Give some examples of everyday vibrating objects. Whichm hxkd,) 74skxnd;f; i exhibit SHM, at least apprk7xnk4x;hs,d);i dm f oximately?

Is the acceleration of a simple harmonic oscillator everbp/wcy9;l lxm 1p6a6d zero? If so, where?

Explain why the motion of a piston in an automobihqa1hsfzx 0(/ le engine is approximately simple har01x(ahf/z s hqmonic.

Real springs have mass. Will the true p.fl.(v azf fc-eriod and frequency be larger or smaller than given by the equations for a mass vl .(- faf.fzcoscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of adzqcm6fkp) h.*6 zi b t)+no8 *7xvsqx simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and :raxqw(yrc v7dl5h a+ +6wm4mthen is releas6cm+v5rmqr: 7ala+ x (w4wd hyed. Describe the scale reading as a function of time.

If a pendulum clock is accurate atk2gha28u ig dm(v w+ iox5/u) y-wphi+ sea level, will it gain or lose time when taken to high altitude? d2 up+ihom2w-iia uk8h(/ g)y+w5xg vWhy?

A tire swing hanging from a branch reaches nearly to the grogc -(b(eq kfe)und (Fig. 11–48). How could you estimate the height of t(- qcbfe)(keghe branch using only a stopwatch?

Why can you make waty/ h mmu uy)yka ,tfh0qkj;1-1er slosh back and forth in a pan only if you shake the pan at a certain freque kaqmy0h,uu1)-m kf;1ythj/y ncy?

Give several everyday examples of rkjf8x7z dn6ij m3 17xkesonance.

Is a rattle in a car ever ayvdi 06 6.b69 qszhl3a8 ewyo(x9t wxt resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its souii3f *cdv9f//+7kui fk 3 im*qawwuq+rce? Why or wi ai*qi3wv9uf+d /7m +/ffiq*ck uk3 why not?

Explain the difference between the speed o e *8djlz 5eq9f+ l+gvxbw7+pzf a transverse wave traveling down a cord and the svjq *7w8+p9zf l b++e zx5delgpeed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on adbn; i8 /4ec4fodckg3-cz:.k aju4 m b piano normally have wire wrapped ar4dgj kkucnmzb .e ;/coc :84fb4i -3adound them?

What kind of waves do you think will travel down a ho.w wz 8k)22qcsjl,de (cc8esne ;coa-rizontal metal rod if you strike its end (a) vertically from above and (,s-enj(ks. cc;2ee8)2z cw qdlca8w ob) horizontally parallel to its length?

Since the density of air decreases with an increase in temperatur, olw-bjevtq zewp9,gj 02+i(h7z d8ge, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves2ol+g8 dv gw eiqj, ( ztj-w9b0zh7e,p in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel+jak +oe2x zlf(2(sew 5j*unuxzbt15 away frotj bu xx2( z1+*ow5+ e a5uz(ksfle2jnm the source.

Two linear waves have the same amplitude 2e1yo-77 z0oe4z((yql 0 fpcb c nvrmcand speed, and otherwise are identical, except one has half the wavelength of the other.7e eyzz l(0f1n( -crmb2v4o c 7opqy0c Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of1(3f;nccnk dh,mh363lm ec-4v kxhst cord as in Fig. 11–33, the frequency does not change (although ktmc c43 eflms3- 3ch(61,dhhx;nknv the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are+ qo: aw7nspr .ca9k k8tmu,8t there any places you could touch it with a knife blade without disturbing the motion caqo pr,.sm :tkw8uat789 k+n?

When a standing wave exists on a string, the vibtv1qi8 wk9:psrations of incident and reflected waves cancel at the nodes. Does this mean that energy 9 wt:8s kqvi1pwas destroyed? Explain.

If we knew that energy was being transmitted from one place to anothe ).mrmx0r+y-: ipefour; ck,.dzsg 0pr, how might we determine whether the energy was being carried by particluf.0 zo.rg:-d 0rppmk m,ex)y+r;ci ses (material bodies) or by waves?

