Give some examples of everyda)dkh y w:1b ondr4*q)jy vibrating objects. Which exhibit SHM, at least approy n4o*1bhq)drd k:)wjximately?

Is the acceleration of a simple harmoc/5s)sc.lfh j nic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobifj j +g8w1yw8/q9lj vule engine is approximately simple harmo j j8/f+1u 8gwvljqwy9nic.

Real springs have mass. Will the true pepneate-t5 s3 c(h u+n8riod and frequency be larger or smaller than given by the equations for a mass oscillating on the end of a5+ecs3t8pn he(nut-an idealized massless spring? Explain.

How could you double the maximum speed of a saafc oslb9h7g )*2k*ag7gi5l /x j dw-il.*acimple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, awzi6sw+la94 p nd then is released. Describe the scal6z p9a+wwis4 le reading as a function of time.

If a pendulum clock is accurate at sea level, ,lhmq /jlcf:: will it gain or lose time when taken to high altithmljl ,:c/q:fude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. bauw* 818our.n*v9fkosue2r 11–48). How could you estimate the height of the branch using only a stopwatch?.fso9beuk8rw ruo v *a18 un*2

Why can you make water slosh back and forth in a panosplro+p: 2e9 7yy/eof y2t ;j only if you shake the pan at a cert2eet+/ 29y;7pojyo ol fsr :ypain frequency?

Give several everyday exampletbb8bml19 7ogb:r ib+s of resonance.

Is a rattle in a caroibv9)1q t ya5e*v+m l)is4fr ever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its source-6ywo/an 61peg/qw 8lctu l.1efma,c? Why ocl1o q./616y gewua8wmnca/ ,pflet- r why not?

Explain the difference betweench qb 5op8kvt/5 k+t5g the speed of a transverse wave traveling down a cord and the speet55go5tkvb k8+p/cqh d of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano norm.mtt0 jfwk1 o/ally have wire wrapped aroundmt/wkf0. 1j ot them?

What kind of waves do you think will travel down a ho:l8+t4 smwi +sn)kevbrizontal metal rod if you strike its end (a) vertically from above and (b t:sekm)lwsn + +i4v8b) horizontally parallel to its length?

Since the density of air decreases ck3-1 w10tmgsb qh/ku- q)ooy kdl9(ewith an increase in temperature, but the bulk modulus B is nearly indep bowg/qmu( qs ct k1 lek-1k)3doy-9h0endent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why b3cdu) 28jwn tcircular water waves decrease in amplitude as they travel away from the source3cnu82wdbt )j .

Two linear waves have the same amplitude and speed, and otherwifz;1 *; oyhz c)xtryg/ql 7,hjse are identical, except one has half the wave,/fyr1lhcht )*yz jxz; ;ogq 7length of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectionq ztq j p4jh0ig78nisx8-z90ns of cord as in Fig. 11–33, the frequency does not change (although the wavelength an70x 4 gpjn zzsihtq qi8-9n8j0d velocity do change). Explain why.

If a string is vibrating iny/d-y o63ecp w three segments, are there any places you could touch it with a knife blade withouo36d ye/w- ypct disturbing the motion?

When a standing wave exists on a string, the ( ..qazpan0j+ hp/pprlz/:tpvibrations of incident and reflected waves canp:p ..zat r lp+pq/(/0hpzja ncel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one pl44ptbn- qjr01et/p* 2i2y tiwo q q2ueace to another, how might we determine whether the energy was being carried by particleeqi2e1yu/tt4qn* t-bwjo2 prq i4 20ps (material bodies) or by waves?

  If a particle undergoes SHM with amplitun fkq 14q ue;**;xixwtde 0.18 m, what is the total distance it travels in one **k ;xnq e 4;qwf1uitxperiod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 c3 1do8 rym)swiy h8i(dm long when a weight of 180 N hangs frwi(iysy8hm)r8d o1 3d om it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kgbxv w11i;nx+ytw p; -l7h *ha6wcez+l driver gets into the driver’s seat. If the car goes over a bump, what will be the frequen7nv w+b 6ewzxp-lh;;+lai y* wx11ch tcy of vibrations?$\approx$    Hz

