Give some examples of everyday vibrating objects. Which exhibit wib 8cauc ;z8r or,loilb87/7jz34vhSHM, at least apprir7bl83 wc holi7jrz bc a84ov;/,z8u oximately?

Is the acceleration of a simple harmonic oscillator ever zero? I*exfp1my+ /;v xd/ tfcf so, where?

Explain why the motion of a piston in an automo)s:k: b yr2koxbile engine is approximately simpleb2:)xkokysr : harmonic.

Real springs have mass. Will the true period and frequency be larger or smal/fuj ac3r.vz 17i;utltz i e;,ler than given by the equations for a mass oscillating on the end of an idealized massltuij;u7l1 zzv fca/.re ;3 it,ess spring? Explain.

How could you double the maximum speed of a simple harmonic oscilpn/ b9*r k5cuglator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical springib6w6*(yk0-gqazfxwfrq2 *:wqp-up scale, and then is released. Describe the scale rea a :(26fipq-u*6-bwq yfr* x pwzq0gkwding as a function of time.

If a pendulum clock is accurate at seeduep2 +u4 1ndi)n* msa level, will it gain or lose time when taken to high altitude? Why1 n2iu*4+ede sdupmn)?

A tire swing hanging from a brzbmf92k wu6 *banch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the bfbw 6zbu29k*m ranch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you mm r, em+2l0f(jetajq p- p7an )8zw;jshake the pan at a c wp 7jrjl+8(;zat0f-me aq,2mnpj m)e ertain frequency?

Give several everyday examples of resonanb nt/) ytrkx75 ;tl8j.t ft6uw*thpqw4r6 v9rce.

Is a rattle in a car ever a resonance phenomenon? gcvwxf)(fdsuk4 74 9za* - btsExplain.

Is the frequency of a simple perife- (v*sebqyjodz1q d *8knf0x u,3 .eodic wave equal to the frequency of its source? Why or why not?(ff.d- x,*ns uze qkve*83d oyq0e jb1

Explain the difference between the speedm:e7) stgi ;e-qkf c-h of a transverse wave traveling down a cord and the speed of a tiny7itk;eg ce m:-)-hqfs piece of the cord.

Why do the strings used for the lowest-frequency notes on a pia jv;wln6 prd 0pley4dq)1x,9 wno normally have wire p,e ql1p6)j;xy 40vr9dn wld wwrapped around them?

What kind of waves do you think will travel dor h oba025 wci+ bt690n6rxdu5afgb6uwn a horizontal metal rod if you strike its end (a) verticallhir5 c0xrw2b bg0 oaudua6nfb 69 t56+y from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in tempert(vr, bhxtxecmm .u*a w+:*5kature, but the bulk modulus B is nearly independent of temperature, how would you expb:mm.xk a(* r +uchx*t,5ewtv ect the speed of sound waves in air to vary with temperature?

Give two reasons why g*3xu (qv hvpa-sbjq +8cz11wcircular water waves decrease in amplitude as they travel away from the sourcecup3q 1sg1-+b(v8 *hjwazx q v.

Two linear waves have the ) jhbgdyw46q2same amplitude and speed, and otherwise are identical, except one has half the wavelength of the oth6wb q4ydh 2j)ger. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betwea e i/rkayh8m7a;9m5 zen two sections of cord as in Fig. 11eahyzai/a89 ;5 7mrkm–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could toc0r a7*efv4cr yk2lfc 1 lw 5sxe2;aa/uchvy w2 eaa4;l/ sae5rfxcf1c2c70lk r* it with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and dc 1pk+hv dn x/efjxw)- c*3,rreflected waves cancel at the nodes. Does this mean that energy was destroye xr/ ,j 1pc*xv nwk3hdcd+-f)ed? Explain.

If we knew that energy was being transmitted f/w:+,cxw8/ s ps tp0uqa3hscarom one place to another, how might we determine whether the energy was being carried by partiachx s/a8w+st s3p/ qwcpu 0,:cles (material bodies) or by waves?

