Give some examples of everyday vibrating objects. Which exhibit SHM, at least ap ueg3l h44tduim5-xoph7t y8yyy.5 b6proit4uyo-myhd8 7el x5 y5.tuhbyg64 3pximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so,h 4et*o98tsws where?

Explain why the motion of a piston in an automo (u0*/ xcekgd5a /ud541h;rbhb fbxqbbile engine is approximately simple ha/b(b54h* be5u;kqf h1dxd bg uc/0r xarmonic.

Real springs have mass. Will the true period and frequency be larger or smaller qj+0f 5rupgtcj8/,zszi*b 4uthan given by the equations for a mass oscillating on the end of an idealized massless spring? j/z0,tf+uc5rsgpqb u j 48* izExplain.

How could you double the maximum sp g)vsy3izb94tzjg+05d0bl wieed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, an 8z2 q mlxjqe;2+c/vgth*avg fs: ,x(rd then is ree/aqg+ tg2x2flq(v :,shvc; m*jzxr 8 leased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, willm cmb;7b:s yln3dd,b.dk- a,z it gain or lose time when taken to high altitudd;,y3dcb -ad7,mn. bbskm lz:e? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). H*72bnb n/bq0kb yby9p ow could you estimate the q 2y/b bb7nknb0*9bypheight of the branch using only a stopwatch?

Why can you make water slosh back ypzo3(u:q- qo and forth in a pan only if you shake the pan at a certain frequenp qquy-(zoo3:cy?

Give several everyday examples of r d8n -*zz-do3 p 2kn;qveb*c(to 6jilsesonance.

Is a rattle in a car ever a r)7zx ih( f36ibbtys )resonance phenomenon? Explain.

Is the frequency of a simple periodic wave eq* yhgx+unv/ fh 47wd 6 saq,ga0qml/9aual to the frequency of its source? Why or *0yg+ slah6g,hxwna u47va /qmf9d/ qwhy not?

Explain the difference between the speed of a transverse(1rf4uur7bf/nm mok4 wave traveling down a cord and the speed of a tinyr(4 bfknr 1o7 fu/mmu4 piece of the cord.

Why do the strings used for the lowest-frequency notes onhic5si 6kr :-0qrm tr+/kw ft2 a piano normally have wire sr+ifh205 -/q 6i kkcwrmt:rtwrapped around them?

What kind of waves do you think will travel down a horizontal metal rod if you ch,q gb79wj o-strike its end (a) vertically from above and (b) horizontally paraloj ,c 7q-whg9blel to its length?

Since the density of air decrewv 8 p1e3m gibr/- dea9udgaiz u-4u72ases with an increase in temperature, but the bulk modulus B is nearly independent of tempee24z7ue m-/rb- gad89duuav i 1pwig3 rature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why ci(luvm hb a6ejyrk )4g9s9ts:* rcular water waves decrease in amplitude as they travel away from the sv(b *rs esjl9:y6a) htk49gmuource.

Two linear waves have the same akr52 uhytx* vxm11,0vhpk 3w rmplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? Byh ktyvu11*0kmxr 3p r 5vh,w2x what factor?

When a sinusoidal wave crosses the boundary between two5 acuvp 7exw*4u5mw7c sections of cord as in Fig. 11–33, the frequency does not change (altcw57au5* xu4 c 7wpevmhough the wavelength and velocity do change). Explain why.

If a string is vibratil,idrk /zn s:fcy;twa:: *qm9ng in three segments, are there any places you could touch it with a knife blade without d ,9l/sq y:*r it:d:nwamkcf; zisturbing the motion?

When a standing wave existsyv +up9x+ro :zfwkw-+kr+ xk : on a string, the vibrations of incident and reflected w xkr+oy+kkw+ - w:r:f9xp+ vuzaves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place toca+ 5,g)ww/u mrwk 3ah- (prai another, how might we determine whether the energy was/(r a-+gu cwak ,imwpw a5r3)h being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distan5z)/qyej(bt ice it tra5ieq /jyz()btvels in one period?    m

