Give some examples ocm gkb;001 ikzr fk3l+f everyday vibrating objects. Which exhibit SHM, at least approxim+0mgf3brz0; k kiklc1ately?

Is the acceleration of a simple harmoni d a-me6ragw9ara:.9mc x1sb4ljw *+u c oscillator ever zero? If so, where?

Explain why the motion of a piston ing*lr k236 srchvepyl6m sa (a 12s8q:h an automobile engine is approximately simple hrgshaes* ckp:6 q8 6r2svlhmy a 32l(1armonic.

Real springs have mass. Willte2 d f/ jto+pijpf372 the true period and frequency be larger or smaller than given by the equatt /i2j3 j7ptf pd2f+oeions for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (p4bm,w6wj -.p+sh lk(d ;csc sj8lcw4SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is rdfi n 8o8ll*,qeleased. Describe the scale reading as a function of *llq8 fn,ido8 time.

If a pendulum clock is accurate at 72 qgyp ./q cin.bwx.t dc7))jm(vfqssea level, will it gain or lose time when taken to high altituy.c)gqc.jxstdq(pbq2)i 7v7./m f w nde? Why?

A tire swing hanging from a branch reaches nearly to the gr pekvbm2ifgf+m 3 +6/wh6ik;uf),n pwound (Fig. 11–48). How could you estimate twe +uf6mginhvi + wb mkk)3;,ppf/ f26he height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake thrcvw v 3c6m4i8e pan at a certain frequency6ci4 3mc vv8rw?

Give several everyday examples of resonancq7ap kf:3j;u2m0 t:jaa3arjr e.

Is a rattle in a car ever ay) yt/si2ode( :c0kpc resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the fz/kz qen:(lbnt0+ :3rg/m qaorequency of its source? Why or why (+:lzgzn3ta0/bok rq:qn m/ enot?

Explain the difference between the speed of a transverse wave; 0s inp)r1*fxc5ukjp traveling down a cord and the spe )ci1 * n0jpupfk5rsx;ed of a tiny piece of the cord.

Why do the strings used for the lowest-fre3zot s0,7 kdhlg g4p+rquency notes on a piano normally have wire z ,+p4g rt3loksd7g h0wrapped around them?

What kind of waves do you t(shv9*q2qx l ohink will travel down a horizontal metal rod if you strike its end (a) verticalh2qv sqx(9l*oly from above and (b) horizontally parallel to its length?

Since the density of air decr7bqvb +6fu(b5kpmi:x eases with an increase in temperature, but the bulk modulus B is nearly5 b7ibpuf(6m:qx bk+v independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circula;.+ ybq fwpx-2hx 7lzh9g9alw r water waves decrease in amplitude as they travel awayb x2w7 + apyhqh;l-.wg99fzlx from the source.

Two linear waves have the same amplitude and speed,q gum2;pxt,p2 and otherwise are identical, except one has half 2 t2uq pp;gmx,the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections ofmhn( mcy l6o-6 cord as in Fig. 11–33, the frequency does not change (al co-y (n6hl6mmthough the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any placay0oy/ 4 z, rqrmi:u/hes you could touch it wity o:qum0 /a4z/,hyrirh a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflectebq 5q4nkc4g jm .au(1b6 v*illd waves cancel at the nodes. 5jnk*qu l.ba v46qcbi1m (l4gDoes this mean that energy was destroyed? Explain.

If we knew that energy was bev slgf l k-7r9y(6ng4jing transmitted from one place to another, how might we determine whether the energy was being carried by particles (mater v- 97(f6 nk4slgjyglrial bodies) or by waves?

  If a particle undergoes SHM with amplitude x jfq1s i6/g */prk+do:bth)p0.18 m, what is the total distance it travels in one pe://ijdpfh6bt) ogp+r1 *q xksriod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it bu0ynisr t+n* 41l5ezb pt is 85 cm long*t e5p1syiblr0n4n+ z when a weight of 180 N 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 wxkr/r* m6 sh+mm when its 68-kg driver gets into the driver’s seat. If the car goes w r/s6krm *h+xover a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg irx90r dokb906er v 1pfish hangs from it. (a) What is the spring 9p9vro0 1ik06rdxber stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is h ,nw.eq bfzhx 0-n-z(7vmfw7fung from it. What is its frequency if only 0wn7z0xfe7fqh w(vf, m n-b-z..38 kg hangs from it?    Hz

