Give some examples of1hq(/w v ni+t0bi j*z8wkaot ; everyday vibrating objects. Which exhibit SHM, at least approximatq*io;(jzwtw80v+ni1k/t ha b ely?

Is the acceleration of a sim o zx,f )im4f21,hex((x(w qk jzaq7tlple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an / kdq(l7m txc qme6/e7automobile engine is approximately simple ht /ql6emd7xceq/ m 7(karmonic.

Real springs have mass. Will the true period and frequency be larger or small5 m- rewgbr9g0er than given by the equations for a mass oscillating on the end ome-gg9 r50wb rf an idealized massless spring? Explain.

How could you double the maximum speed of a simple v +*xghm, lq6fharmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a veragdhb7 0oj0u-rj3 f-ntical spring scale, and then is released. Du fahbnjgd0o07-3r j-escribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when ;or6l7zs e+fxpdp4)gozz *t y vz7e66taken to high altitude4spf6gez)v 7+ 7 ; doz*zoz6 prlxe6ty? Why?

A tire swing hanging from a branch reaches nearly to the ground (pkwh6f-6bb752k d q0 hk+krg iFig. 11–48). How could you estimate the height of the branch using only a stopwatch?fqhh bw62gdk0 b-kp5+r7ki k 6

Why can you make water gp/al9fo mq)3 slosh back and forth in a pan only if you shake the pan at a certain frequenc9opma /lgf 3)qy?

Give several everyday examplex;yw jc t8)hl8oki*8xs of resonance.

Is a rattle in a car ever a resonance phenomenon? y808pki .df:hg uj,sjExplain.

Is the frequency of a /:z0za v8,wmbz ht(bmsimple periodic wave equal to the frequency of its source?z/mm hwbt8zbz :av0 (, Why or why not?

Explain the difference between the speed 0o+ jl2rjm 1xzof a transverse wave traveling down a cord and the speed of a tiny pier+ x jl2oz10mjce of the cord.

Why do the strings used for the lowest-frequen32jb ply pnx-/cy notes on a piano normally have y/x2bp3-ln pjwire wrapped around them?

What kind of waves do you th0zgt h(cu45 lwink will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) ho t0l4uzwh (5gcrizontally parallel to its length?

Since the density of air . omsj.s)k35:ggs . nsqao; dwdecreases with an increase in temperature, but the bulk modulus B is nearlsgs;)3j:osq dwkm ..s5no a. gy independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease 25;; s4n5 iifnhzfzdsin amplitude as they travel away from 5nh;n zi5s 4;2dsizff the source.

Two linear waves have the same amplitude and speed, and otherwise are identical*6bgq oma.lee) di1 8l, except one has mbgal861e qed.*o) l ihalf the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the bound*+f 4ut iex,4 b/vfghtary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain wh4f*e gf4+, tuv/txbhiy.

If a string is vibrating in three segments, are there any places you could touch)mkf s m)j54xn it with axjk5sm m ))fn4 knife blade without disturbing the motion?

When a standing wave exists on a string, the vibra35rtcuuzkqh x tu 3;((tions of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Expla3huzt(qxk(;tc5 r3uu in.

If we knew that energy was being transmitted from one place to another, hu kr )(t-dxg3how might we determine whether the energy was being carried by part d3g-rktx)(hu icles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total di(sf fy8 (a3lq t)0wv/: madphnstance it travels in ovf8fnw:qa m0asyd hp(3(l)/tne period?    m