  If a particle underggdrj73qp u k(/oes SHM with amplitude 0.18 m, what is the total distance it travels in one3/rud(k gjpq 7 period?    m

  An elastic cord is 65 cm long when a weigax.q) w; tb9sboj7uomu, -n:lht of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cordxnom9. oub:qj tul;,7 s-a) bw?    N/m

  The springs of a 1500-kg car compress 5.0 zvxxz- ndepy092r.85.ru*zwet d n :z(u ga)m mm when its 68-kg driver gets into then05dz ) ayzr(xv .-mu2rutxzw:.ne 8gd ez*9 p driver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm 7td z d:/-. 6sjup)swtbz9lx iwhen a 2.7-kg fish hangs from it. (a) What is the spring stiffness c6js i-.dz 9uds z)bt:p /lwt7xonstant $\approx$    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 inuu/+ ,ix lzgm45 p7ehung from it. What u4x7mpizge+i5 n l/u, is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2zx1lgrta*hwkrz 4rlg 6;x07 / at times t rr l07*1/zw6;xx rgt z4 kghla= 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 c3.wkts.9mnf x(( vt knaught in a spider’s web. The web vibrates predominately with a frequency of 4.0 Hz. k3v(f nt9ns m.wk.xt(
(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 s*lh eyu w:2h,,eb 4 qbxw/vws7pring vibrates with a frequency of 0.88 Hz. When an addit: * qws4yeeb uvxh,,b7/lw h2wional 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 viaivl+xp np4 r/fh.89tbrates 3.0 times per second with an amplitude of 0.+8pf n ia/ht49xr. lpv13 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 spe)muqj, 9sg7n7 jmqeg.ed of a SHO half the maximum valueg7u)9j sg 7mj ,.qqnem?$\approx$    A

A mass attached to thmpc+ u7zxb1zpu3 a4 ,pe end of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.31v7ru;iug otb , ,44ad lzt-/lt5 m. If the spring is stretched an additional 0.130 m and released, how long does it take to rz4ur,/ gttb-lo7v ui4dl,a;teach the (new) equilibrium position again?    s

  An object with mass 3.04gz7w 1yof9v32t k ea*jfzr2i 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 fforfk93g1 e2tw 2vzj zi4 7ya*rom 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 com 3z j8)balzxmzo725 pspress the spring of a toy popgun 0.200 m to “load” a 0.180-kg zl 8s2zo57xp)jbmz3a ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionlessp;j0z3b +yvdv4s stt.ik;yu + surface is attached to one end of a spring; t +zp b.jvis ts3;v0ytud k4y;+he other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the xxpu.r;j)1 tlh *nqw3 equation x = 0.45cos6.4t where x is in meters and t i1jpw nr x;.lqtxu)h*3s 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 equilibrium is the energy of ayw,6p7qf,a f h-mx.kzx8h,hg SHO half KE and half PE?,h6m gfk.x,-h,fxq zyha8 wp7 ±    A

  If one vibration has 7.0 times tx lzkyz ;yxt m1n76u49he energy of a second, but their frequencies and masses are the same, what is the ratio of th ymzyxz19nx6k7 l 4;tueir amplitudes?   

  A 2.00-kg pumpkin osci5(ee ze d+/crillates from a vertically hanging light spring once every 0.r/e+ dz5(eice65 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 paralk-qnp2;t pu omg6o(lz4id hy-m6n ;e(lel vertical springs, each 6-i-n l k (d;qtuz6m 4no;h2mep po(gywith spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38won udj4 m7+81sow +1h 8lkdvfsin6.5t where x is in meters and t is in seconds. De+wlw 14 so 1mk+o8d8unvj dh7ftermine
(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. 2a6fk krk)e0h-wom y,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 end of a hork7ndv+qvq ea7f3r8 by)e4 f v5izontal spring (k = 124 N/m) is struck by a hammer, w e7avvbr 4) vffq5n dk78q3y+ehich 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 withl:u ruuaho e:tw/65t) spring 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 equilibrium 6ut)w h otl ::u/eura5point (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 t,g6x gi)6f2s0u3jkv:hh khy v z28zsa wo springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal spct)/b4l4 cuhjd li ;y;ring whose spring stiffness constant isdtl)y /u hj;b;c4 l4ic $ 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 fi; g3fq 4z3eorrom a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretch3;zf ige43r oqed 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 exact7mwt 7-5ipp 6vswm0 koly 60 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 swingnzc9 0y4hg 5zz per second? (That is, one complete vibration takes exactly 2.0 sg z5hznz09yc4 .)    m

  A pendulum has a period of 0.80 s on Earta llu,n9:v*o ah. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Eartnl9uval :a, o*h?    s

