Give some examples of everyday vibrating o2z(lj4o iw;srzq+0 yjbjects. Which exhibit SHM, at least apprz; 4l zj+o iywsj02(rqoximately?

Is the acceleration of a simple harmonic oscillator ebcy:x;sis :rj)u, io;ver zero? If so, where?

Explain why the motion of a p-39lqre2os nj/g q 4hoiston in an automobile engine is approximately simple j qesoog/ 432n-rhq9lharmonic.

Real springs have mass. Will the true period a6qf;;pjdg1cht m kjlo (x 0x/ p220faynd frequency be larger or smaller than gif0dpa2y6;xgq 1(xp 2j/fhltcmo ;jk0ven 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 hajtuzuauzapr4f ; u+) ks)18:trmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scnf*d fga2 p5fqs s81p-ale, and then is released. Describe the scale n sps*-gqp1afff825 dreading as a function of time.

If a pendulum clock is accurate at sea level, will it gm,dvskx* ( *g8 o7bpwkain or lose time when taken to high altitudg7o wkdms,b*p* 8xv (ke? Why?

A tire swing hanging from a branch reaches nearly to/da z4)s b2gsr the ground (Fig. 11–48). How could you estimate the he4sdsr2)azb g/ ight of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if*sct h1fe1 0crrc 32rw you shake the pan at a certain fref1crwce * 2crsh r103tquency?

Give several everyda bu4rw9s jv0+/ raa+cjy examples of resonance.

Is a rattle in a car ever a res,r( sd *zog)phonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal topkvncon8 2 jefy( g6id,sy).6 the frequency of its source? Wp) ,o8 icsn e 6k2y(n6jg.dfyvhy or why not?

Explain the difference between the speed of a fb3 g ;4 fvuae3bh9ir6transverse wave traveling down a cord and the speed of a tiny piece of the cordf6vfi a;33bgb9ueh4r .

Why do the strings used for the lowest-frequency notes on aw/d a566iwbg e piano normally have wire wrapped ar gd5be6i6w/ awound them?

What kind of waves do you thi- zyoan1*y*qb nk will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontalqy*- *b 1noayzly parallel to its length?

Since the density of air decreases with an increase in temp q(1e1m,wil5n4.blnzvi t5xo erature, but the bulk modulus B is nearly independent of temperature11i n qtw(55bo,ln xl e4vzi.m, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as th5im2-f:fams q0kn hje i,(x l.ey travel away. hi(q ji2mfmk-x fl,sa:0ne5 from the source.

Two linear waves have the same amplitude and speed, and other(xm0) elut1 c4sqa5gd8oq1 nywise are identical, except one has half the wavelength of the other. Which transmits more oq5) (u4t0gmcyxn 1l1d saq8e energy? By what factor?

When a sinusoidal wav +bf1;7sjkao e(/fzsc e crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavee fbso7/ajs ;1kfcz (+length and velocity do change). Explain why.

If a string is vibrating in three segments, are there any placeqx- nvd6mdz,zw4**xbj8 mrk 4 s you could touch it wir*mk8znxdj*wx -d4v 4m6qz, bth a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incidh xb(kb b6g0p7ent and reflected waves cancel at the nodes. Does this b gbp06x k7(hbmean that energy was destroyed? Explain.

If we knew that energy was being transmitted fr 79 zno b2x qho2cz tr/zot9,x.r6nk,wom one place to another, how might we determine whether the energy was being carried by particles (mater n rrx2z/o,t9 2zo,okcn qwt9b7hx. 6zial bodies) or by waves?

  If a particle undergoeu9,yinp7m/g38w 6:/ gvlbqc 75 jt sdaimbam/s SHM with amplitude 0.18 m, what is the total distance it travels in on3/qtgdbj: gy7mi cum,m8w/ nvs9 /ipa l b5a76e period?    m

  An elastic cord is 65 cm long when a weight of sra*i;jsh-u+4szr/8 b )hb rm 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What isb-4 +rmzi /aushj)8 ;h rb*srs the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68t qnt+ ,a*joz9-kg driver gets into the driver’s seat. If tha+,q *9jotznt e car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches -y)pc.f7v u 3zdl2+tzk6voj o3.6 cm when a 2.7-kg fish hangs from it. (a) What is t)6 vzldu- 32yf.k7oz ov +jcpthe 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 wih huvs :uz:ld/+a 2dg)uei-5 mth a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its -2:d+z gehvi/ma :l 5hud)u sufrequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11+f34 6v 2v btj2 *ctyryzoez7u–2 at times t = 04btry*ec2z2j7yuz36 fvt v o+,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. Th.jpvyslf x4)d937caeiky 91j/psnd8 e web vibrates predomi p)e npx7vdfs.ds j9 y9ij3y18a4/lcknately with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with ,5 n5 9xt-2 q dyizml,*ssnwzja frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What md5wnx z5 ,si ytq2*-nz 9,sljis the value of m?    kg

  A 0.60-kg mass at the end :t1j5ge wmlg7 of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. gmtg15lewj: 7Determine
(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 1h gpyho--hioz06u8u maximum value?u6-i zp-1h h oyuhgo80$\approx$    A

A mass attached to the end of a s-; akq9rktdo td b.3q *bs3n-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 i /q)qp o21rtj -qhbbhnp/5l8 spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it thr ot-b5piqjh1q/nb q pl 8/2)ake to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is aod kln zgz *2psnw.v7sl8 keu2hd, 0w(6 kq8l+ttached to a spring with spring stiffness constant k = 280 N/m and is executingl,8en.8lhvs+2o* z70q(d6 ls2ukpknww zdg k 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 t-zal, cca /dc 6lu4t+of a toy popgun 0.200 m to “load” a 0.180-kg ballalcdz6 4cc,- a+ tt/lu. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, fricti.cl glpd(- u3cgaec )6onless surface is attached to one end of a spring; the othu3acglc-.( edpgl 6) cer 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 *s le9sm64/xs b4or jtrlid*3 in meters and t is in seconds. Dmsli/ *rbrd sx693tje l* o44setermine
(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 gg6eeji x io9x4gfnl0/5;q4t the energy of a SHO half KE and half PE? e6 exf4gjxo; iq/09n54lgit g±    A

  If one vibration has 7.0 times the energy of a second,53f5 pkx00be(zzvsuh,u fm45nnt 5ei but their frequencies and masses are t (m53x0 vsi55nbf e4upnf0 u,ez 5zkhthe same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a va sp4yp82h8q7e ee7 wgertically hanging light spring once every 0.65hpe 78gyw48e 27qp sae 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 idkxwqpv rd t 95gqhf*yeg 1 k3/l7p)1q)entical parallel vertical springs, each with spring stiffness con/lw)9h pdkvtpxyqkq3 * 1 7r)gefq1g5 stant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.+fay 51gvyfu b dsr2er4(pat w81r.r 138sin6.5t where x is in meters and t is in seconds. Det1br.ryup f8g 511rfdvtr we(ya4a+2 s ermine
(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, w4fibyb7nm 2r8lj, 9 tuhat 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 0.80bvt4 vcxymeoi0z end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial 4ziv vx. 0mc0e8to0yb 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 witpi-t xim lx*,,h an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point m,t- ,*pixixl (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,t khqhe19ed.jaf r .63 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.v). tbz)/jy fe8njwb r2/qq/d+o ;nuo600-kg block attached to a fixed horizontal spring whose spring stiffness vj8bq+onf)/./)2zq oybujn; t wr/ e dconstant 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(h:3h/aflcil y(i u*.atvka+ jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the un /vu(ytia a*a3 hfllk hc(:i+.stretched 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 xe-yp1 q;edm3 exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it irmx0z;0,hvw n s to make exactly one swing per second? v mr,wn00; zhx(That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wh9fft3odi 2 kf5ere the acceleratid 2fot9fk 53fion of gravity is about 0.37 that on Earth?    s

  What is the period of a s1urxhy inx co6 2wbgxq ,+76b)imple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, txc+1 p,/cvvjt y(zxq.j 6+nry he pendulum bob has a mass of 365 grams, and irc./vjyp,(t6+qjn cy vzxx + 1t 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 clox onq9lbhm7.b;l b h*0yv-5opck’s pendulum has a length of 0.9930 m. If the clock loses half a mihl;50 blm b bh.xp-yvqo97 on*nute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for tyi g: a)0bxa2i+rf/onhe 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 oscil9gi x((fwdd 3zlates at a frequency of 2.5 Hz. At it is released from rest startinf ((9xdg3zwdi g 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 thed bn05y 62aq jzggc:8gzjj )z0 bow of his anchored boat every 3.0 s. He measures the distance between two crests tc)ajz6g58q:gy0 zzj 2 jndb0 go be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of z5rlnt 4dw yt84-w m3t /pzmz8262 Hz and travels with a speed of 343 m/s How far apart are the wave cre4wmltzty5wz8 mn3/ pd- 48t zrsts (compressions)?    m

  (a) AM radio signals have frez i hx:8)oz.b:i;cllc3d o5yht)lh(fquencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed 5;.:tc yxh) l: ocb3o8fidhl(l zz)hiof $ 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 lo7whn iwadky ol j1+skn9g94* 3ngitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same e xuv (p9 md0 +ihkxmag*+nv4n-lastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, an+ d xa(n4u* v+pnmh-ivgk0m9xd by what factor?   

  A cord of mass 0.65 kg is stretched betweenucu(k5tv + * f2eyb*tn two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from oneec5(2*vybft n u+ut*k support to the other?    s

  A ski gondola is conn7o6z p/4, u f7tpwv:fb/fdbdxw .jk3fected to 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 run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return. d7pd :o3fxp w. ,fb4ftz/k jwbu76/vf
(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 f8 aqw 6/cd; y2t;0n oq/jrlsfbelow the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s latef; /w6roldfnq a2y c;0 8jqs/tr. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this differe2f, ii td+bw-;5 dmadhnce helps in locating the earthquf+;dd ,htmi2wb-i 5 adake “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 bejop16d4tt;7f n6w wu v approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitud76 wo;f jpndt4v w1tu6e 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 ampliwx((+qj n5gvxtudes, of an earthquake P wave passing through the Earth and dete+ nq x(wjg(5xvcted at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through uc1enkiq-lok; p 1y0(g,:b fythe Earth is measured to be ikkgp,yen;-0 1fcqoyl(:u b 1$ 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/4 3cx2q+yx:brh esw yv t*z.x same frequency travel through the same portion of the Earth, but one is carrying twice the x yv+ew /r4 hsxcbt3*qz.:xy2energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same*p jg k d)ad()q,h76fillv(sw o wo(h- frequency, but one transports three times the power of the other. What isakp jwfohid, (7 og))s-vh w(l dq6*l( the ratio of the amplitudes of the two waves?   

  A bug on the surface *fn2pwqn 1d- rof a 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 pass1-pnwn 2*fdqr es. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in h39vsu ,jqk bsm v3*)rFig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. ru*vsshq k)39jmv ,b3(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 vibrates at 4mmc+1ze pbj9 *6ojwvc.7au5l40 Hz as its fundamental frequency, what are the 7ob*+zc6u9p 5vw.mjcaj 1 lemfrequencies 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 frequenc3)4v5aev0ser+ z7dvk5q x rh ey will it vibrate if it is fingered one-thirdadr ze4k rv0q75esh) e5v x+v3 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 frequency 7qud-s eait,1of 280 Hz. Name at least three other freqsie q,ut7da 1-uencies 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 frequen udw-w -8 4assm1x(x65mpgmlicy of standing waves is 475 Hz, how far apart are two adjacent nosi4pm 1l5 muwg8xx -s a-(wd6mdes?   m

  If two successive overtones of a vibrating string are 28-mxif:mo),v4e st. ju0 Hz and 350 Hz, what is the frequency of the fundamen.vemo, - it:m)4sxf jutal?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the br3mhs9ibt (j3didge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones? dthsj 9mi(33 b   Hz

  A particular guitar string ittmz7d;/ exxit4f/ym 9d2:tep.bb 4ps supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shop9 /dx/;b te7dx: f4 bim2ttt4.ypzmeuld 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 is supposed to vibrate at 200 Hz, but it is me h,j-ulnz(ax+ asured to vibrate at 205 Hz. By what percent should the tenx az u+(njh,-lsion in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a sms hwwa r,u q1jnx*413iall-amplitude mechanical 60-Hz vibrator. sw 1iw1xhnq43*ju,raThe 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 co tg5*xu :hk ydq,/qxrs+2-n may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns ma5*/,doxqkhr +xcs uy tg-:q2n y be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at ju76e9h mib7,vq fi6 esrst 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 wat qe hvii69e7 ,fsmrb76er wave?    m/s