Construct a Table indichfg;l*9npyrayb.mcy *hp / 4:ating the position x of the mass in Fig. 11–2 at times t =y.lgfyyh9;n/prca* 4b* mhp : 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 caught k5ad:a:azu/trfx :* zin a spider’s web. The web vibrates predominately akr/:z zfa :u5a xt:d*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 a frequency of 0.88 Hz. tbp3b +nawsbe9j/noz ,4 c3gd8a)0 t rWhen an additionos, b9a3a4ztbg08) pb t3e dncwnj/r +al 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per -de b/oc +vs1-fko9qub,c )pnsecond with an amplitude of 0.13 m. Determincpo+c-1b q/v o fdsu-9e)bnk,e
(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 z+d d;-l .9n +nwtnbe9*sys tbhalf the maximum value-lnb est yb;n9 9+twn sddz*.+?$\approx$    A

A mass attached to the end of a sprinjd6e,dpah.q*rd +za 6 g 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 spy7ric,1wdus13g jv- zx 0 nod0ring is stretched an additional 0.130 m and released, how long does it take dn ycw00u- ,orzjvgs7 1 x31idto reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnessxvj*7h)pstlcbr 4(s ; constant k = 280 N/m and is executing simple harmonic motion. When the jcbts (7lpr h)* x;4vsobject is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m to7 13q zwwd:;6pgefp )j/ blanr “load” a 0.180-kgnaw6 frp7 w/j; dbl)g3:pez1q ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is apde a uzwikz865oe+8.ttached to one end of a spring; the other end is fixed to a wall. 3.0 J of work d 8 o6a+wupzke5ie. 8zis 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 = 0.45co .cs7b 1yzmh .cmgkqen: v:)q0s6.4t where x is in meters and t is in seconds. Determb .sc::vnqgmzh.m 7qk )ce y01ine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and h3uu9xwpx0(jsab r 34 qnq fo,4alf PE? ±f ,0o3u4q b934r uqnp wajxsx(    A

  If one vibration has 7.0 times the energy o0ysjz-ajw1uohx18oc4y f2 )wf a second, but their frequencies and masses are the same, what is the ratio of their amplituujy-oax2)8z s0y 1c h4jfow1wdes?   

  A 2.00-kg pumpkin oscillates from a veep5) o jrmi1m9jtenrk m/4a. .rtically hanging light spring once every 0mj oam9jer 5kim./t4p r1e)n..65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical pam ,k9 b*(7ax,orm57zat hkono rallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrationtk9hbo mo ka(5*x , r,n7moz7a?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in nb9: 1a((-w pwyhfr bkme wn(rp9y(w:1 - abfbhkters 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 ) *e5y5 aiop1n /fktutof SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the qup .7 4udg9x-azb;kaend of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.9-d.9uzkg px; quba7a46m/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 with an amplio/zt p a)xq2o94d3 9xkdlg .bh3b.dmwtude of 28.0 cm when 0.260 kg hangs from it. The mass passes through thqt dbd4/g)3m.93x bazlo hk 2dpox.w9e 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 stiffness cq mf7d7k+h;h fonstants $k_1$ 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 vat/;i szem 760.600-kg block attached to a fixed horizontal spring whose sprinet; 7zav 6i/msg 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 high 3k0lm c-hx 6hpbridge. 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 unstretched length of the bungee cohc3l -6xkh mp0rd.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 6)zjbf3n 9(fph0 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per secp4pko hv sgv6( 93m si/b01jdhond? (That isp /oh4 hi p6mkvb1s3(s90 jgdv, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. xrp5fcl *nv7 x3 )siv2What is its period on Mars, where the acceleration of gravi3l*5ncf2spi 7xvxr )vty is about 0.37 that on Earth?    s

  What is the period of a sim9i)1g7r ut kf *ciz7ob:+jmq eple 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 pendulum bob has fzge6 3goi9 o6:9kc0y5x cqqja mass of 365 grams, and it is released at an anglq :xig 936cf ey0 zkqjoc56og9e 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 ab e0dorft3. 8r hmi+f) length of 0.9930 m. If the clock loses half a minute per daf ft 0h m.rb+)ie8dro3y, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for tag . y j+r/q3ub3nd/asdk67hlhe 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 oscillates at a frequency of 2.5 Hz. At it is released from aos,od1cl e4-c/2 p u l0:zdhorest st4p coc e0a2/sl1 d ohoudl,:z-arting 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 tha(7c3*i se7h yp:y dlcat wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are t 7acp*ycsd :(eh7 3iylhe waves traveling?    m/s