  What is the period of a simple pendulum 80 (f 3freb89vt vcm 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 a masbahd7g7*q;fj bq. k3 bs of 365 grams, and it is re*d; b. jbk7abf hg73qqleased 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 haos0s+m ,3tjmzs a length of 0.9930 m. If the clock loses half a minutez3 m+s,tmj0o s per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximu+tyao .z/d;l/gzm +c o mgg(,om 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 frpz ay0v y/*2v,2qoijh om rest starting at an an *ja,vzv02yqo /y 2iphgle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored bbg.:sm+6 ndhdp67 tgf oat every 3.0 s. 6dgnb. f+m ht6p7s:dgHe measures 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 witjxtfyfb/,2 w49dzqp 2bn r+c+h a speed of 343 m/s fwb22j +b z4 xp+dyf9q/rnc,tHow far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequenc 2 md:y(yzg)t ,1ulkz(gi-ym e7kbbh(ies between 550 kHz and 1600 kHz (kilohertz) and travel wk edyu 1lmtzi(hb b:(m)7k2y z(-ggy,ith 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 invaby)u, nfm m45eu8lt+s;je 9
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, bu )iir*:glm+vi5qp /zet one is twice as dense as the other. Ii*qvg+5z/ ) lempr: iin which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between tpilm2y1 )d)umwo 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 tym1) i)mdlu2 phe other?    s

  A ski gondola is connected to the top of a hill by a) (,pusahgoic9z -5 ;) wonqoz steel cable of length 620 m and diameter 1.5 cm. As z9oopc onz) )s,; 5h i(w-agquthe 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 the8 sb0y8vyh4n .ua2qu k side 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 deep is the ocean at this pos0y u.u2qhnk 88v y4abint?    m

  P and S waves from an earthquake travel at different speedc49h (n5x7(v(f /9a znaok ucc92hukyrrsy0b s, and this difference helps in locating the earthquake “epicenter” (where the disturbancc z2o4yf7uyru(sha ( ccxr (kk9v5nhb0 9/an9e 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 surf0 kx** 9jtx8m6mffhrvace wave can be approximated by a sinusoidal transverse wav9v ffr8 *xmmtk6 xjh0*e. 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 acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, o xq cozyw5 kd+pj.5)*/h8roppb y7ct3f an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from b7c3h) yq5 .8ptzjyd 5cor *+kpwo p/xthe source?(a)    (b)   

  The intensity of an earthquake wave passing through t6t;j uk 1oej-vg+/pkbhe Earth is measured to be uj bojtpg/kk+1e; 6-v$ 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 trwawn nf8,*e gei pjq0j((1g9u avel through the same portion of the Earth, u8*,aw1 0(igjn(gep jqwn 9febut one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a lnh;je;mb,r 1hf+m0eer6v 9 j stretched string have the same frequency, but one transpone 1f9erhb; j,em6 jvmr;h0l+rts 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 tog8b+tnlveg j 1+s4m40ake l w4 move up and down a total vertical distance of 6.0 cm, from the lowest to the highest 1etw4b0gl4 av 4sekj+ng+8 mlpoint, 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 towazrik+utn +1* srd each other. (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 F1ntki++r * szuig. 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 vi4 )s: jw hmhz1 c-v5q/5s udy)pm)kngmbrates at 440 Hz as its fundamental frequency, what are the frequencies of thns1vh pm5hdjzsq)5cu m:)/)m 4 gky-we first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfing5mxma srl9kgy-6 6;fcered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only t;amy59rf-kcgl6 mxs6wo-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of2t mw0xnjr0s,*b z;b*wuw9 lf 280 Hz. Name at least three ox l 0j zr*tfumbsw2 ;wbw,*0n9ther 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 92m0/ ak zb4wpbi)/s If the frequency of standing waves is 475 Hz, how far apart are twow4/ kaibpz 0b) adjacent nodes?   m

