Give some examples of everyday8e ntj+.qi 7z-ah5smu vibrating objects. Which exhibit SHM, at least approxi- u7zsti. j8n5qeam+ hmately?

Is the acceleration of a simple harmonic oscillator ever n.;uaa/ b7uz1adxg.s zero? If so, where?

Explain why the motion of a9wxikr 7 y 2myv1.blde z1w,v8 piston in an automobile engine is approximately simpllyyw1d9ev1i827mvbzxw,rk .e harmonic.

Real springs have mass. Will the true period and frequency be larger or smaller 3;lck eillq,0 y,9 -r45bipwldr2v bxthan given by the equatyxr ,r-,leq9l lwpvk;d 5 bl4ci2ib30ions for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speec;q+bjd cn vz)9/yan ;d of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attachex0 0g.hq,(va8phogc q d to the hook of a vertical spring scale, and then is released. Describe the scale reading as a function of ta 0g(.qx, g 0hh8vpcqoime.

If a pendulum clock is accurate at sea leve( iu7 crdv:5ev te36url, will it gain or lose time when taken to high altitude? Why? e53 6ciu(vde7r vr:ut

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–4v 6g/4(h7 xvzthrb ct18). How could you estimate the height of the branch r / tgzb 47txvv6ch1h(using only a stopwatch?

Why can you make water slm u10*ju 7 1kdcwl(tbqosh back and forth in a pan only if you shake the pan at a certain frequency1j 7ucm*wkdlu(t0q 1b ?

Give several everyday examples lx76v w4pg3um of resonance.

Is a rattle in a car ever a resonance phen5/n2s mrjk;y a ea*zur5bca)6 omenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sourd9 kmj r o4wtosf5,7r9ce? Why or why not?ro,dkjo497m9tw 5rsf

Explain the differenc 1ilh)kvcrd4o4;ol1c e between the speed of a transverse wave traveling down a cord a4 4drh1cvoo1;k )cillnd the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequencs /2 as me;ojb2;g+heby notes on a piano normally have wis+jheem /;b2a sbo2;gre wrapped around them?

What kind of waves do you thinii*kmn*.-rc g w9t jc3k will travel down a horizontal metal rod if you strikicnt3.-ckr9w* gm j i*e its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an inri oj92jlfqn;t5 n)d( crease in temperature, but the bulk modulus B is nearly independent of( j5nqf 29rdj;lton )i temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circ(nma.. - 0suno57ej vq-e polhular water waves decrease in amplitude as they travel ao-es lvun -.op70m.anqj5( ehway from the source.

Two linear waves have the same amplit5bib y:) 2+9o fmp0)ckrsqnmeude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factor)+q )bmeski0yc:b fopr9m2 n5?

When a sinusoidal wave crossekb+orzl- z3lw4*9ym w gu6mh(s the boundary between two sections of cord as in Fig. 11–33, the frequency does no g+9o kzw4zl b-whmmuy3r6l(*t change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any pl pwrz/kyvqf9+4b+j8s av u/i/ aces you could touch it with a knife blade withubrq/ v/4vz+wi +/jf9s k8yapout disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflecq*s5jo/r x+k* iy rv t(hof:5acr 03f yh;t:wgted waves cancel at the nodesh; ( /5v c:qy sj+a3k0fyxw tor**trigr h:f5o. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmi bm, tgmj(pn.(tted from one place to another, how might we determine whether the energy wa, mj(b.( npmgts being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplituejfes l30g ,:uj2vn 5xde 0.18 m, what is the total distance it ,xv5nlgf uj23: eesj0 travels in one period?    m