  A fisherman’s scale stretche o n9nu5vw9+k/+dbje ls 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spro k 5l9+j u9dnv+/ebwning 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 *um1 qq7/q6tz;uq(1ptex bk i frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequ epzq1ut/1qk;6*qitm b(7u q xency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fiz yu e(*1so; u6:evmhpg. 11–2 at times t = 0,t1uhz*m6 es(uo:v p;ye = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 0.2. obxj,ve2g409 kyjjq5 g is caught in a spider’s web. The web vibrates predominatee2 xy4j 0j.qbvk,jgo9ly 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. When cfw-05cpz) g1nf6nz4i c1 m hfan additional 680-g mass is added to m, the frequency is 0.60 Hz)z1nccfh 1z0gf -46pn f5wcim. What is the value of m?    kg

  A 0.60-kg mass at the e6wedocpxfoxoj6n -f).c11 a/ nd of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Dedxcoffx 1 )ceo1j/wn.6o6a-p termine
(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 theq.gm era36hxn-4ske9r5g xu0ud 1 hc+ speed of a SHO half the maximum value+am crhg-u3rg4q d6en1.k u90 exh5xs?$\approx$    A

A mass attached to the end of a spring is stretched a d8n (jh(f8q zg +;+iubf7c ugxmistance $x_0$ 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 thenfw3+) ae5em jt i:p4r:b (*9qmbclsl spring is stretched an additional 0.130 m and released, how long does emnsm4lb:f* 9)j:pt wi5l+3(rqbaceit take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring sfdo7my 1,+h zgtiffness constant k = 280 N/m andoh1zf7,gd+y m is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress0fr- 1qw,hb m : hvytno-uz78a the spring of a toy popgun 0.200 m to “load” mq:8b1z ruy-h-owah0ntf ,v7 a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfa ygp7 nw2o*d6hgc4(np4qxr ) t,nnal9/geao2 ce is attached to one end of a spring;yct *qg e(6 lgdxn npn2ph/n w24 7aaoro)4g,9 the 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 accordrmlyu5 dh0e w7nf7-7h ing to the equation x = 0.45cos6.4t where x is in meters and t 577hld wfe y7-umn0rh is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium1f(h t )tf 1uwfreg3dd: rfy91y/bey .yo*.sk is the energy of a SHO half KE and half PE? ±.e3esd:fuw f)(y1 yhr. 1k *1fyot9fbgt/ ydr    A

  If one vibration has 7.0 times the energy of a second, bu29wubch:xn vhj ki.b6q9l2 8rt their frequencies and masses are the same, what is the ratr jkhb9n8qvl6iu9h 2:wx .2c bio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a ) -gqy+obzur ez9q)(bvertically hanging light spring once every 0.65 s. qb)o9-u ) rz bygez(+q
(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 suppora 07w6tolon :zp :m*pxted by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequencmz n0 7oopl:*xw:6apty of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t wherv7: tw3dol us9e x is in meters an7olv 39: wtusdd 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, ykcs;(e*- dt pu7hqt 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 end of a horizontal spring (k = 124 c ;;x4axni9bvzgk( )lN/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Dete)algik 4 (9b;vnzx c;xrmine
(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 coiwzk; sc- 5l1dnstant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from idcw ;k-is1l5 zt. The mass 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, vjk;q1 g q;mzx ny8y(d a)1v/zwith 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 azv7 d+)(fcupv 0.600-kg block attached to a fixed horizontal spring whose spring stiffness7c)vd (+fuzp v 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 brir-x 3-jobvah4g4u))s/;9lqshtf x w udge. 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 b;/3su) ho9x-r hgvluq4 fx)bj 4w-taselow the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 6aqso* :5c(j vk0 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple penduact++ hi 4o8f,dsoulr8ejm*8 lum be if it is to make exactly one swing per second? (That is, one complete vibration *dtcam+hj8s8eo+ri f8o, u4ltakes exactly 2.0 s.)    m

  A pendulum has a period ldq we*1b1rg1 of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravityqg*rld1be1 w1 is about 0.37 that on Earth?    s

  What is the period of9, 4qjm+ku ; dryaz)(sqa dx97zxbsa6 a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 09fg,rt+ iqlh8;1 pknz.760 m, the pendulum bob has a mass of 365 grams, and it is re kt1z+hnpq;irfl9,8gleased 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 length6ct o6 1w4,6p(u*v dlhf whhoz of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened,w4hh1phf t d6 c(6o uw*zlv6o by    mm.