  If two successive overtonv e)-kcw xt( 6-t5gqx*kgz3i3do)pnves of a vibrating string are 280 Hz and 350 Hz, what is theg5tnq-)(63wg-c3ti vx )vzxk ekd*po frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distanc disw *)t( uxx:y 6(mea:2 asgjzjdk9/e from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental a d/)9d *xsta(m:6xe ja: giyzs(kuj2wnd first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, bu v0ttdhf.6 t7eydp4 )et it is measured to vibrate at 205 Hz. By what percent s h6p4tt7feedvdyt)0. hould 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 mfm9d8epyg 9:Hz, but it is measured to vibrate m:9p8e f9gd ymat 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal s nau9,-xbpnd5 1r3krztring is attached to a small-amplitude mechanical 60-Hz vi-r 3napb1rxz5 kd9,unbrator. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the stt56)d etqez6nfz+* ma ring may be adjusted by moving the pulley. If the hanging mass m is fixed at qnfz tate+em5*d6)z 60.080 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 0p6ys y3b dti6a-:jne right frequency, the water alternately rd -p60s3tyyajni 6b:eises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the v v mz/mqqg 1q kvg2+0hsbz6gd4**7xbEarth between two kinds of material. If itg qd*bqzkq*0gvb6 1v/4g+hvm xz sm 72 approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changesx8 ctik-d4z .9y xiej)39hvlu from 2.8 m/s to 2.1 m/s If the incident wave crests make a 3i9349ecy v- hxui.tdj)l8 zkx4$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, ep fve p6fopjt4bbe 0s*s.ig1y*/;p, dense air. If the sound wave hits the cold air interbipfeso0/bs ypp4f*;6e tpegvj*, .1 face at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a *1 bqx7rarzq01stk. jboundary between two types of rock at a 38*qqjr11t ks b7x0 azr. $^{\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’s manual, thmxt+ y:cg; j+cidrz*9 ej m+ z: t+icxcy*r;9dg dish has to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 kp rrxm .asz-v- lfs)6;t*4sajm/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 warni.r;msx) s*r- 6 jzavtslfa4p -ng, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constanl:y+q3zr,y klt 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 (approximatel+kql, :y3lryz y 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from agm*tq8yad7 ddq+v-c 0 window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the netcg0m ty7 dddq*v q+8a- behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The )m6muvi7 /rikmass then falls 33 cm before ituv6 )rmm/ik 7i 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 (Figdxa 3a5rtw w26. 11–54), compressing the spring 5.0 m. (a) w 5daar6w3x t2What 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 right m.vyys,bk jpdf4 7r b5q3rq.rm +pkap c1.7(w pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11wy vk43 ppam7qjb, d7. .yr.sq5k(pmfrbrc+1–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the cen( fwq5wc,aa 0nz *rg:hm2(s u*f/wvivter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sr(5waqhf0w *,vv(cng aszw fui/*m:2ound emitted?    Hz

  A 2.00-kg mass vibrateq+/jiskt3 y7 ks according to the equation x=0.650cos7.40t where x is in meters and t in qyik3jt 7/+ks 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 j722lyk8.pq pv(fkj0 7 iupz awith frequency f. What is its frequency if it acceleratesfjy(2 lkjvi 7p0k z.a28q pup7 at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stan3l u/e(ycr (9m9bu bokds on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raurl m9ceyo(uk b9(3b/ft 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 :/v/d6.ndf)wr js 1us ,:qgf0i f bazvHz (G) and 440 Hz (A). v,srzd ds/ u)0fqvn/6b wji:f1gaf:.
(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 twnw;q f6h zbbw vk-57v4o-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is t n hq65 w;vbb4f7-wzvkhe 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 frequeu;q3c:psa8b;2 ckm ok zdg0k;ncy of 264 Hz, and the tip of each prong moves 1.8 mm to eith038gquk2sc:;ok k; ;amd pcbzer 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 freqc0q np2 j3vzkgm0 k,f(ng b.//j0kz9y huqf7iuency 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. b. kkgzu9zfn/g 3cnj(f 7q20 phk0 qymjv/,i011–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a rhlnly o ml0ae*2x 01z9le/y0 wkf6+oding that can slide w1 kxy2z 6ll+o0lea90 hn/0fmw doy le*ithout friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of en)ohi9opxd 3r* 0 *hcfxactly 2.000 s — each one-way swing takes 1.0*d* in3hfh) c0por9ox00 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 dix2x7m zk :k5uarection or can swing as a pendulum of small amplitude, bkuxk25 z:ma7x ut 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 underz t/gi+2 ( zktuk8 c)uiavjg9+ 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 end. Where will the two+uti uc vgkt) (/a9g2j+8zikz pulses first meet?    m

A block of mass M is suspe ii,te(yl65bp /mq0: ur hfg: pk4zw5tnded from a ceiling by a spring with spring stiffness const45py5 ikuh:g m6,l wf pr:zi b0/q(ettant 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 block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cr.f0:avsns qi+ ane 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? [Hi+fivqns a:s. 0nt: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which alsofob f c12q1j2z 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 spring1j 2 z1f2cbqof, 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