  A sound wave in air has a frequd2wg yvg6l 8 0mp7w0pnq26k gyency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave credp yy8w22g00mpwq67 v nkg gl6sts (compressions)?    m

  (a) AM radio signals have frequ, ( l.ics vkwx7p ppclq/j,:9 wow6.qxencies between 550 kHz and 1600 kHz (kilohertz) and travel withv(cqx w,/.,lxopsp9lw q jw6p7 .ick: 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 longitudinal waves i;cb jlwz*c0x hr,f( nx2 s9qm;n
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one i v8j1ecm1sk 8ls twice as dense as the other. In which rod will the speed mjevs8 c8l1k1 of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the teblfwbcl oh)sl7- x / +py0+b9onsion in the cord is 150 N, how long will it take a pulse to w )09+lbhl7sol-o+ cp fybb/ xtravel from one support to the other?    s

  A ski gondola is connected to the top of a hill )x /z. d5v-rvtp3exudknsu* /by a steel cable of length 620 m a rzk3 )t/n - s*d5v.depxuxv/und 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.
(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 d,o.*-u 8j7qq r wtjhxhis ship just below the surface of the sea. He hears the echo of the wave reflected fr q87jqwjuh*.d, txro-om 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 th-h xsfh75 bix4is difference helps in locating the earthquake “epicenter-f5bhhxxs i74 ” (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 5jtgx (y a-hko9)+gve 0vve:k wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the accelerate9o -kg )0k vta (vgxhe:y5v+jion a>g]    m

  What is the ratio of (a) the intensit9bl 6qzd91tf fies, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two pof6f1 blqtzd9 9ints 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing : uy )cnxgz3.kthrough the Earth is measured to be ukz.:cxng)3y$ 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 frequencrmit2l; v5fl+ -c/o pcy travel through the same portion of the Earth, but one 2vitp ;-ll/ cf+orm 5cis carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling alonauck e-ft( tayd88a(5g a stretched string have the same frequency, but one transports three times the power of the other. Whe-t(t a58dkuaa(cy8fat is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a .syu q43h() fq7jc(f oeoi3iv pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum f( 3hioqy(ij7qs).vou3ce 4fKE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch the r ond/ dncjql*d;li9z97yq31 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 i y3o lqcri9zdn* 9j7d1/n;l qds straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fvpo w-mw:ju/a1.tf7bd 7wi .uundamental frequency, what are the frequencies of the first f:omv 7.7wu . bi-wjfd ta/pwu1our harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 ;.* o vhw w)pq:yvllj1Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only tly1h.wp)o v v;l:*j wqwo-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loopsrcif8wffnp3 p -n*a4u7x3nu/ at a frequency of 280 Hz. Name at least three other frequencies at which it will resonate3x u a cru-pffn4wpn *3f8i7n/. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of sta s+f zy(rb;6f+emct l(nding waves is 475 Hz, how far zbml( f +y+rs6ef;tc (apart are two adjacent nodes?   m