  If a particle undergoes SHM wzmzd8 1;9bq qnt bk*3aith amplitude 0.18 m, what is the total distance it qz38zmqk*;9 1bdb tna travels in one period?    m

  An elastic cord is 65 cm long wh(obf3fblhun 4x 9(*yku3xl b4en a weight of 75 N hangs from it but is 85 cm lonbl u4kxl(bn 9 b3fx(3 huo4yf*g when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg n 38rgyrxfi*tk;s/f ss7,9kq driver gets into the d3fs7tx gf k9,kinqs*8; rr/syriver’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 when a 2.7-kg fish hang)p2h r1)eycb ls from it. (a) What is the spring stiff)h)ylbe2 rc p1ness 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 vibrar1q 4ta( apy3tdu. ol-9: fpljtes with a frequency of 3.0 Hz when a mass of 0.60 kg is hung f lt9uyp p-jr(t13aa4. o:qdlfrom it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in y traph;o:2 czyo fehuu// ).+Fig. 11–2 at times t = 0,t te)pay:ou . cfo/hzuy; h2/ +r= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 c ;bezy1zx5js8aught in a spider’s web. The web vibrates predominately with a frequexyzszb ;1e 58jncy 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 s3ydk: 0fnx6e7rdq x:v pring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass xfxyrknqv6d :3 d0:7eis 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. bicmg u. 85ri/4je*mf0 times per second with an amplitude of 0.13 m. Determine g*mucjei4 mbi /.8 5rf
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO hcs3s)*nvfr v 9s6s if*alf the maximum val s s*3i6nf*rcs 9)svvfue?$\approx$    A

A mass attached to theqa/:aj u r0un/ 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 stretcdqhmi -5;8s tches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how l -5tcq h;misd8ong does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is c ua -0l,kg(iy,d1dnl attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. Whennllic,g d1yk 0 (-a,du 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 compress the spring of a toy popgun 0.200)tms -snk4t-vd h waxh++b6x00y4moh m to “load” a 0.180-kg balox b +nax04v hmt0d6s4-ty)-k +hhmswl. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to o-yz 6xj(jk)ls ne end of a spring; t)- lkjz6xsjy( 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 aydrp+ *a5 cy ;8aksrn g7p7m2eh,xam8ccording to the equation x = 0.45cos6.4t where x is in meters and t is in secoaak7,;ym28egs h xcr*5pn d 8a7p+rymnds. 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 a SHO hal1y fazxaf79y*wc+; rif KE and half PE? i7*z r w+af9cy ;1fxya±    A

  If one vibration has 7.0 times the energy of a second, but their freqw ;hun5 (iezmv),3 ivquencies and masses are the same, what is the ratio of their amplnv5(uq3iw ;)hmzei,v itudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring onciijn)d /6pia +e every 0.65ini /)d6ja pi+ 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 parallel vertical symawx7.q 14po.ik rk+prings, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibr1 w.q akkor. +4p7ixymation?

  A 300-g mass vibrates according to the equation x = 0.38spl57e1)gwzpm89/uk.zd wyyein6.5t where x is in meters w8 z79u/pmdyw5l.e pkzg y1e) and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, wha5n/ jroiladzy;x4i4b89 ya9t t 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 horizonta6whewplyla /q /;v crm890)x6g pzk ;cl spring (k = 124 N/m) is struck by a hammer, which gives the magyl 9) lp/;8 6cwphz6w/kx; 0remq acvss an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with hv *vr+b9ykuylp-,3p 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 point (x=0) - y9r*yk,lup +3vh vpbwith positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness covg; cil+9j8g ynstants $k_1$ 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 strilu7rie6pj m0h5 7 iwf,kes a 0.600-kg block attached to a fixed horizontal spring wei7, fl iwpmh75rj06u hose spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reachinunw+8 a:0h oyig his lohuyn+8i 0 w:aowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee 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 exactlyd+ebk3 oq,-dl v0ykys,)z )ex 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it isko6xoyj2 3a +8b 4hfsl to make exactly one swing per second? (That is, one complete vibration takes exactly 2. o46y 2ao8jfxbs 3khl+0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, g);* uvlf/d+ ouaa/x ewhere the acceleration of gravity is about 0.37 that on Earta olauf/ +de;v/ugx *)h?    s