  An elastic cord is 654 250ut7eq nn nj(x mhl+jiz0v64b cwi cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hanj w0xjve5q44iimzut0 n+2lnc (h76 b ngs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 (m mov+cd-tg/mm when its 68-kg driver gets into thedv+ m( omt/gc- driver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches*/ g2oslzpfv:uf k;*q 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness confk*f ;g/ql:*upz2ov sstant $\approx$    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 kgveyqt;h6h.; 1rwwh t q z:5is/ is hung from it. What is its frequency if only 0.38 t; wzvqsh h6 e:r/5hw;1iq.yt kg hangs from it?    Hz

Construct a Table indic0+x8lbyp bdjpc,2t,i:z cr 1sating the position x of the mass in Fig. 11–2 at times t =:,rcisd0p2p,1bzb+j 8xlc y t 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 in a spider’s web. The webwhzj/b1hvf 5* vibrates predominatjb5*vzf hwh1 /ely 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 wi)g9n9 l+b+t twwd5ng-4onojkg*.e e nth a frequency of 0.88 Hz. When an additional 68oe9g goj.kww +n-d+nt*)ne4b9tng 5l 0-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.*+7(e0z- cgln r c qx2krbmsk times per second with an amplitude of 0.13 m. Determinerlrxgkbk0 nc +zq7cms2e*.-(
(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 1,0 wf:kkaml t9pzwl( the speed of a SHO half the maximum value?l wl m9k1kwa,fpz:(0t$\approx$    A

A mass attached to the end of a spring is stretched bopa-n( 2jdk9 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 as h31l 9w rvztq5zh(l2 vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position aga2hv3ht95lqlzwz(1 srin?    s

  An object with mass 3.z2 5,+x0xt jj.:bsv sxlw/twb0 kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a sp vsbbjst.0zxxxwj /2w+l:5,teed 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 ofo-g 2m 4cyzk +esr ht;9ag5,tf a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the,o aczg+he2 t t;y-4fk 59gsrm gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one enwqcl+pvk. u+ (5g* jbed of a spring; the other end is fixed to a wallkv(jc5 wg quel .*p++b. 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 = 0.45cl 9s79hgewx4hpqo6 t/ os6.4t where x is in meters and t is in seconds. Determinels 4p9x9qg7e /htw6h o
(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 energ*l2p+gfb4.s uo a1k;c gmdp ;cy of a SHO half KE and half PE?m+ sgpu*2ofkl4g;pc; a1. dcb ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencies an lv+xwgs, g.*9fg b0iwd masses are the same, w s.wlgv*bw,g0+gx f9ihat is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically w76vz azzah ,/.c 5nfwhanging light spring once every 0.75cz ah fz6 /wwz.v,an65 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 supportebq* e- pvmfrqae:t q)fn7i6 1+d by two identical parallel vertical springs, each with spring stfvat pqr7m+1 -* )ei :bnf6qqeiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accois84i( 2w6):qgxgbpj+wyori rding to the equation x = 0.38sin6.5t where x is in meters (oixq+:y8 gp)b gw2jrisw4 i 6and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. Fdfs7 ,0owr08p sgykl)or 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 end of a horizonta/ci0*islf w h*l spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed0cwl i* is*h/f 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 with an ampl2cd6 s-f69yg x3dfbr iitude of 28.0 cm when 0.260 kg hangs from it. The ma6f 2y -dxb9 gsdfcr63iss passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, 1zyuqjs/) gr4with 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 0.600-kg block attached ml*nl)e. zwp 9to a fixed horizontal spring whose spripm. zen l)9wl*ng 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 highxe5dxe1v5n mrk36)hf 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 sp h3rx6)e1fm 55vdnxkering 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 e .csybdb 8u22ixactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simpled(7- ,u* ow3pgqb ni1mlh8vyt pendulum be if it is to make exactly one swing per second? (That is, -v3h(1n,iy*ub8gwpq 7odm l tone 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, wh; uopnrn8b*wyrt,z d 4298gaiere the acceleratiotz,abnr8rui2p4 on;d8* gw 9yn of gravity is about 0.37 that on Earth?    s

  What is the period of a simple penduljy ewa18amv 0.um 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: mw(szw7mp)p. xd.u p a mass of 365 gs7p p.)zdmpm:.wxwu ( rams, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock losek 0rqwzc, 6hg ;/;htqoi o:qk7s half a minute per day, how should you adjust the length of the ; ,7zr;koq gq0ct/hwo6:kiqhpendulum? shortened by    mm.