Derive a formula for the l+ u9p)0luggp4u-y, okl6bzpmaximum 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 ati-b0 )kcyo):gjtuc r*f4woy0r3w5 wz a frequency of 2.5 Hz. At it is released from rest starting at an angle of y0:)c-jywcb t g5*u)w0orw o fz4ir3k15 $^{\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 anchoredl pl+0t;pgy*ueanjh) z3l 6a8k,gk mg+9v6 g d boat every 3.0 s. He measures the distance between two cp6j ak6hmzku9l );+gleg y,v+d3an 0tg l g*8prests 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 jyh/ 39+xazrlof 343 m/s How far apart arexazj y+h 9r3/l the wave crests (compressions)?    m

  (a) AM radio signals have frequencies betweenmph;1 d3 bgve5 550 kHz and 1600 kHz (kilohertz) and travel with a speed d1g ph;m5eb v3of $ 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 in kj:wjrki8- :q
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one iivjh 2t+3e0j:ghsn;5o i(t w ms twice as dense as the other. In which rod will the speed ohj3 (t2th go:w eijv;5+mni0sf longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apur+8 5z:mxqm uz tw+/part. If the tension in the cord is 150 N, how lour zz ut/8pw :mmx+q5+ng will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected tonk(j8pnvi73ekg+w / f:1a1qz-yq xvu the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the ugexj:8v3fk kz1-n/+n(1 qw p7yvaiqterminal 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 his ship ju1u)o8/sz fph sst 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 deespz s h81of/)up is the ocean at this point?    m

  P and S waves from anzxtx:f9 (v 8wg52oolb-jv lt; earthquake travel at different speeds, and this difference helps in loc9x j;(ftv2b-v5og:o8 xlwltzating the earthquake “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 apkuid 3avzdog8y m8s sv pu3/akd87(81proximated 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 witi d8gopu3 a1v (ks/7avu3zdd88sk ym8 h the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensitieslhk i +s00y 4qc4bpkg2, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 kihl0pc2ky44 k+q 0 bgsm and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave paslq:u5 qz0r7lnkbg-/+ u jo;iesing through the Earth is measured to be n luqg l-50 rjb z7ki/oq;:eu+$ 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 travel through the same portion of t0)vk4 m wg:ibphe Earth, but one is carryingb :g)v0wkm 4ip twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched ,n0qz uvzula2mh)/9l p ukoa:2 ye5c-string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of then/ 9mu2c z0h-5:u 2p yqovaa,)lek uzl two waves?   

  A bug on the surface of a pond is obserffnr6fih*e4z9 d4e+r ved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest nr6fzh ei4df*4rf9e+ point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving to c 1:-4a/,whfw 7a2orh.d nrecmp/x ibward each other. (a) Sketch the shape of the string at the moment they directly overlap. rn2: -bh4cm.axww /7 1fc/o , eahirpd(b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its f. wo5aq+tcb-l09l dk1jl8jpg (imp m.undamental frequency, what are the frequencies of the first four harmonics5.01 pwldgajcp ll.t+bk mq o(imj8-9?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequ esdz 6,gdv2- m-lskb4yo7 8m0x/ cvkhency will it vibrate if it is 2lshbzs-ve40mdg-kd o m/c87xv6k ,y fingered one-third 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 fouoe33c il 6c-bvr loops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonate.eob- 3 lcciv36 $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the fr1e dpx;n:xw x;equency of standing waves is 475 Hz, how far apart are t d npe;wxx1:x;wo adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what s97l -ta3uwu dis the frequency of the9ws-uul 37d at fundamental?    Hz

  A guitar string is 90 e(7 l;,a. m: xb h(xqbt8pq:oc;d ynaq:o5sqjcm long and has a mass of 3.6 g. The distance from the bridge to the support post i: ho;bqdatl aoj,exqxq(8qmp7 :yb c (n:5s.; s L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it *ezrxym9pp4 +is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three f* 9e pm+xzpry4requencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar strifi;1+ iry .2qhtx -k3 cq7dgyrlu/k6qng is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decrease6+ry-lqik 1 i;x hgdu/cfrq27y .q k3td by    %

  One end of a horizontal string is attached to a small-amplitudekrv sn*v gm a/xvn;/wb-p26a )j1in8a mechanical 60-Hz vibrator. The s m/vawarvb s j-ikvnn 261x8)/ag;n*ptring’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be agkar 7ix-x*jv.m6 yq1 jz 8ra.djusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm andrmjxvy1jrx8.6i. - az*7 qa gk 1.5 m?   