  What is the period of a 4isybfg) l;yr)d* x/dsimple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob hjs k ox:tse2-1 (f.b t*z4zczbas a mass of 365 grams, and it is t4zk jces:z*x fot.(12 bsbz -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 odk,,w:yg* a glength of 0.9930 m. If the clock loses half,:gdgo ky*,aw a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximumu *8,ic2y makq 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 retyhm-( y *xh-g2ts a.uleased from rest starting att- shmy-h( 2y.tagx*u 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 that wave crests pass1;-.m5 ;pz om6yjzj8gsn c dzp the bow of his anchored boat every 3.0 s. He meas1-n5jz mj g6szmyp;c;z8.dp oures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air haswaws g u ni0673p6z) vyds1a2d a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests )7 dwuaiz6 1p0yn6ssvag32dw(compressions)?    m

  (a) AM radio signals have frequencies between p 4wxki lcx :xd3gly9de**.o6 550 kHz and 1600 kHz (kilohertz) anigxyl .*xod p3e*:6w dx49 lkcd travel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed 5iwgwp3n* o /pikpy4)j/;dw hof longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as 7gienht*i p.7bzk+z * the other. In which rod will the speed of longitudinal waves be gre +* .bg 7nz*zhpiike7tater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 2jb;g+4m,l v ewpw5nn18 m apart. If the tension in the cord isnb,45;wml g vj+ e1pnw 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the toqj9 jr bh/s-,pkil g(c b(b79wp of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to thq,j -/b9sk9bbjlrg(wp(hc7 ie end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship jusq vfla03p-abdb* ; gk6t 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-q a p0kla;b 6bvg3d*f ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, anbnp45tonpx y 8x dk35,d this difference helps in locating the earthquake “epicenter” (where the distu,o5 kb dx3npty84 pnx5rbance 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 siny(m ;f iatsvt ilr0x2u459xm6 usoidal 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 gr;(m4it ym 0vixr65f9ua2lx st ound? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the aalbqxc(9(t16p9+ 1l rjf4i lv zqc:zp mplitudes, of an earthquake P wave passing through the Earth and detected at two points 1f qlvzpb+61ti( 1:c9l9lpr c z(x4qja0 km and 20 km from the source?(a)    (b)   

  The intensity of an em9y m(( bop)y j;3n*k p2p76ihq/;o noa itpltarthquake wave passing through the Earth is measured to be yp(to7m3ph;* ;nbyii)t(q ppa l6ooj m92nk /$ 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 freq),yrqf0f9nq tfp :jz2uency travel through the same portion of the Earth, but one is carrying twizp 2f)ty:f9r,jn f0 qqce the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequ7 yb 0bk jcrbr0z+78mmgyje-9ency, but one transports three times the power of the other. Wh bmkrb9mc 8 jeyr7+ ygz0j-70bat is the ratio of the amplitudes of the two waves?   

  A bug on the surface of .fiw ig 6he/,o-,cejza pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease t ,/ whfzecj geo,i-6i.o 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch t1gvc+n*z(x gthe shape of the string at the motxg*vz( cn +1gment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, ;q, 1yxfjpg(t what are the frequencies of the first four harm1;xfjq g,(y ptonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered,qc *e8wd *84jiiow/; .abgx4 hyvutp . At what frequency will it vibrate if it is fingered one,jxto;c4w.8egw uib/ 8dvihy p 4**qa-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 four loops at++ fok:a(3eq)rjv mlt a frequency of 280 Hz. Name at least three other frequencies at which it wi o+v+mlq ate:jkr3f)(ll resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of st muhc tde:x++t 0 mc(lz8qr9+,xgqg*oanding waves is 475 Hz, how far apart are two adjacent nodes?(8udt+qq+:t m l,+rcgo0*z mxec 9ghx   m

  If two successive overtone11dbw4 p/3 :eam4ah pi;e; eg4:wsejbafhqc 4s of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the f4;d;egij1cab1a4aw ms bf pe:h : h3e qw4ep4/undamental?    Hz

