Give some examples of everyday vibrating objects. Which exhibit c2yvtn ub/49;owvh7l SHM, at least approximbt wo/v7lv 2nuc hy;49ately?

Is the acceleration of a simple heiqf 5/pf md-8armonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an autom ttw5 (9zlv1-ms-gz zlobile engine is approximately simple harmoni- zwlsz(95 -zv1gmlt tc.

Real springs have mass. Will the true perio/oid3l3zni geo vr 18c9do6a/cno(;zd and frequency be larger or smaller than given by the equations for acz31v oea8lr3 i9d;oz( o/6iodn gc/n mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harm;3w(l ajf-n7/ zlwwg conic oscillator (SHO)?

A 5.0-kg trout is attached to the h/2 a66g*a;d vavw zp6oyisa 9dook of a vertical spring scale, and then is released. Des 26v;ypwo9a zvagd/a*sd66 iacribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will itdd/r z fh./og)o 0sha5 gain or lose time when taken t rofh)aodsh0d/ g z/5.o high altitude? Why?

A tire swing hanging froyr d/ ,,mt)fgsm a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height/,)rtfd sgym, of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you s . st0+zfk0hkex+b po-hake the pan at+fs0o bz x.khk-+0 tep a certain frequency?

Give several everyday examplek;panw4 vhsh8e yu5zp*f . 3 /3hhgkw4s of resonance.

Is a rattle in a car ever a resonance phenm7 mrbzcup 8wf9f58-gomenon? Explain.

Is the frequency of a simple periodic wave equalu n;3v7ezs wu( to the frequency of its source? Why or why wsn (ueu;37vz not?

Explain the difference between 56xmq /2zdlgs the speed of a transverse wave traveling down a cord andlz2m 5d6sgxq/ the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a pianh 6*ntyk:1k -s1/x yj8 zqmmhco normally have wire wrapped around t *:-y /mm1ckq6tn8 1xsyhkjz hhem?

What kind of waves do you think will travel d91 bw s8ygo8k ne6;nyhown a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paonyhnw k; 1s98g 68beyrallel to its length?

Since the density of air decrni 3yp86b7c-*q uvrc ieases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves inqvycib3c i-8*6r pu7n air to vary with temperature?

Give two reasons why circular water waves decr a69e-3djsaskvt g5 9zi(3useease in amplitude as they travel away from the sourjt5 9ev(3e9sg au6d 3zs-kias ce.

Two linear waves have the same amplitude and speed, and erub p ;qzdczm:800ha,gnlpe21 h+ep+ vfk. ,otherwise are identical, except one has half the wm,va2k q1:0b+,h;8ezdnul hp ez+r.p g0fep cavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between rr3jh,.r )omvtwo sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do jrhmo. v),rr 3change). Explain why.

If a string is vibratibl),jdwm 4n9 ong in three segments, are there any places you could touch it9o)l wn4jmb d, with a knife blade without disturbing the motion?

When a standing wave exists on a string, ta; :+wcuy-pj0rn 7cxuz vzr-/he vibrations of incident and reflected waves cancel at the nodes. Does this mean that a;v/7+cz uw: rjc xypn- z0-urenergy was destroyed? Explain.

If we knew that energy was being transmitted fr6vmfb smr ej3 t.*:0ugom one place to another, how might we determine whether the energy was being carried by particles (b.6ue3 jr*m0m:vts fgmaterial bodies) or by waves?

  If a particle undergoes SHM with amplitudej:rc ox)f/bru2j; 5iw 0.18 m, what is the total distance it travel5w/:ibofu ;)x2jjc rrs in one period?    m