  If two successive ove0da/, b(+ xxz8ij uo2nx9,lowr to,ndrtones of a vibrating string are 280 Hz and 350 Hz, what is tljwxt r ,( z,o90/a ,b i2ud8nnxd+oxohe frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the o4s3tzr d-q xbc-6mc:bridge to the support post is L = 62cm and the string is under a tension ocosmt-rx6c:3 4 b-z dqf 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 2o*d( ,zaz5 z.xf nvo)q00 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changeda.f(,o)q5vn*z d zozx to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrat:6u /rr04w wc7ppl/5ngez0eagn 3 al ve at 200 Hz, but it is measured to vibrate at 205 Hz.ar:weecg7lg wv06uzl p ra 3/ /np5n04 By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-a-mrc18 5wv(vmuhj.xw ) 0i eyfu3(dwgmplitude mechanical 60-Hz vibrator. The string’s mass per unit lengty8x1v3e(uh mwv ij .ruw(w cg)m 0df-5h 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 ox)) 5sdx+m): o 1 lnhktn,bst9dic(b mf the string may be adjusted by moving the pulley. If the dnxxs )t s+bnc,hmi 5)k19:( btom) dlhanging mass 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 water back and forth in a tub at just the ri k16 8lm k5yvcuyzkv1j er.;c(ght 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..lyr(y 1 m6581c vkz;k ejkuvc85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary vh0mmq78 opeaorc p jt();sk-9)r k 7ubv ch(*within the Earth between two kinds of material. If it approaches the bo9 o(sphac v8qkvmrj* )o7 ;rbkt7p)hmeu 0(c-undary 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 thwccq t/yg1,p r,l3tc*e velocity changes from 2.8 m/s to 2.1 m/s If the incident wav t3 1rcwl/q,pc,yc *tge crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air3 imqw) xi2)sw when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle i2qms3))xi wwof 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 wyp- d 3oub+mad;*pwm0 ave strikes a boundary between two types of rock at a 38p*obd; 0uym +pw-dm3a $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’l:pxr:ldam sbf ( +90zel4g b1s manual, the dish has to be pointed in the direction of the satellite, eabr:9lx(sl zfgb md +:0lp41but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pac4 kxo wa(6sud)ific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately (uk s 4xdwa6)ohow 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 bumlrxzk m5azj2b gli1p,pc ),-o **ca1rper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg,lj*)m1pcp, 25arko*z ,lx ci1brgz-a collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window 3kwi5zj+zyo0.qx(q p to a fire net 18 m below, which stretches the net jk+xp.305wzqi zyo (q1.1 m. 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 frc3bgu0ld q+.rl- om, meely hanging spring. The mass then falls 33 cm before it stops and begins to rise. Wh.u3m+,o g 0 llc-qbdrmat is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 19ab6 3s*:(sslm noz vo1–54), compressing the spria*m6( zv3no bls 9:ossng 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 8 cm) at just the r+06cnpg urou 3ight pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the sp g0cn ru3o+pu6eed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from o/fafx 5vacst9 w5pq o-,7e h(the center of a 33-rpm phonograph record have a wavele7os9xt5 ,ha/5a(ecffqvop -w ngth of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equag)r aw o o(s)-m;v5iedtion x=0.650cos7.40t where x is in meters and t in ser)m5gso d(ie;) wv-oaconds. 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 fres 3j7ts- ecgb;(iz,requency f. What is its frequency if it accele(-rg7 s;z,eiejt 3 scbrates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats onoj)b- bgkyoo5m(21jf y* jbx+ a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a wj(b x+5g-yb jm o1k2f*jb oyo)hile.
(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 39q vkh-v tyqh69tul04:2 Hz (G) and 440 Hz (A). qty6h0-qlt k :4vv9hu
(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 co2oy7haq g lmm:x 5qd5m4ts0.nrd of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section v dt .g4qm0nao752lx m qym5:shersus 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 o ,ala*db ;w6 8cinl.zf o67gpof 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculap7b*; o acl.6w zd6o il8,gfante
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cyqbvb7 sz.d)k vq 98)l:osvu4 gcles per second. What is the maximum amplitude with which the end kglsb)q)vbq9v usv :4zo7d8. of the 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 “freavky) v2l eb;:e” 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 vibrations of such a str;)b:e2 kvlyva ing with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takg - k/qxkbd0i-a 74jtux 4iyuiqt* y46es 1.000 sx/xi0 7-yki*yt-q4 qt 4i b d4uuka6jg.
(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 oscillat2)zxebsamujcui 01zx-lqpw n3,+ . q 9e in the vertical direction or can swing as a pendulum of small amplitude, ,zn3u xqcxm+ b0ue.w iz29-1aq)slj pbut 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.y pv9 jtl4d8a a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite en8j4 v.9td laypd. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffness8gx13s3 aeggu constant k. A penny of mass mxgg 3 8eugas13 is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 22 ,jp 3y xv4*v- rj2e)nzlfya t6m long and has a diameter of 6.4 mm. A breeze starts the carj4p -t6fv,axly)3 2ez rny*jv bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plag n;tg* mo3oj6w5ktuw l3a3 :08xmqmrvl4 ds2te 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 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 je d 60mgt;2glaql*o njoxust3v3k4w8wm:m r53llo is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz