Give some examples of everydd 28 iwaayx97way vibrating objects. Which exhibit SHM, at least approxywd7xwa i92 8aimately?

Is the acceleration of a simple harmoniu,cv;/djl 3jo c oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile(tk 1-xrf p93iv nvtv: engine is approximately simple harmonicvkn3( xr1 fptti-v:v9.

Real springs have mass. Will the true period and frequency be largx8-fgap 8 7hnder or smaller than given by the equations for a mass oscillating on the end of a-8a dpx7 hg8nfn idealized massless spring? Explain.

How could you double the max(5ati w/yrr,f u6(kbqimum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of gjeb7 o8i4n )ga vertical spring scale, and then is released. Describe the scale read) 7gngei8j4ob ing as a function of time.

If a pendulum clock is accurate at sea level, n)g p:)0 -dtokgocb;wwill it gain or lose time when taken to high altitude? Whto;o) :n-) c bp0gkdgwy?

A tire swing hanging 0llxdt+i (5q: xx1 wvwfrom a branch reaches nearly to the ground (Fig. 11–48). Howltx15(ww +xiq :d xvl0 could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in ;ial2b,-emtrx6yu7 na pan only if you shake the pan at a certain freqy7m xba;,n6i-l u et2ruency?

Give several everyday examples of4+7y w g iavidze9 +k-gtdw3y. resonance.

Is a rattle in a car ever a resonance phc z9prhe sb i2j2p1z.fr.e *u6h;9xwkenomenon? Explain.

Is the frequency of a simpl,/urxjv k ,+3vvki b7oe periodic wave equal to the frequency of its source? Why or why noi+ kj xr3kbuv 7/,v,ovt?

Explain the difference)m3 o8/q z*eiw 7imyok between the speed of a transverse wave traveling down a ci km7i ey*qw8/o)m3zo ord and the speed of a tiny piece of the cord.

Why do the strings used for the l)6f gdgd +*h .mojeoa:0xh/hb qnu9fq:3 nwa8owest-frequency notes on a piano normally have wire wrapped arounh9 xmw/ :qdngoha8)qja0dgf:o6 h.nb *+efu3d them?

What kind of waves do you think will travel down0hts8 bqa tinjtd0g++3e+ 4my a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paraj ts04g+nabq0etidh 8+ ymt3+llel to its length?

Since the density of air decreases with an incj.d6/3:u n4)rp )ryyv n rfenorease in temperature, but the bulk modulus B is nearly independent of temperature, how would yo/:n.nuy3efv))jrn p ror y6 d4u expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decreaqbty.7z i(-b n87oaw,8dwyncse in amplitude as they travel away (w.bcq a-b yzy tn o7i87ndw,8from the source.

Two linear waves have the same amplias1yp/hbr1bc 72 m1 mptude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits as pby1b/ph2m1rc1 m7 more energy? By what factor?

When a sinusoidal wave crosses the boundary between t f2q9;stffab ftig4 ;3wo sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and vefb;tf s23agtfqi9f;4 locity do change). Explain why.

If a string is vibrating in three segments, are there any places you couh9;qvc,pky.cxc w4sp.l /ia4q +,kul ld touch it with a kn;.p4 vkqcyqx. ,plau,ksh wi/9l + c4cife blade without disturbing the motion?

When a standing wave :kpeaf2s1 huy/r,z7v exists on a string, the vibrations of incident and reflected waves cancel at the nodes. Does t/ 2epa uzrf :1sv7hky,his mean that energy was destroyed? Explain.

If we knew that energsstmo;f x6cp)b:sm;tw6f 8 .iy was being transmitted from one place to another, how might we determine whi;stmsfmpxw 68f b: ;)oc6.stether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with ajwgkxs-+z (2 w9 ot5;rrxzff, mplitude 0.18 m, what is the total distance it9wsg krxj+ r,2o tz5w;xf(f-z travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85ngmnf;d2 c z0,rn0fu+; aw 0pm2x+up i cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?panux + 0 umc0fz f; gp+mi2w0;nr2,nd    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gxpn+ r gdu 0f5vvj-+e(ets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibrations?rnv +5v(gf pu xe-jd0+$\approx$    Hz