Derive a formula for the maximum spef03+f ;,aiih6t7uh*zq9xu iemy)rg j ed $v_{max}$ 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 frh+5ab *n,gfrkf8a*f -n eix9a om rest starta-anr*h kf ,beg nf+i9fx*8 a5ing 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 that6tqdvx ivx3m:. y,xs- wave crests pass the bow of his anchored boat every 3.0 s. He measdy,x x xtqsvm .-:v36iures the 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 3 kj3c3e,7gtmcf(+ rgw 43 m/s How far apart are the wave crests ctm rc(g ,7jwfk33eg+ (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 *j/2xifhq9koi2sb wwl h fk:2l,s 0 u5kHz (kilohertz) and travel with a 5 i s 2l9,uh0/ *soq2wffw2:b ikxljkhspeed 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 ino*k c qz018axk
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice asu 5w; laeh 8i287qcy/s nftnw0 dense as the other. In which rod will the speed of longitudinal waves be greater, and by whatf8t; hl8 5ai0cnqsu27/ny w we factor?   

  A cord of mass 0.65 kg is stretched between two umsp3/5q3 pv u2im pmedq 4m0,f:;kgysupports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse upvu2p, 0ieq4/pk : smfy; 3mgm35m qdto travel from one support to the other?    s

  A ski gondola is connected to the top ov og b;-9* w+egkpvy;tf 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 bumogw; 9gkv-e;vytp*b +ps 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 hitwp z 0o5;450;n0fy twvropci s 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 deep is the ocean at this w0zt0 rfc i4w0;5nyov5;p to ppoint?    m

  P and S waves from an earthquake *3i)bz w7kf1to5k sns2uls2o travel at different speeds, and this difference helps in locating the earthquakes3n k)iku bt2s12 *oofz75wsl “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinh xh(iw zh527ausoidal 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 acc7( x haz5hhwi2eleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplvo ymk d a-s( svaq.+iczml4pr157w,0itudes, of an earthquake P wave passing through thezym sv,5arw-q0lcdia7ov . (p4 m+ks1 Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing th.bfq+- s8xuz1qriy 7 trough the Earth is measured to be qyu.ts +xfzb q1-78ri $ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travzlq2 . i 7,8,fe7+wamgc keszcel through the same portion of the Earth, but one is carrying twice the energy. What izl7ckagcie+ s7 f.2,qmez 8,ws the ratio of the amplitudes of the two waves?   

  Two waves traveling alongxs ep. e5zg )itr4h3(g a stretched string have the same frequency, but one transports three 5 (grxhsi.peget )z34times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond 5puqrf 9bi3lp6kad6 u 0 r:dq-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 pild 5qu9 3:6-p6f qu0rdbrak maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. nbze 4y lt2eunhqn .4wv*)a/*k uyup,**skp4(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 Fnkpz)*4ky*2p,*v4 e4 nnaeq.stl why */u buu ig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, whuoz6;/g(v mg +yclau+;nt yr.at are the frequencies of the first four harmon glr+ c.;;gut m nv6z+uo(yay/ics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frvvcudmxz;cbmikyn 216 o*; 51equency will it vibrate if it is fingered one-thi zn;5 cydm21cikvbox6* 1 uv;mrd 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 ax 4; 41pcw/rxmh5iv wwt a frequency of 280 Hz. Name at least three other frequencies at which it will resonatv4;/w4c1pw mx r5 hxiwe. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s oz p m725 f*c, nsxosnj56gmkaxsi ;8nh-+ 0peIf the frequency of standing waves is 475 Hz, how far apart are two adjace2pmfcj*a, 6i+ m- kznsx5gxsnph5;0e7son8 ont nodes?   m

  If two successive overtones of a vibrating stri;fsao3 ; s(gjgng are 280 Hz and 350 Hz, what is the frequency of the fojsas(g ;g f3;undamental?    Hz

  A guitar string is 90 cm l*rb:z8* l ovblong and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two llo b:v*bz*8r overtones?    Hz