  An earthquake P wave traveling at k.0 k. .7 er9ie5,cduk ofhrm/s strikes a boundary within the Earth between two kinds of mater ed5fr oe7hi.9k.,curial. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from 2.9umcbqe1h*al 23w f5o8 m/s to 2.1 mqo h53elw1cu* 29mfab/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense awl :8c v.)udzdir. If the sound wave hits tcz v:dld .8uw)he cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary betwe, kcmge 2:gz:hlzev //en two types of rock at a 38v kz ,:hgl/zc e/em2:g $^{\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 3 zmsa6 a-bbdb.ypqi ky)k( tu7::3r jthe user’s manual, the dish (bt:y3u pj:z -7)d sqk.mir6kb 3ya abhas to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km.a1 ,z;r-eme k mlcxb- and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusualxbe1 ,mlz;m- .are-kc decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spriojte6*6w .d osj f5-wlng 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.ewldjjt5 6of o-*ws6 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a w+0zc9gi 7apniw8e *eh 6p0i giindow to a fire net 18 m below, which stretches the net 1.1 ma epih+w 0pn7g c9e0* iigiz86. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mafr w(,pmfd*pwj ,xn7sd0(1k7dxgj r1 ss then falls 33 cm before it stops and begins to rise. What is the frequency of thexdpj k1*xnj 1(,rdgfdr0psw7(m,w f7 oscillation?    Hz

  A 950-kg car strikes a huge spnz i, 5hj7en5daoz0a :ring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m.z, e:zhn0a5 dai ojn75 (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 coffee (diame2e.rh h r.xe6l ,yc34d-, )gve pkppiqter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more unt2) . x,-de khe pqyrrip,gvp3e4c l6.hil 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 a 33-rpm yfpo y/1ez6 1xot:*a mphonograph record have a wavelength of 1.70 mm. What will be the frequency of the sooo fy1/6ep1zxay :* mtund emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t wherem:(qcrex4 4j ma (hd,f x is in meters and t in xma (q, :erhc4d4 fmj(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 frequem-i j9su-(d pfncy f. What is its frequency if it accelerates at 0.50g (if(u m-p-js 9da) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it s)q7.atd+ ztnmv0i:jn2yo6o pinks 4.0 cm deeper into the wjzn) dno6aq 07t.ytp2+ v:moiater. 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 instrumen6 +o0x:kt utwmpbu. d0t are tuned to play at 392 Hz (G) and 440 Hz (Aw x0.pbuk t +:6mtud0o).
(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 trav y;a8y-wqvkp*fqj b -(eling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the (j q;yw yfvb*-a-p q8kspeeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip o 5t9 m oo-pzs-aze,hs,f each prong moves 1.8 mzsz o s,9,5pahtome--m 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 simp0/f :q5vuvkzq4dvmyl6)(j a qo7pcn(le harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the bomy(ov7c:znfqv( ) 4/ lu60jq5k pqadv ard 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 gx7ye p3p;p,*,s yp*a jcn+gqring that can slide without fria+*7c gpspg,px; jpeqyy3 ,n* ction on a vertical 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 2.0q awj.jq )jw g);3yfl300 s — each one-way swing takes g33)ww)qfya.;qjj jl 1.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or cpilti7cvig: 37h;fdz8 /6cjn *n5ogi an swing as a pendulum ofg 6/5hn*i iztpc7fl ;7od: 3gjviic8n small amplitude, 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 wwt/a ,/g f r 8:wg q8i8,hjaa0(lriskx1zk j.a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pula ,jf:8j ,8irh/a ws(zixwr/ gw1tq8.g ka0lk se is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffwuiz dmualigbyqj+r+5j 7 6md78*0:nness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillationg7 6 a7wj: j8im+*uqbydr5zn+d0li mu s 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 jo.m-c8i:xdx l unkyard. 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 :xxi8 l.dm-oc9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which x: /wwghzsr5/a-jdg5 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 that the shear modulus (Section 9–5) of jello is 520 d hwg5xagz/j: sw-r/5$N/m^2$ and its density is 1300 $kg/m^3$    Hz