  When you slosh the water back anxbbl .ra 4iovqd-+5p)iy-8,d bvn6 igd forth in a tub at just the right frequency, the water alternately rises and )+y4bx ,.an6-i qvpibbgl5v -rio d8dfalls 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 boun4,e3tzo3mye odary within the Earth between two kinds of material. If it approaches the boundary at an incident angle ofy3oz4 te e3,om 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” whe e--rvvp6wsuwqixu++ cq2z.;re the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests marvi q cu z u6p+wx.qs2;+we--vke a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense air. Iphcc gq639 m73spae2q f the sound wave hits m632pa eqscqh3cp7g 9the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rocmkv 7:rs l5 nz.uix65i 5+gygsblwh1+ k at a w+51lbg 7n.zs5i:hmxl6 yi v5gu +skr38 $^{\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’3j8ao (kqiu0v*am .fe1az 9m* lxni7is manual, the dish has to be pointed in the direction of the satellite, but an 0u9oj mzx eimal1.f( 8 *aqi7*vk3anierror 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 Pacifi 2wfm k sbf1g9,;iuwo7c Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore tubofgwmsfi9kw, 2 1; 7o see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring sti .vf3f0;rp v0dj +5wklva 0vymffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately lm3w jf0av+.dyk vfpvv 50r;0 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps fromt jqkt:,vbm8r6j 1 0li a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net j1bttlkjqm6vi:8 ,r 0behaves 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 sp ()m172o4arw pbf c)e,d asrfu:nkbe3 ring. The mass then falls 33 cm before it stops and begins to rise. What ied:m2 r, )f( 4)sonau7bapb1cf wk3 res the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), co(ilkl33,uhs w mpressing , k3i(lh ulw3sthe spring 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 bw pcu8ic5* x8right 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 speed of waves in the coffew8cixb* p58cue.    cm/s

  The ripples in a certain groove 10.8 cm from the center of aj*3 cvppv-w t5a az.-w 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emittztv5-3j.pcawa-*pv wed?    Hz

  A 2.00-kg mass vibrates accord(1psq pc6i5y ring to the equation x=0.650cos7.40t where x is in meters and t in seconds. De(yci pqsrp615termine
(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 frequency f. What is itko5n0ix. ir+nafwt l *4)ru7y s frequency if it accelerates at 0..ryw4rnax 0i f) nliok 5+u7t*50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands onn f)wu2)vl*koke he72 the raft, it sinks 4.0 cm deeper into the water. When he steps on 7 *vh2fe)ek2w kl)uoff, 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 Hz/iv qhx 3utvtp 038p.f (Auhfpx3 80/ 3pvvit.t q).
(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 dopba-hh-f9el0 wn the stretched two-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 h eb-lpfa90-hsections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prongbtw:tczyvphi5u1 .0pl6 3 h:g moves 1.8 mm to eith6bt.v:iy5tpw3 :puh hc01glz er 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 siepsht(s o6w 26yux98b 2egi .emple harmonic motion 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. 116o9ey su22pg w .xh6e(eb8sti –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 ring that c tke0 l:wf2p9ean slide witept:e fl0w29khout 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 exactly 2.000 /m9g lpe7i .r7qwojw*thah. ;s — each one-way swing takes 1.000 *p7hwel./o9q7. ;wg tjrmhi as.
(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 coy9 jym(dv u :d k//67zqo8qsvdtm62aan swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizmy9st76 yo/qdkdvd8:2uq /zv aj(om6ontal 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 mahf926fb gcth6kj*j5i 7 gn xv3w32yz iss 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meetig* yi w gf 66nc2bthzfv3x7j2k 3hj59?    m

A block of mass M is suspendefbh f2o4b2(lg:fi f 6n 0n;rtrd from a ceiling by a spring with spring stiffness constant 26 hl0:o;br nfigff(b42t fnrk. 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. Tc z2lz+(c7m98d shzchp e y6(xhe steel crane cable is 22 m long and has a diameter z zl (s 7 ch8h+y6cz9pex(mcd2of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gle2+ u qwo:m k kouv-(xf.lvqz33gc 2/ives 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, estimaqocx.v2u3 /-kw fe uol+ (lmv2 3qkz:gte 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