  An elastic cord is 65 cm long when a weigsgw05p7qe io+ ht of 75 N hangs from it but is 85 cm long when a weight g70so p+iqew5 of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg card4b gr9 4 t;0cl:d0gq v8rrlku compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vidu4vgr9 tkgl 0q ;c 04b8dl:rrbrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish g r7r0hv za*sjvrj6n+(r4snk 6g-6of hangs from it. (a) What is the sprro6 7n k4fgsrj an- h(0jv66+gz rsv*ring 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 04unmc3jp,dtb j ,1bn,+ 7ydzq.60 kg is hung ,mzq 34 tdnu by,+j1cbjd7np, from 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 Fig. 11–w/ y qo+05icgxscx5cc6 +yv.m2 at times t = 0 xc/igxyo +cqmv5s6cc .wy5+0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g isopjfpt/84+;u e2 raqtl* s3mc caught in a spider’s web. The web vibrates predominately with a frequency of 3/tpmqjftc+o; 4*au s pre8l24.0 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 witn,.,jbrjkkj-lp) , bj h a frequency of 0.88 Hz. When an additional 680-g mass isr ,.kj,) kjpj,jb-nbl added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per seco,41orng g)vcy nd with an amplitude of 0.13 m. Deteroy4c,rng 1)v gmine
(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 thax7c7/cl , wmre maximum valuec xa ,r7m/7cwl?$\approx$    A

A mass attached to the end of a spring i5myjx hfl h6p ijl93g4d.93zcs stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.bwtxoix 2+rv;e2fc5 5f4 k+fd315 m. If the spring is stretched an additional 0.130 m and released,oxrdf;+fvbek+2 w 255t4f ci x how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached ;b9m(v sgv fpe67d xp1to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its eqfgedb1(p9v;vms xp7 6uilibrium 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 dj-94j * yepc4m qbpp-t *0ecgpopgun 0.200 m to “load” a 0.180-kg ball. Wi9c-jpm4 e cqdbj0* gye4- p*ptth what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frict: pq(bst -ko3eoa3co+ionless surface is 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 +:3ot-pb3e akos q(cospring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t 6e :2 jwolbwj*where x is in meters and t is in secon: *2oj6lbjwe wds. 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 equqtgv- hql3 (c8ilibrium is the energy of a SHO half KE and half PE?g (qth -8vlc3q ±    A

  If one vibration has 7.0 ti27n1 gx.hgf rdmes the energy of a second, but their frequencies and masses are the same, what is the rat2g7 x. 1hfdnrgio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically ha1y2 iaro) 4rjpnging light spring once every 0.i) orap 42r1yj65 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 supnc u5vmt /b wmj6s/*z mvo0:4zported by two identical parallel vertical springs, each wn mj/zstb 6 05m4uo:zv*m cwv/ith spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according lwf/*gg 8 ul;bp,zg/giq;t,q to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determine i 8g q;;/blgg,zpgfw,/q u*tl
(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 tqj5ckse7;, r.koo*iowo examples of 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 *xf*ulgpryj 8(+sx7oj f1zo + rest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial spez fjp8lxog j+r * 1y+u*(7xofsed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with an amuz*c1b 8:ct brzu.i0 0yqfa 4bplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes throuzubui yt0:z8 bca4.01 bqfc*rgh 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, with sprtcb4 o: bp44 avza* oc475w rwdj-5qwfing stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizo (/n nom8yf/rzntal spring whose spring stiffness constant mfyo/z8n/nr (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 reaching hivetil213/ +l d ag2(ubz. gsojs lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstret+.lg /jliz12osb 3(uvdga2 etched 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 ex0c8yfqd -15ur9 gat hsrac (b2km7zv,actly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is / e:mn64w0jo,kx ze fpto make exactly one swing per second? (That is, one complete vibrationx40:fo6e j,zw nm epk/ takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. Whativi un1c. )bk7 is its period on Mars, where the accele71b )nivk.icu ration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum8cy9o. nvni* h 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of 3/nggm 3i iv)+n65 grams, and it is released at invgn )mg+i/3an 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 le2.r di jio8q68ks1:xqkun1snngth of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shorte68.qii u dkq ns8n1xosr2:1jk ned by    mm.