  An elastic cord is 65 cm long when a weight of 7dd;i0550h/+ymgir/u (rbb pw c 1h joe5 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is thodibp ier d(yrgcu5h w1/05b jh;/+ m0e “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car cx6h7x a r v+ xiw7rux6+d)4 utapjap6)ompress 5.0 mm when its 68-kg driver gets into the drt 6h) 6adpr 7p6xr+v+uu47x wa)xax ijiver’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 hangs from it. (a) What;61zqku1aaij:bck /v is the;zcu :a b 6jk1akv1/qi spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 1g sr:5z+k+u6hj pnv lni; /pm0.60 kg is hung from it. What is its frequency if onl6 j nl5h+i: /zpp u;msnv1+grky 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the uwj8/ qb2mt*kb3ei7e mass in Fig. 11–2 at times t = 0,qm 7 b2k*t 3ew8ubie/jt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates pnl vs/,bhqb;f7* x7s uredominately with a freque,xq 77hbuvs*lfn / ;bsncy 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 frequency7iifqhk a (v(w77lx q; of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?q(7;flq7 x(7vhia wik    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 timejz0.iv9la,c( xt slc7s per second with an amplitude of 0.13 m. Determineiz . x9jllv70sa ,ct(c
(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 half the maxvn r5:6igsq *ie;a- rjimum valvg *i-s6q5 j; rinar:eue?$\approx$    A

A mass attached to the end of az3 2ssf.qg5s5vkwt 0h 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 vertica6dlm 4*+tc, wbqy 1-j6kaj/e bnky7cxl spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does nj q,kck yldc+ 1/x tbeb6yw46ja-m7*it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnessesrrxbmlq 0l;gi(+) ( constant k = 280 N/m and is executing simple harmonic motion. When the ol(+0 e)qmrl;g x risb(bject 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 h0i*u o*yd v. wn/o 3c;jy)cvjtoy popgun 0.200 m to “load” **c/jiv voc. dj;o0w) uhyn3ya 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface ,o9ak vxd*wb z.- wd1fis attached to one end of a spring; 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 relea-fw d,*z9 vaxd bowk.1sed from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x =ews-:i,w n .me t9n0pd 0.45cos6.4t where x is in meter9dw -ies:., pt 0wenmns and t 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 equilib(vpfsr)bv1:w -xq3 vjrium is the energy of a SHO half KE and half PEx-(:3vr bvpj vwqfs 1)? ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencie,;llc / 4iechfs and mas4hlc, lic /;efses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates fkn7rs)smx 8s muhr /92rom a vertically hanging light spring once every 0.9 urrn2hmx8k ss7 m)/s65 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 spri)+j8klwt5y.wh r p;9psd6umk ngs, each with kr)wp9+ t;k p65 sj8m. yuhdwlspring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the eq6a f :eoyjqnc0vc1+d6uation x = 0.38sin6.5t where x is in meters and 6dj:fqvcc0a1 eyo +n6t 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 ofvxtd4p2y i 11jhy.nhw3r/cd8 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 hor1 k t(y7c-+yjrv si5jtq*ija)izontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/(k*1tyijijc 7v y q)s-rat5 j+s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with am-bxb xt amlx.a*) *38wioqj 4n amplitude o ja*-8x)xa qxlmo4tbb w3.im*f 28.0 cm when 0.260 kg hangs from it. 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, s7oq zeg uvztm2ag d17n- :+m5with 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 g2ga,hg- lw k2attached to a fixed horizontal spring who , gwkglg22-ahse 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 kwrpkg (((*qf yg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. Herp qy*f (g(kw( 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 q ;s*tw5b9.q5pn qaj2iy3wlhexactly 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 swing pemz6g k// l04oqw0.e ,pmtsacnr second? (That is, one complete vibratim ,cw0 .p60a ekglz/q/notsm 4on takes exactly 2.0 s.)    m

  A pendulum has a peri21 ; soyp(r(u-su+ypeo v *boiod of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that opsuouoy1b-+ e2 (yi ov(srp *;n Earth?    s

  What is the period of a simple p.7bai/siox/ vc6 gkt.endulum 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 ssm0fp7aa6.l.760 m, the pendulum bob has a mass of 365 grams, a f.s6smalp 07and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9dg dbvl 2k-/p -dmd03+0haa eh930 m. If the clock loses half a minute per day, how should you adjust the length of th d+/2 d0-baledap3hhdkg0- vme pendulum? shortened by    mm.

Derive a formula for the maximum s qwqu)ypzj;ro0s:+ y 0peed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillatwyxcbe:zmvi si -*9 h+b34kc+es at a frequency of 2.5 Hz. At it is released from restci:bvsx49 h+y-mw 3ie zbk+*c starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat everwj;o-sk*)hlp p0 6ktry 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travelinpk-l ;j)t*6po skw0 hrg?    m/s

  A sound wave in air h u3z2nnng fqa w7-eb596o5mpm as a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are tzqfmgoa65 ne7pn m9 b-35wn2uhe wave crests (compressions)?    m

  (a) AM radio signals have frequ;pf d 2e 98.srzyj5zteencies between 550 kHz and 1600 kHz (kilohertz) and ;z58es epd jtfz. r2y9travel 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 of long d wmwwf1kdo(7: g87zvitudinal 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 the o /movl5v5 6bo gz9k7cc8l5bev ther. I vkcb8oe65o zb7c5 5vlgvm/9 ln which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two sumo 3t v q;py-aedy10o(pports 28 m apart. If the tension in the cord is 150 N, how long will it vodqo-tpm0 1 y3ay; e(take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a0 -m b 51pxwejrh:r)9ez 5ylgf 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 terminal and sends a wave puls9l- bw) e: 50fzgyjmxrhrp 1e5e 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 uz7d ,abx; ej qof+ysmc y*)nr;x 3)b: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 qadbey o3)u :xmfz7rnb;c ),xy+s *;j. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, ans9:9q;tb7fvy bh7e2 ay,cp tud this difference helps in locating th euc ;thbtyq, vpf2:7bay7 s99e 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-producea z4/b -b rvb:vsj*s7fex;/ eld surface wave can be approximated by a sinusoidal transversbbbx;s7f v4z al j*e/ :/re-sve wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) t-+p eq9wulgi 2s,+c bfhe amplitudes, of an earthquake P wave passing through the Earth and detected at two pointsg9 2ip cwu++q-,b elfs 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave 7x+ vv7 :pa qbgh)joy2k.bd m7passing through the Earth is measured to be bm 7dvxy2) gj p.ako7 qhb:+v7$ 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 +9iy8-ca oq2)x pbmkj9f l) hgsame frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of thh+q opa)y- xjc2 mgfk98i)9bl e two waves?   

  Two waves traveling along a stretched string han xoi3 7k9x) zlwais 35yg5w(rve the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the twykiag3i 5) zxw (n7o53r9swl xo waves?   

  A bug on the surface of a pond is observed to move up and down a total v24g6vmzrn .eri0 .ls certical distance of 6.0 cm, from the lowest to t4e26ivcr 0 smnlzr. .ghe highest 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 toward each other. (azgrmt5,2 pp( w) 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 Fig. 11–36a, at the moment the pulses pass each other, the string is straight. Wp,r2p (zt5w mghat has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz a4prlkse8i-, h ,/ ksi 4zofxa9s its fundamental frequency, what are the frequencies ore9 -,ai8xl4zkko/h4i ,ssp ff the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when udg.ey v q6nd nh+1gcst)j8.9dnfingered. At what frequency will it vibrate if it cejnqs+.v9 dd)tgydg61 .8n his 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 four loops at a frequency6 aedzx/cdq74 - 2mrdi of 280 Hz. Name at least three da dzq-d6c7i r x24/meother 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 92m/s If w+pr9w;id nlxe i(1ny/uh -eb2u)0 di the frequency of standing waves is 475 Hz, how far aphiew nu1d; eynr2lud(b+ -9i 0)xpiw/art are two adjacent nodes?   m

  If two successive overtones gc 5:7kea;j ux*z,tduof a vibrating string are 280 Hz and 350 Hz, what is the frequencyj7 k*g5zt : d,uucea;x of the fundamental?    Hz