  An elastic cord is 65 cm long when a weight of 750 h(l w1ovbjtn(p7q o1 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is tn1hoqjw l7b 0o1pv(t(he “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets inttjsfe -.xh 9p+etoemy7jw30meo o,7(o the driver’s seat. If the car goes xejp97(o to0eoj-esemf 7.wmht 3,y+over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2t;1 7apj6b h:ljr0j bc.7-kg fish hangs from it. (a) What is the spring stiffness constaht p0lbbc; 6j1:7arjj nt $\approx$    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 vibrateqol. /2qq+;n siuwwq4 2 a3v2bh4cryvs with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. Whatiwq4 s4vl/22q qbvo+c2aqu3; ywhnr. is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicatix81:u cu dwk0 c8lj8yung the position x of the mass in Fig. 11–2 at times t cu: lkyc888 j0xduw1u= 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caughtk-(d-ur qv1e:g8 quxm in a spider’s web. The web vibrates predominately with1m d:v-kquer( g8 uqx- a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a springn36 cyg byj1 lq9xs/9;w-w6upyj w7si vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, thew 7b9 3u sys/yl1pjxynwcq-g6 6j iw;9 frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at th/pr:xjmndtil wt16k 9 f. +ajh.cl1j:e end of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Detenchr1tdw6mf9 +ptx/ajk j.i1l:l j .: rmine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the spe.v, pss p7thp)a(d **g0ye wvaed of a SHO half the maximum valu*ysa.pe)*v pds 70gtphav w,(e?$\approx$    A

A mass attached to the end iq ((u4-dpypt of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring isgh*ep+(s r, bdb.libe, *0s mi stretched abb dph+ibrsm*(esl.,g*0ie, n additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attac/(vhtki-s2lr67y1u/yhfi * ypy ) enq hed to a spring with spring stiffness constant k = 280 N/ kei7t)q r/ny6vhp2 f(y*-i/y1s yhlum and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of ).td c,a8w r(j6ap*drijzy 4ba toy popgun 0.200 m to “load” a 0.180-kg ball. Wiy8p*a wcadd(,j)r4jb .r t6zith what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontqqlbmu yk3ri11*8o *oal, frictionless surface is attached to one end of a spring; the othqilq1o 3 8rmu*byo*k1er end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x is i;2)apzh+8 ;gtoo rtcfn mete )c8p;2ra +zo;t tfhgors 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 ff1(xz) gik bg,eli55v3 bq ddrc:la3 1rom equilibrium is the energy of a SHO half KE and half PE,gfr3:ac3 k5bq)l e 1(xz5gd1iidlb v? ±    A

  If one vibration has 7.0 times the energy of a second, but thej m u(qc) .jr76vlu-3wyb8aqtir frequencies and masses are the same, what is the bqw8.uymt(6 7juc- v)r 3qjlaratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from gy7bl xky;.wyog/+ u m)z;m u:a vertically hanging light spring once every 0.65 s.;g)/g+zwoy u mb yyl.ux;:k7m
(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 idenqsx*pfj uo-2 21lql u-tical parallel vertical springs, each with sl-2o * jl1spuq2qfx -upring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equationvk70 gi1v .: 4jv03:zmrs)medqqyacs x = 0.38sin6.5t where x is in metek.04immj: v)c 0zserg 1da q 7v:svyq3rs 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. a3 y601dsdl4t1rnxdf3 c zgf.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 dy .y;kfaq:x 4s 2m,pwend of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/qs, af .kp:x4ywd2 y;ms 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 clq9 tyaz x1:5ponstant 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) with positive ytz:al1p5x q9 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 x6jt24r8f x*xcb a3szconstants $k_1$ 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 attache+yqif 21cdw:v dmucsu h7k:y8y56/mvd to a fixed horizontal spring whose spring stiffness constant i:w / dhqkdu si:umvm2yy81cf+y756 vcs $ 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 hii6 wo iahfn.9hcb, -q:s 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 ocb -i,iah9w6. qf h:onf 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 vib:3z7qw/btm* rurqc3y wi dz; il ;fb..rations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if zkf*m6 x 79+f nn 9xd0cnmu4emit is to make exactly one swing per second? (That is, one compluf7dx+ fm n0ec9xn 6z4k*m n9mete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wherdhvfc(ps8j6-x v gz6 c-bw1te/o + pe9e the acceleration of fwcoj8pv6 6tvb1(-e/gd+9-sh px cze gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum : nejnyu qty7pk e5e, f:hjfn;0u.q05q1.obe80 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 ;wk 8ig o1is2wmass of 365 grams, and it is released at a ig k1;s2w8iown 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 pendului )2zoh:yhz24lyit0 7.bha. nnvq fp9 m has a length of 0.9930 m. If the clock loses half a minute per day, how shoulp y h:4 ha bvh2yin.72t)i.ql0znfo9zd you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the vnma j9os*.m/ maximum 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 frz v;dj2u+f (agequency of 2.5 Hz. At it is released from rest st+fgju ;zd(a v2arting 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 crest;j7wpfz dpial/9k ry,8od7m irv k9 .8s pass the bow of his anchored boat every 3.0 s. He measures 8.j 7wr/7kd a9piipyml z,9rodf8;kvthe distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air hacgaeh eo3t9 1kd9 (5 .a1gfaw:4xmxq rs a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the 19 3:cw (xtf.x5r 1mk ea9ao a4dgegqhwave crests (compressions)?    m

  (a) AM radio signals have frequencies betwe-i-7lb zewxqqe1jg v 1bi+w+.p,v hg/en 550 kHz and 1600 kHz (kilohertz) and travel with a speedqvwqe ,z +l-j 7 .1hig e1g/p-ixwb+vb 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 ignp i+2 0( vojui,h1 :qpsjnc.n
(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 densewtoh 19drmhha ;b;ey3a3j0 8x as the otherm ;o yhrae3 h09jha3x1t;8 dwb. In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is st vdse8v 6rt6*pretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one suppor8dsrvve p6t*6 t to the other?    s

  A ski gondola is connected to the top of a a 8lr*tf- e*pjhill by a steel cable of length 620 m ajra*lt8*p -efnd diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side g0t 3o8:0zktso( )l 9ys( m owhvye9osof his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below0 9 h(stk8swoy eoo:9 yzm(l )sv30tgo 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake trav x0c33 pih8e;c swb4lch8mo r7el at different speeds, and this difference helps in locating the earthquake “epicenter” (where tr8o74cl8hc3cw3mhs;be x 0p ihe 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-producedqp kpk+z9eh2wwzq xm:5,n(a.w9atkv eo6(p 4 surface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what ama2ep(z e+km pwn,(:9 .wkqt95 pzaxkw6 4qvohplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an eart7btof xo +l4ipa6ssf *k)6qq-hquake P wave passing through the Earth and detected at two points 10 km and 20 6fo4 +b7qo*kxs )-slfp qita 6km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Ea.7rv/gy8 w8ep/sol hg rth is measured to be eh8.w7o vysg /8lrpg/ $ 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 vjf68;fj8c.lfr ou:j uency travel through the same portion of the Earth, but one is carrying twice the energy. What is the rati8cf r u;6j8:jlo.jfvfo of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequencp7hk k4w a1rq6y, but one transports t7q wp4rhk6 k1ahree times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total ve6uiuw bc23e3ed1e 0mrm1z5 hyrtical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decr ec1z e0253 h6ibmm3dreuyu1 wease 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) Sk28. imalkc/pnp f 7s*eetch the shape of the string at the moment they dire2 i/c*e.p pmka7fs8 nlctly 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, what are the di,ri: ztztt6g2m1-p frequencies of the first f ii:m zt-tt 2pzd6g1r,our harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it vb.bt w2kjo7uca0/tv hn+ a)2vibrate if it is fingered one-third 2/)w cj n.v a7ha2obbuv0 k+ttof 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 frequency .sevk1 /gc dc*q-t.cxof 280 Hz. Name at least three other frequencies at which it will resonate. *x cd ct-.g/vqkse.1 c$f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of o)r:jtp, k v6istanding waves is 475 Hz, how far6trvoi:jpk,) apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, wha5x 1hq3 e6t+yi v9utzp14cxnht is the frequency of the fundame 61+th 9h4xnt3 u qic5v1xypzental?    Hz

  A guitar string is 90 cm1) a war( x6(n aylza,foejc62 long and 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 fundamental and first two overtones?ay,w rz ((axa)o6 ln 61faejc2    Hz