Derive a formula for the maximuy8 ,yh6+++le rjty bdym 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 fth15zif2v8 / 6/ ptnvpe e6iedrequency of 2.5 Hz. At it is released from rest startingzp /8dee/i fv 6v65e2htpi1tn 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 pasfnic2jxteg; m1; 6wn ;s the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wavegtj;en2wc 6fn ;i1; mxs traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speetkqma+1q*j 6ob.9u3 znnhvbf 0oy0g - d of 343 m/s How far apart ar9z003n tqkqm6- o gn +fobauv1 bjy*.he the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kil7o8oyyo6w2 * a,neul hh9p qo+vt:+is ohertz) and traves ohow:+6 2t8uq7 oy,9h *vop+yan iell 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 longitudinal waves tf yf8bygdm4xl6wg+n +23 t;lin
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, b)r q4arwun;bf+hqgm8 )0u63mgq6yy v ut one is twice as dense as the other. In which rod will t 03qu6 yrufqw8vbry m); nqagg 6+m4)hhe speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m enj9xw 14+e7z(oamhm apart. If the tension in the cord is 150 N, how long will it 7mhejm eo wn9 (1+x4aztake a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top o;o oxci soug :9zt.6um(,lj p:f 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 sc6o9lxgz t:i,:juo(; .m puo 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 just below the surface of the seamsw-i4t n0)umlmf0g d zc. :a-. He hears the echo of the wave reflected from the ocean floor directly below 0mwu gn s:l.mmc-fta i-)zd04 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake trz le6xx)fjbk; wy:uujtkbi+;() :e j.avel at different speeds, and this difference helps in locating the earthquake x6.y;jwe)x)k +( lzei bu :fk:;jjt ub“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 surfacc5za2. kiq:f1 w/h6nayl nd :pe wave can be approximated by a sinusoidal transverse wave. Assuming a frf:qn5:kd1 ya/cl2 zi.pnh wa6 equency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitude.06a o q*lsdvnp) ne8ys, of an earthquake P wave passing through the Earthlsed* . onyvn)ap68q0 and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is mez1ko ;2zz nx,kh9ei -easured to be z,ein1 zkekzx29;o-h$ 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 thi: 4 xlsu8 -fkj5mr+ferough the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wavekul 54xr+ff e mj8:-iss?   

  Two waves traveling along a stretched string have the same freqy7j;y:0 kk uje.8uocyaunm .1,h x ex4uency, but one transports three times the power of the other. What is the ratio of the amplitudes of the ek;.y hyk8,emu: nauyo1j7. xcjxu40 two waves?   

  A bug on the surface of a pond is observeua :6tmulb h b;lt3caf -904 8uktb7oyd 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 ripp m u07hl 8u34a;ukt-b: lb9cf6ytato bles 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. (a) Sketc1 htux4hlkq 6.h the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a fewh 61.xkuhtq4l 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 fg0 x ir2j(tj:trequency, what are the frequenciesti(tj: 2gr 0jx of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrateee c syo6;fh:h2 6gu:ps at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrauoyf6c :p6g e:;2hseh tes as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency-y iv 89owq :xy x arukle6;)1hjj2:sd of 280 Hz. Name at least three other frequencies at which it will resonate. yk :sdjji ah98 2)oxwue6rql;x-1y v:$f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a st9qd slqcdf**ro446tzth 8fx1 q 7ox 6hring is 92m/s If the frequency of standing waves is 475 Hz, how far apart art *otxos9zq* 7184qh6dc hx ldffrq6 4e two adjacent nodes?   m

  If two successive overtones of a vibrating string arswow (-sr6zepn4:1krarj 29 o e 280 Hz and 350 Hz, what is the frequency of the fr noswar41koprzw :92e-(j s6 undamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 wbf5)k18 gs,m)bwuf kg. 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 t),)f5bwsfmw8g u1 bkkhe fundamental and first two overtones?    Hz

  A particular guitar m7j5);bcrvqj)o n i0 mstring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension 0 )jmc ri n;qj)57bvomin 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 supposedkby (nxz- j;wnd -g7r 7zp78xb 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 tdp xry(-7wn8bz7j-; zgb7xkno correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitud c+n) 5m( :u5rkhmacdbe mechanical 60-Hz vibrator5rhk5 cam b+ :dc()umn. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the lengtfxsjz* s78k)hnr94f ni( gcg4h of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many differen( k7 n8 *4jfgh)rs9c4gsznfi xt standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back t d4 si/,;yu+l(dxear and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at/ (d4+rlt s;a yiue,dx 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 boundar934nlvnu4rg a+k n5tx4 gjb3 ry within the Earth between two kinds of material. If it approaches the bou4gv34r5gktlunr+ 3 an j49b nxndary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocit-wrn8au +so z2y changes from 2.8 m/s to 2.1 m/s If the incident wave crests make arau2wzn +-so8 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 coz0dvu g1 -ui-mld, dense air. If the uu-v-zd1im 0gsound wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two tz *c3( 1.ueqokxdk.ti ypes of rock at a*(q1 doxkteu. z.c3ik 38 $^{\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 c a89sbwr7oj3m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an erro9wacj3sbr 78 or 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 acrosa.aixa9(e-51hyg 5wvri (1oeya .nxh s the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamisih.91(yw raa-v5 aox xiey 5a1h(egn., some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper0okxos, p;p -u 0khh:y has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car,-kh py00 p:s,ohu ;xok with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18w7e:q88jg8hsn) m le)j uxvf; m below, which stretches the net 1.1 m. Assume that the net behaves:ws7qmxne ;e) vglh88j 8 jf)u 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 freecq-4v o/gje. )jztkkv)8)w xt ly hanging spring. The mass then falls 33 cm before it stopw.j-xqvj)te 4 )/c vtz8 o)kkgs and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at ov7wr 0u9so.rc(ypamc e.n9n/i(h8 h a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) Wn0c(mr.cre .vs97u n aoy9ihw h(8/ophat 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 jukf+ k5mg4z+yly rb)0 ust the right 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 ik4brylk0gzf y)5+u + mn the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phbcf6 t;x h4ex1onograph record have a wavelength bef 4xx 1tc;h6of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=b4:ph1 qpdekk-d-y s 00.650cos7.40t where x is in meters and t in seconds. De d4-q hd1p:0yk ebkp-stermine
(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 frequency 2.q** lf(ysawnc a d8r,z c)cgif it accelerates at 0.50g (a) w ).*,gya*2 cndza8rqs l(cf cupward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg ug g7(y2+meis0zzff np;k(u6man stands on the raft, it sinks 4.0 cm deeper into the water. When he steuu;+nzpzg6eg0s (m7( yk if2fps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 3u+vga3nc 4 xe;92 Hz (G) and 440 Hz (A). ;34xg una evc+
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched t + b6/dq zi(nmqr;gu2owo-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 im i6qdnq/rogz ;2b+( un 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, */ ,rcuuzsih(; ip+/,gxo dmmand the tip of each prong moves 1.8 mm +u og;ux */(,chmsz mdr/, piito either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 gr48 wq-ejlh 8ix 2ir5cycles per second. What is thilji x84e28- w5hgrrqe 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 r. f(4(sfoukuey9bpa 6 ing that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the re6a4peu f9 f(ubo( .ksysonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a periuun00h1h0te+ bv,s yf;g1d oood of exactly 2.000 s — each one-way swing takes ed1n1,o0;f0uh u gbvh + ot0ys1.000 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 (iil.wvp 5o j5a;tz;w oscillate in the vertical direction or can swing as a pendulum of small amplitude, bu5twl. viap;ji (wo5;zt not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a 3du9w na25 k k:tbir lv)p5;yptension 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 meet?k lt955:;v2inr3p u)kpwby da    m

A block of mass M is suspended from a ceiling by a spring with spring stiffnesb3a5n00canq .s5gzwxi3qo8p s constant k. A penny of mass m is placed on top of the block. What is the maxxcaz. qwn i0og bs30n3p5 a8q5imum 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. Tht7s eg0 s3u4bis2e21l ,bgm qfez 8bb9e steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the en gt e e7bs29l gzm30fssiqb2ebub84,1d 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 alj ro2e 8om4pl )6(x8brkt(icmso gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vi(lbx4(8orp cri) o68e2 km mjtbrate. 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