  A guitar string is 90 cm long andh wyhu //trd1 fa by:y71do++s has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamo+1a tfs 1ry//dbhy: hywud7 +ental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it ik+((keq)zh8p o 0hdm3b 3hkhis measured to vibrate at 2 o8() h3hdk3(+ iqbp0zkmhehk05 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposden:mb, 3jb l; 3x7vaped to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent avbxnjpl:d ,m be733;should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 86;bph*w4 hbsj8l qoj60-Hz vibrator. The strinw;48j*ljoqb8bs 6hp hg’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 adjusted by movddr0bv9i6shwm ml5 d,s 2 i9*rk9gi k7ing the pulley. If the hanging sw50mvbidrimr*i99 d6k7g,h dsk 9l 2 mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequen6svr2kf t.xwq03 ;qancy, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tux6rqfa t0 . vwksnq32;b is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s stdng g6q05q *zutnr-0 erikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incid ggqqez*u650nn 0tdr- ent 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 mthft7.is 84achanges from 2.8 m/s to 24atmth .78s fi.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warmz x v(c2ujext3rqr /:7 air when it hits a layer of cold, dense air. If the sound wave hits the cold air in: e r7jvq2x3/(ctruzxterface 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 +44gc vsrdeo0types of rock at a 3 goe0+ dvs4r4c8 $^{\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 xom2fc8,qb ka:s6b12r x asc9zu kaj-;qu+8x in diameter. According to the user’s manual, the dish has to be pointed iqmcaj2-az,k;k1xu9aufx6cb8xs:r s2+obq 8 n 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 km/h travels across the Paz:0b.ov7d nd3ex dxn )cific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximate .d3vnn: )d70zxb doxely 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 has a spring stgmcn3wq/ szn7(k+8i wh(s7d sn8duk )iffness 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 5 mi/h). [Hint: Use conservation(7wsnh3d k z s8dq/)nwmu+cnk7si(8 g of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretcheqzzh z3 g,80jes the net 1.1 m. Assume that thzhz qe083gz, je 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 i ml-fdyv cket)267g3hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the freqi 237ml)decfv6- k ytguency of the oscillation?    Hz

  A 950-kg car strikes a huge spring atijz ov;5llj(pe) l w9l/wb27 t a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of t2vl9 wlilptb7 w;/jjo() lz5ehe 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 pace of buwkb8 zz/,(c4k,z b babout 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–z,bb(4w8,bzz/ bukk c 55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a ., 8omng+se3 odkcn5 f33-rpm phonograph record have a wavelength of 1.70 mm. Whafk, g 53oo.nd8m +snect will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equarp dn(xgx8vlrp;ha . 1o5)kk) tion x=0.650cos7.40t where x is in meters and t in seconp kxd5rp (ak8ro;1l)nhx ).gvds. 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 fr(+z0ixj *+depa: nvfpequency f. What is its frequency if it accelerates at 0.50g (a)v0j*d+za+np ( fex:pi upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kgvf50 cga 8-xei man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a wvxf0a 5ci8-e ghile.
(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 / gnrco/y 5im-roew*)q3(jdt tuned to play at 392 Hz (G) and 440 Hz (*wc dnm)/or(o r- /3yg5jq eitA).
(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 stretchthd2h qs5j j ;l7hedg)i/ q30ced 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 shgsihj lt 0q/ qeh3d25)dc7j;ections. (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 84exxm:*sa* czyrkns 94 r5wt a frequency of 264 Hz, and the tip of each prong moves 1.8 mm totw* 4s9nm:*zy r5rks8c aex x4 either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillate,rm c(oy: aqg1s with simple harmonic motion of frequency 1.5 cycles per second. W1 qoyg:, m(carhat is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slidm 5b .z2-pqc/nvdrod--h4o br4rw :zue without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonhm4/wnddz vzuo.r5bb4-opr r-2 -cq: ant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each oner*qr4 3f afuh/-way swing takes 1.000 sf/quhrf43a *r .
(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 thi39a tdpe, f:wf(ik7le vertical direction or can 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 horizontal swings, and by what amount? [H79tfw ip: dfia,3(el kint: 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 of 255 N. A pu--uf rgbpdc ap9+t1(glse igac(t-p9gb du-rp+ 1fs generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ce r *xudum+-fm )m(eck/iling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the)k-+fed mr*/u cxmu(m 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 steel1 deaggfq0an.qqmb ga/75vjo +n37 i/ 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. Whatgiq m/5gnefn7. d q1jv0a7aqab3+ /go 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 n .v eq2)m z:jlxsdp- c0x2d+xalso gives the dimensions of t-c vx0 : senl+xz.d)qj p2md2xhe block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz