmsb k m; b;s2z:ect the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppoq2r.rqef:m-bjp )22ddle69wl *lxr o sed to vibrate at 200 Hz, but it is measured to vibrate a2e : l*.pxl 96m rqldqorf-22bdwe)rjt 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attuh.j jxjx yj9;v.);u kached to a small-amplitude mechanical 60-Hz vibrat.. v;j ky)9xjhuj jx;uor. 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 pulley. If :4adplj* :fsr the hanging mass m is fixed at 0.080 kg,l :*:pfd4ar js how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tubf. 2*r1zzwegd c:r;-4 xui.5nsoq bzi 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. What is the speed of the wate d2f *s4gqco- r izx.1w; izuzb.ren:5r wave?    m/s

  An earthquake P wave traveling at k.0 km/s k 8kj )p:acj/d135m;gzo gebu strikes a boundary within the Earth between two kinds of material. If it approaches the bounbc5j /:oum3k kg);peg18d zajdary 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 un-r 5i*.e)6mdezmnccm7ll wv 2ms+x 7vderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests ls*c d-ic7xm 5vnvz6mwl. 7)2 mm+e ermake 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 (ywso1hh:ikpm5usox b,;1b7 layer of cold, dense air. If thki1b1hs; xuwosm 7bp(,h5yo: e sound wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wavee0fboo -vm8 i. strikes a boundary between two types of rock at ai8m0o.- vbofe 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 diamqme t)2/,(9f)lfuh 3cdvkoyseter. According to the user’s manual, the dish has to be pointed in the direction of /u qkf)32v(h ,e )of ytlscmd9the 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/hzdfeqp0k+ t* 1-vkb:x 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 dpebzv +qk*fx0-k t :1shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a sprinx +w7+ssvr/5 yz04o vbe*3ug c6pirgmg stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.c43gi6/7ey svmxpo+v r rgz + *5u0swb]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches thn--e;o-y 3 *4w,nxni8z 6fbrw n3 6wsdaf lvmhe net 1.1 m. Assume that the net bedr h zv-w3i8* o fane-;6sy3f 4nm nwnbl6wx-,haves 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 pla:hp**1crg 3u+ts ay90;o7grsdrj d ycced on the end of a freely hanging spring. The mass then falls 33 cm before it stops and cu:3gj 7d0;g a ocy9rrspht+*dyrs* 1begins 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), comaf1ywo 90 d1:+by b1zlhj ki9qpressing tyawj 19 +1hyfl bo0zq kb19i:dhe spring 5.0 m. (a) What 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 ca1x w,jg *4mau,9h8gvky p) kloffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over ywa x,kau),kg4 lmh91gj*8vp 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 a 33-jr ,ry07e ha ,axq7-zvppamz d1u1* 5orpm phonograph record have a wavelength of 1.70 mm7 ey -p ahpr0m 71,,v5 zuoazja1rxdq*. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equat2lspwwn4m y .owm1a)7ion x=0.650cos7.40t where x is in meters and t in seconds. Dw7 )lyo2mwn swm4.p1a etermine
(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. Whas,i* enb0e9clt is its frequency if it acceleratesi, e0nc lb9*es at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a)z rx gn40us )j*are6l 75-kg man stands on the raft, it sinks 4.0 cm deeper into theselr rz 6g* 0))unajx4 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 musicy h;zce8 f9/lzal instrument are tuned to play at 392 Hz (G) and 440 Hz (yl8cz h9 zf;e/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 the stretched two- sog.a78d8)fx4kdcfd0 mn q 9ypart 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 sg a)d 8.oqf8xcsy947dnmk0 fd ections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong vflr5-1+i ldu moves 1.8 mm 1fi+ ru-dvl5l 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 motio aek4-j5x0 wjln of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of t40jkxeal j 5w-he board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slip,)nhy7c6 f tmde without friction on a vertical pole (Fig. 11–57). Determine the wavelengths o,c 7hnp6)fmyt f the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each onqg-(rv.*1gz 7yl5 q nw3xluc ne-way swing takes 1.000 s. cq( lu7r-.qngz5w x1gly*n3v
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the v-ki)q hml q1-f4xki 7y+ndr 4nertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of-1d ql+ h-xki kqin)nm4r7y4f 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,y4b 6.fal 5gjve7gho of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two a76,j l4ef y 5gb.hgovpulses first meet?    m

A block of mass M is suspended from a ceiling by w;jl) ip/gh n-a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What i)i jw gp-hnl;/s 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 bff eqyf3p9.3at 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 fpfb3fq .ye93. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello res3- ygyu-*z1x kt4,mfwhbj- wdts on a plate as shown in 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 d4-g- jbhfuyy-zkww1,m t 3* xand 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