  A fisherman’s scale stretchesf ;k f /;are v80sq(owmhl*9se 3.6 cm when a 2.7-kg fish hangs from it. (a) What is0 ;ee*r o/lsv w98af;hmqfs(k the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a freq 43g +anzjmgo:uency 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 frommj3 4 o+ng:azg it?    Hz

Construct a Table indicating the position x of the masaqcd;95eje z ,s in Fig. 11–2 at times t =c;q ,j 5edzea9 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 g is caug:;.9sf bjb;dpf. ripy ht in a spider’s web. The web vibrates predomi;.b9ris p ;fpj :fd.ybnately 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 sprinc1(dv )xyc:ecg vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is e cyc )1(cxd:v0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with anvagxr zo* 7/c/wxnm9; amplitude ofx;c*9zarmgnxo/wv /7 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half th p gpc(h q )4510cxj3hdhr:mcje maximum val 153gppj( jr4cd) chcx:mhqh0ue?$\approx$    A

A mass attached to the end of a spring is stretched a distance pkp:/3yn rgelk1 gn7:$x_0$ 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 is4lf(e9m z8914q/qnb y b/zyz0u tjibv stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium positio qjqml/y( fztn8z0/4ieb14b9v zuy 9bn again?    s

  An object with mass 3.0 kg is attached to a spring with spring6.vd6nb;fbp3;j *u o/exkmgkykr 3;+z*awt w stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object6dmbyz;kk 3a xrfgvnp+ u6 /ow;bk3wte;*.j * 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 thnryi2+cyt w:, tp (*lxe spring of a toy popgun 0.200 m to “load” a 0.180-kg b(xw*tty2cr:+ ,ipl yn all. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, m/akkelv77 mm;xw z05frictionless surface is attached to one end of a spring; the other end is fixed to a wall. /klme;75a 7z0kmwx vm 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 equzfi 01+q6ckoa ation x = 0.45cos6.4t where x is in m +kz f0c6oiaq1eters 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 equilib4k; tagtc0ud 1ewj)a/ rium is the energy of a SHO half KE and half PE1eg/d aw at0)4kt ju;c? ±    A

  If one vibration has 7.0 times the *a2 *dza(v+df4bc boy energy of a second, but their frequencies and masses are the soddz*b a4fv b2*ac(y+ame, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin osciny z82vnm y9/yllates from a vertically hanging light spring once every 0.6n98 zy2v/ yynm5 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 identicao/mqwnm9* 0+zxvm6 z il parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will zn+m z6vio xm* /qw9m0be the frequency of vibration?

  A 300-g mass vibrates radx obdgt.u ).22hy95nqov-v *aa .zaccording to the equation x = 0.38sin6.5t where x is in meters .t-oax aqbda n.5vygv*. z9ro ud 2h)2and 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 Bsh7o utn 5m.n() ue7j/ew*se j. 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 re0n7qtvc+k8f w st on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which v8+q7kt w0fnc 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 sprtw/k1kmn: i5t81n ie ving stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equ:tkt5kvmwen/n i811i ilibrium 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 stiffness cr9 vk5h fn.t )tiz/jg,onstants $k_1$ 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 ats59n5p4w ya7nfc 68p sixfsd* tached to a fixed horizontal spring whose spring stiffness 9n wfss6dp f*sa4cy n857 x5ipconstant 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. Aftecd, w9+ qzjrejce2 e+785taa 71qfknir reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.+c5eate 1q 2a eifq8ck9rndj,+7 jz7w 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 exactjsg z, t;(vkh95gqa 6ely 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be i9f8557dz* bueu n:j y :nwnfgqf it is to make exactly one swing per second? (That is, o87fnwy5ju q n9*d : gue5n:zfbne complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. Whame fpv2 py,bbz3k/: k;t is its period on Mars, where the accelerpb2zvkeybf k,:3/;m p ation of gravity is about 0.37 that on Earth?    s

  What is the period ofk ./piwhn4 ay-d:x;jw ax 9xb7 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 pendulum is 0.760 m, the penk5 w*t(ionc3v mx9 *luebf, +rdulum bob has a mass of 365 grams, and it is released at an anm 3fu( rit5* 9+bxc *,wlveknogle 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 m. If the clock-e0y:zi jpll *edkzdqo:6 9y) loses half a minute ij:e6l:9zy0*ky pqo- e)l dzdper day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speema9 f.u5lec5r :rg5 vjd $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is relearl-*)fyq sbs0x -:j7otaum y,sed from rest starting at an angle o x)mu -7y-b,o faqr0*tsj sl:yf 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every 3k ( 9g)7euuq nm2lrb jlc3wk-).0 s. He measures t )9lkju cel 7qw2)mnbk-ur3(g he distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 d8sy9 4* nba6a r2yw1:hj w z(r.igcgblbfh(4 m/s How far apart are the wave crests (compressions)? ( 9b4zdbg a ny j:rr6*wab8l1 hhy(2sif4wcg.   m

  (a) AM radio signals have frequencies between 550 kHz and 160i ; pf2v7s,jmp 8syqkw/:g2v ed+k;hx 0 kHz (kilohertz) and travskxe:jmgi kv7v ,f2psh2qydw/p 8;+;el with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longr ktbk ui;90;mw+a1g kitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modul9c**rkw( mdmnd6d b;e9+ rldipk65bp us, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by wha 9bn(l*erkcr*dbwipmmd; 9 56+k ddp6t factor?   

  A cord of mass 0.65 kg is stretchy y16tp6;a2mfy qly3ved between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the otv fl m13y;6y2yy tq6apher?    s

  A ski gondola is connectwdat):v o0 zn9fp 7 m9ticg:5zed 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, itdv9 m:oti ptgnc7z: a9z05wf) bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the l7ez8( 4 rgjabside of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How de(ja8elz47g rb ep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, andbl /z*2bcwfqps k6.an zu7y)* this difference helps in locating the earthquake “epicenter” (where the disturbance took place). yu*nz7f/lbpc2.zw sb q6)ak*
(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 nov9 4xtjas5- sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which a o4-atj x5v9snctually 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, aptj p/jwv)iw):r3t:r nd (b) the amplitudes, of an earthquake P wave pr)tw3r i:p:)/vpwtjjassing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passi ,urmin 5, wf7 ed2)8lfjole7cng through the Earth is measured to be 5fledlw j r7,f7meoi82c , nu)$ 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 sam1dn:i dr/p4lyrb cs. 0e frequency travel through the same portion of the Earth, but one is carrying twice thel yd/0bpi:rc 1ndrs4 . energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but onm* rn0o6mqn8 re transport m80o*r rnmq6ns three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move jbo79.poc: da up and down a total vertical distance of 6. p7cj 9adboo:.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each othe-1 hd ;8kfoyfgr. (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 the energy at this mome 1gyfo8 d;-fhknt?

  If a violin string vibrates at 440 Hz as its fundamental frequequ nwp4n (/5kclz/hrns1 45zincy, what are the frequencies of the first fourwqn4p(si nu 5/n/ch1lz z4k r5 harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what fl;2xfp; du,z zrequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.) p 2zxl;,fz; ud   Hz

  A particular string resonates in four loops at ak cd ;q-+bd)c2/qii aa frequency of 280 Hz. Name at leasiq bic/d 2) ;-kaqadc+t three other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standin3s09bbx1ekynlcjmqbn/ r4r:3j3( g7nmq vt + g waves is 475 Hz, how far apart are39 tn1jkmbjy +br:v 3ql7s/ e4b r nq0(xg3cnm two adjacent nodes?   m

  If two successive overtones of a vibratinw ya.j++4 x 3 98v,.bq7zwvasikalbbfg string are 280 Hz and 350 Hz, what is the frewwka 9zvf,7 3+s ax.j vbb .q4yli8a+bquency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dist67sw f4ake31vy(4ek (,mwvdg iou0amance 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 and first two overtonesswmku d 164kvfvi,eewa(y73o4 m0 a (g?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it i3cva l ae2dkg(7) 5icms measured to vibrate at 205 Hz. By what percent should the tension in the string be changed 3am)l 5i(c 2vke gacd7to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed ro i1;jcap.3fb2hef; p5f2h r5pv bs.to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be chanp12e.obpv3h a;5jrfc.sf; 2 pf rhb5iged to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude 88, 5 ng5xono9vfjwyjmechanical 60-Hz vibrator. The string’s mass per un 8wj5on,95gjxoy fnv8it 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. Ife2he t /ty ujj-zh/p+6dfe )p7 the hanging mfj6z7/ pj)yp 2 /uh+-ettdheeass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the waterzz*ui:tb 6y2yq b ;:jmup(1fg h39dt p back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the cen p ;ybb1hpt6 q3uzdj:*zuygtmf 2i9:(ter. 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 water wave?    m/s