  A particular guitar string iy.nlaz0o i.q1eyv/x9v c1+jj +9 nwgos supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the str yo+av ycq1 /+le9vo.zgnj10jwn 9xi. ing be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppos.0odub c,e v3 ka;n9wwed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent oab09 v c,n;uw3 kwe.dshould the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string iso)bwwwm a*loy+ 9ss ;3 attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mas; sw*b o3w+a 9ylmos)ws 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 mwo,sy* g(f mo qu)5mqu:4:vhqoving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 105 (m4o uvfq)q::gohq,swum*y cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the ri 5nf gzgr/mhei7g 2e19ght frequency, 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 tub is 0.85 Hz. What is then9/i1gg gr5 fhem2ez7 speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s a rd1tkyjzb7dq( 82a 5,pkqa 7strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an ia j ,zrbkadpy 12k(5q8dtq7 7ancident 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 cd+n vbeb .o6l:;esk7rhanges from 2.8 m/s to 2.1 m/s If the inc snkv;b6l or7:be+.ed ident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense8 yha,nmp+.w3m6b bgu air. If the sound wave hits the cold air interface at an angle of8m .w bgba,h+u p63nym 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 w /ds;lim-4nk5 x u)pquaal:2zave strikes a boundary between two types of rock at a 38 a pzud;4lx a)u lnm:/kqs-5 2i$^{\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 dim9j tzi3 b7(v2u, nrp(wj5 fmlameter. According to the user’s manual, the dish has u,n 37(9 5lwjmj(2trp mfvzbito be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km an,i t)x da7v1r au-6fd2ybx;pjf w9vu5d velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approx ;f69vd,ryx1vx2ai t) dwu-pauj57b fimately 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 stiffne( q)+lrzr3e :ahhr(zoss 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). z:rr 3 hr ezhl)(qoa(+[Hint: Use conservation of energy.]    m

  A 65-kg person jumps frngg/gpt9l0 )wkt p5y r 23ouk/42wvk:4p dv lhom a window to a fire net 18 m below, which stretches the net lo dguk:wwhtk4 k5 ngpgpr/94v 0t2)y 2lp/v31.1 m. Assume 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 q/8r*v pw i5wion the end of a freely hanging spring. The mass then falls 33 cm bef / ii5w*wvq8rpore it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a 4fh5rd4dl d+wq m7n j ;jw1sc4speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) Whatmn5hjfw1cd4s4 +lwd;q r7 4d j is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right b+bti2t/ p/bu1ae jd,pace of about 1 step per second, the coffee sloshes more and morej1d/e2ut+b/ t, ibbap 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 from the center of a 33-rpmgg+6n:3 rmm ;,rrmabg phonograph record have a wavelength of 1.70 mm. What will be the frequency of the gn+rb6 r;r:3 gmm,mag sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.6ogh ub v 6eb3r*+45zni50cos7.40t where x is in mbnu z4g5o3 r 6i*hebv+eters and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency 72vl pt.wyl 7gif it accelerates at 0.50g (a27 tpyw. lv7gl) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg apfu, k4f6a1czyp56 l man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrate16lc,56fakayf pu4pz s for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz)m,m ( hoxprrl n)l6+rx3bw5o7xpm*p (G) and 440 Hz (A)3b wr+l xo pmmomprx) 6x5p)7lnh(r*,.
(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 thevnu ,8)bi.kedgwmckj l i86c+ t0/4xz stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versusxckz d i) jb.084ngv+m/ku6w8ic lte, 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 ofth 3pn p.wo)xp4 ya:.uzxyd 71 each prong moves 1.8 mm to either.:hpa7wnt xyzp ud31)yo. 4px 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 cycles p+ r8srqb2xei-2l ofi :er second. What is the maximum amplitude with which the2f exrrs b:8+liio q-2 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 ixgi5x-feo +8u:i + kcslide without friction on a vertical pole (Fig. 11–57). Determine the waveeu8 ci-f:x +kx5gio+ ilengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a q ) su,;n)hioiperiod of exactly 2.000 s — each one-way swing takes 1.000 s. )h qi )s,uin;o
(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 ob9-pza 9 gfw.tscillate in the vertical direction or can swing af.z gpwt -ba99s 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? [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 oeqcvnwb2-pp4 9u7 hp; f 255 N. A pulse is generated at one endp bpc9u 7 v4qph;wn2-e, 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 h5)q )-odikz esuspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What qk5 )edh o-)ziis the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg cau23)x6+f, 2nm xvipjf(pqz)ls0 ew pkr 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. Wh j(p)fkn w,fi)lxu60z ps23xv+ mpe2qat is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate aqavu)gsc*-v w0j290cw)yi gd s shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrati g )d0 y *-jv)u29igawvqswc0cng 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