  A particular guitar strinlro vke/dkp1 x1ii+*2g is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percenkxe 1ro*iild 21 kvp+/t should 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 1e+4k/pl pka gHz, but it is measured to/ekp gl pk+41a vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude m6sk uw bey6a-bn,3e,uechanical 60-Hz vibrator. The string’s mass per uniaw3,yb eu,nb6eu -k s6t 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 movqecol27;x m3 uing the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing waxec7u3; o 2mqlve 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 thbx(q(yf/n)n y -v4knde 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 tx qynk /4-()v(ndbyf nhe speed of the water wave?    m/s

  An earthquake P wave d z60hsl8.taztraveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If ztdzl0. 8sh6 ait 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 5cj/79o zq s,c /kyhhsjrx(x5the velocity changes from 2.8 m/s to 2.1 mszh5/ 9yq5 coj7jx/cskr (xh, /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 a68rka c* fmz+h layer of cold, dense air. If the soundfa*km6h8 z+ cr wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave striofq31/m/0pku c 8u; lfj-idkjkes a boundary between two types of rock at a 38-kj/;8u k0duo i1mf/c jqf3lp $^{\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.(m x9omlrwf .45 m in diameter. According to the user’s manual, the dish has to .9 4(f mxwomlrbe 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 0tuh0olsy8w (fb 5ef.,/ivbd250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them 5vw .b, itd0e(luy 0 fobf/8shattracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of tfoq 0ee : uevk1,tt3-550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, 10,eqt:o3vk eeu-ft tcollides 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 ethaqa*f7d 4.n4m fzdx z(/kb0e5jj + window to a fire net 18 m below, which stretches the net 1.1 m. Ass.*j jnza5 q4xhb+7m4tkze0ffaded/( ume 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 th z.s2lz 4va,uhgkz + iwva9y)0e end of a freely hanging spring. The mass then falls 33 cm before it stops and beg va uazwk94,).ig2yz+ vhs0l zins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/k+lhl4ga: (v;4 h semqs (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness cov4gqhl kma;+ :(h4e lsnstant 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 ri.an)9:1nltjk wtimw /ra cigb4,n+v4 quu.,qght pace of about 1 step per second, the coffee sloshes more and more until eventj.qr.u4w:cw4n nia+t/t1m)iv g k9 ,qu a,n lbually 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 fro h8jnn,1ln0y xm the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the soundnx n81y0j lh,n emitted?    Hz

  A 2.00-kg mass vibrates according to 1j2sein i6 5cuthe equation x=0.650cos7.40t where x is in meters and t injc2 51eiu i6sn 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 frequ v4z/os2 n-ek 7mmdtt7ency f. What is its frequency if it accelerates at 0.50g (a) upwsmtv7z 2o d knm/74e-tard,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kakje-a: wm7vo. *t5nrg man stands on the raft, it sinks 4.0 or 7 -k.tejn*av5maw:cm deeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 Hgsl0bt-j,:( pia hd i1z (A).(p 1 jib0lh:a -st,dgi
(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 n ipy0edr43lf.(d5j e of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is th4f (j3np.05idd r lyeee wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency nrc ju1i4/uf 9of 264 Hz, and the tip of each prong moves 1.8 mm toc r f19n4/uuij 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 motiobyropwca) b) 9;d,+m zyp p73acn3;mt n of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will t cp3zobrm9+yam 3b)p)7dc;w;na p,ynot lose contact with the board during the oscillation?

A string can have a “free” end if t4s-o-w9df2 .pnt+j m svlyoo 1hat end is attached to a ring that can slide without friction on a vertical pol s+ -d42ljf 19t y-ovops.owmne (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 2.000 s — each,67w/uozpvw o one-way swing takes 1 /wzw,uo6vp7 o.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 can swiup)u h;, hb3elng as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillatiulp uh,3;eh)b ons or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension oz05-ki6 gvi 9d5hiplia59x q af 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is gla6h 5-ix5id g9k5i9 zqap vi0enerated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiutds5e m9bh*5b t alcs,25ij4uq16m )sas r4dling by a spring with spring stiffness constant k. A pehlbscmttsd5ud5 a9 a4msb1) sr i4*j56 u2e,q nny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cran8 slli+3kzs57cy y5 dse cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of th55sly+7 yld8zssi 3 cke cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also give+4k-ft6d n.bml +p6avdiog9; b xr1xfs 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 vibrat- bgpn4t 9kdoi dax+vrf6.m 1x;b+l6fing 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