  An earthquake P wave g r 6- r/hd1dpwct /fmya t;lbx0-90oztraveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at anl1rz ;yd mfchxt -t0bogda-0w r/6p /9 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 vel ibnf i)*tw,sm,vpd64ocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a i6)i4p*v w,snf t,dmb34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when t+ubld sp0k2(d t a*3fdam)6jit hits a layer of cold, dense air. If the sound wave hitd0)lmk fst dpud3 ta6aj+* b(2s 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 wcu+i*3uuvc )n x- auf+ tr2adtu ha*6(ave strikes a boundary between two types of rock at a uuhi*3cnacu2ta (v6u) aftur+ -x+d *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 0.5ux ; 2r(0lexbd m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, bud20u(rl; bx ext 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 acrosg5ss/v-2ibj sv; ti b(s the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and ;ij2 v/ gvbitss5-(bsboats.)    min

  An energy-absorbing car bumper has a spring stifg k y *ui,v6w69y(*qwq6kcr oifness 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 energi9k*6*i ,kyuwyc 6 qwo(qvr g6y.]    m

  A 65-kg person jumps from a window to a fkac6 m9oxuu **ire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple springao u xku9*6mc*, 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 plfadevgwdwq / 8*-e-v:aced on the end of a freely hanging spring. The mass then f-gwv8dq e:*dveaf-/w alls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), ci1 z3iy/8saqjr ,6(t lrk5hyfompressing the spring ha(/q 1,f zjir5tl r3yysi68k 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 coffee (diameter(dbp pg/6hg qzd6,9.dn;qpj xr-)xfm 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually nqx;69 j)gg6,(d dp/mrzdf xp. bqp -hit starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groovov y;1qj d5zlig5lr4 9e 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sounl od5j4g;irq1v5y zl9d emitted?    Hz

  A 2.00-kg mass vibrates according ez3mgut0, ; qlto the equation x=0.650cos7.40t where x is in meters and t in secoug3z;e tlq,m0nds. 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 oscillatesoj v:zc)xqs*c 2fe8 ul6qj9c5 with frequency f. What is its frequency if it accelerates at 0.50g (zv2 )9c q8fexccu s:j*oq65jla) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the s+ndxs +8bn2kwz4m.9je fih5raft, it sinks 4.0 cm deeper into the water.+ s 9wfdk+bj4em5z. xhsnin 82 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) and evs),jmw+( zwt7av z 6kng(a8440 Hz (A). ntv(wskevj az6 (gma)7+8,z w
(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-part cord of Fig. 11ru ).xw*d ;)lipc;col wuy8k ;–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) Is the wavelength;plx)urcol).;* iuk 8d w;cy w greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at +u*pp(wi.udyfh9 -roxr m3s2 a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to x( rw+yhrm9ouiup- p3ds*f 2.either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of fre0umhlx 6s :zt:quency 1.5 cycles per second. What is the maximum amplitude with which the end of the boardhlz:tx m: 6su0 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 iu9g gp c 03s9g0xzk9xwz j1x5“free” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibratio9901c9ks5i xzg g3xpgz xujw 0ns of such a string with one end fixed and the other free.

  A “seconds” pendulum has a periom: 3foq5of9ujgca ez +u5+7mhd of exactly 2.000 s — each one-way swing takes 1.05 hu om:ga79muf+ez qc 53ojf+00 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 dirm;jil:lqa 5 08(hucirection or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillatio( 0ru;ac5li:hqj 8 mlins 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 ofn7-v-wb i)g) j-wxn du mass 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated-d)7xgwwvuibn n-- j) at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceilog)zf ll( 4 +tz6v h8x)hzsekbc1n.+u ing by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the z(hgt8ec)xb.v+u 1hso+ fn6 4 ) lzzlkblock? (Assume $m \ll M$)

  A crane has hoisted a 1200j8hwrmn .j e zg0r27shu* wvf-r918kh-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? f2w h 7 nrerhrv089 j.ms*w-j 8guzk1h[Hint: Refer to Table 9–1.]    s

  A block of jello rests on a pl j,v gm:lp,cy;ate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then youv, jpmg: ,y;cl 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