  A guitar string is 90 cm long and has qv)pn75/,z ozu3 d5c-vln7fd2chgq0q* reyna 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 freqzy-rnv f0n h5vc)*/3 lcqn qpedq5u72 7zdo,guencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured ly (svz9* , 1wsk-ijwc+iqk-mto vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three ql ,*k (wsk+jwmv-yz c-9s1iifrequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed toxufwai6my qs) o7(4p9erq.2l z g 9kh1 vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what p (qq17pg9aos emfl.49u 2rz)yhkwix 6ercent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizon6 qaz(f5bk +e7;ubxwztal string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit l z;z+kf 7qx5(bubwe6aength is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pullvu:ql7u/0nt5h o f1lc .x, *rux4x coopv) lj;ey. If the hanging mass m is fixed at 0.080 khl. pcl45v0xtv: u,1uon; uoqjrc o /xxl*f7)g, 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 right fr,h0qmc)l:wylq b( /duhff p *y24w6uhlx+f7yequency, the water alternately rises and falls at eachl c(/ 27*yx+phqm u)hw0yf wqhl4y6l:duf,fb 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 Earth buq0qm; . dueqmp* -2ldetween two kinds of material. If it approaches the boundary at an incident angle of qe2*-u.qmd;0 ml qpud 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” czd:-zhzf2 a--g5ac d where the velocity changes from 2.8 m/s to 2.1 m/s If the inciden-2hdc-zz :-fg5zcaa dt wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelinc;c+:12xz 0gy9a:rn dc uliqyg in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface atcdlcz:2+9xuynrc yai01g:q; 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 rob*4np ;bej7 ukd(9m zmck at a 38b7 n;e9k4d ujzp( *bmm $^{\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 zm0 lz/0 zg3nryk+cl+ diameter. According to the user’s manual, the dish has to be pointed /k cml+lzrgzz+ 03n0yin 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 +5r adox /phweqn-3 jl:0 yqz(750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sedx(p 5aoyz 3lrq 0q+n/ w-:jhea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper ht74qqo lnwj 7jk7gv8-as a spring stiffness 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 4 g8j77jvl7qn qotk-wof 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to qm)2esx6qyw7 iu6kq)a fire net 18 m below, which stretches the net 1.1 m. Assume m6kqiuyeqq7 w)2) s6x that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mg 1d-cgx8 d(ejzw7h+iass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillationwxz (je 8 hg+7dd1icg-?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11.96rh*enrgj- l.hjl)a lmt.d7 qcp4a–54), compressing the spring 5.0 m. (a) What is the spring stiffness conln dl.h je7ghr) la*prqtm.cj-a96 .4stant 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 coffeee.l.fk ,qfe,z (diameter 8 cm) at just the right pace of abo.kl,efqf , e.zut 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 coffee.    cm/s

  The ripples in a certain groove 10.8 cm s 4yx 1:lg8wc7nsobq19,jub c from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emi1o nc1q8u sbgby9jlx ,wsc 4:7tted?    Hz

  A 2.00-kg mass vibrates according to this/q 9s7ai*a re equation x=0.650cos7.40t where x is in meters and t in secon9s *i i7qa/srads. 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 frequency f. What is its frequencfyxr.jkk)zi578l3 ot y if it acceleratxlkirj8z5f.7ky)t 3 oes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake/,an mvankj- 3. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, thenjma 3a-/v,k n 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 pl7 /-qrphoz(v kay at 392 Hz (G) and 440 Hz (A). 7o/-zkqvr(p h
(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 downxp hj+7t1k ika qv70w vk5xa++ the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wa7a50wx v kpi k+tavh+x1 kjq7+ve in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength 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 prowo mb 7mno80p.ds52twng moves 1.8 mm to either side of center. Calcu 0b5wo78 dw2o.mpsmtn late
(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 fre mc(,oo r4c,cwquency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble plawr,c( ,occm4 oced there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attjqz m(kpey0* -ached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string wiy(qp*e0k-zmj th one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing tak;qj,eilf ,8c hes 8icj ,e;fh, lq1.000 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 oscia+:obaa9.2k stqugt9 llate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the peria+ okgub .q ta:9st2a9od of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension o7j vhfu 89bfguj6s*;l f 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 thl hus;fvjubj796*gf8 e two pulses first meet?    m

A block of mass M is suspe7frld u ,2x+/aojra1xnded from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top/fjud ax 71l,rorx2 a+ 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 120069p))bm fsamq-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Ref9 smp mq)f6ba)er to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also givezvlrzs / y3v30w co3)1y7lker s the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) )yzsl13ov rrv clw3z 0k/37 eyof jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz