Give some examples of everyday vibrating objects. Which exhibit SHM, at 3f hd 5j sx3)dz+h9aoyleast approxj3x)hy 9dzfh+ 5 asod3imately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wherk n5hu+x2 pngz 5j+x vve(oo2g(ls*5xe?

Explain why the motion of a piston in an automobile -hurjhmnfy/. 7k 69 il9as7jbengine is approximately simplea79ukmnf7.69lj hj / sbyi-hr harmonic.

Real springs have massc9i;b yo qp+7kxke0 a,. Will the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.9pax cyok70iq,;k b+e

How could you double the maximum speed of a sim5i -*te wixg0rple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to thl -j )4 cquahh/fz2or)e hook of a vertical spring scale, and then is released. Describe the scale reading as a function of timchzfl2j)) q-rhu oa/4e.

If a pendulum clock is accurate at sea level,j3r j2n6 clv;j will it gain or lose time when taken t nr6vj2j;l3cjo high altitude? Why?

A tire swing hanging from a branch reacxd6t)umtd hi + 2.6puvhes nearly to the ground (Fig. 11–48). How c2pu6d .iv+6mtx)d thuould you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and for cxq9y.fj ug53a9e 0ej2zuj /ath in a pan only if you shake the pan at a certain frequz ajufj xje2530ca.9eq9 y/guency?

Give several everyday examples of resonanc:/3h 5b/p(cpalfxp5o exh a: ye.

Is a rattle in a car ever a resgat /+vrx9vw)0 h xo/honance phenomenon? Explain.

Is the frequency of a 7/* mxg5jb yyff1zcn+simple periodic wave equal to the frequency of its source? Why or whny 1z ff/xm*gy j+57bcy not?

Explain the difference between the speed of a transverse wave traveling dowp 3 43,hi1 bzruyfh8jjn a cord and the speed of a tiny piece of tpu jb83h zi, 1rfj4h3yhe cord.

Why do the strings used for the lowest-frequencqn0yv(3wssh48,br .pdmu q0 ny notes on a piano normally have wire wrapped around them?8,.( ywuhq 304 bnqdnmsv0prs

What kind of waves do you think will travel down a horizontal me-: s.o 5hnd pfv;r+ 0ipxg/djntal rod if you strike its end (a) vertically from above ao:h-pdd+pi s0n/xr v.n;g5 jfnd (b) horizontally parallel to its length?

Since the density of air vs9t f35e +a3*sql6 ltgtlay ne/lc-0decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in airaecgln3-lt f9 a0s+*el 6yvq/t l 35ts to vary with temperature?

Give two reasons why circulauc7wf4vob8d m8,9)3wklp;sqc. u )q rj3g me nr water waves decrease in amplitude as they travel away fro8wb)).r9op mwc gs jd4uv8;l mk 7cqenqu,3f3m the source.

Two linear waves have the same amplitudj6ucv o5n3hfx1n2 8vye and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more enernhvx1c 3vy j285oufn6gy? By what factor?

When a sinusoidal wave crosses the boundary between two sx+s8)-l5piplnnq0 j wr0 razz /0yt- eections of cord as in Fig. 11–33, the frequency does not 8-lraszix0j/w qn n)e+t pr 05p-z0ly change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places youx8pveb:r79fu n7mn h2(ody-r0e( jqz could touch it with a knife blade withz7bdx nvmpeuo(7q8-rr:(y j h09ef2n out disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflectr+ 0rci)0j qxu;yhh- jcsxp)0ed waves cancel at the nodes. Does this mean that energy was destroycjju0 )ry-;0p h0h xsx+ r)icqed? Explain.

If we knew that energd05 0ggt 7ftufy was being transmitted from one place to another, how might we deft50u ft gg70dtermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m,k9(c c;ksy1ew kqknta9ed( )6sx4gy . what is the total distance it travelss;ytqg e)xk.((ky94ed9 kcn s caw1k 6 in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from i7o6pd ck + htbo 5tr-oh99l*vyt but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of tto ok9 ltph6-*oyrv9dbc 7 5h+his elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when i-(t6 7upl0br v *7:zbnbp ogd)ziq n3its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency ofzt7)nur (b:p-3vz6 7gbi li0qnp od b* vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7(,nu a a y9djvbs4m 5m461evln-kg fish hangs from it. (a) What is the spring stiffness ,vdlumyns a9 5mn1 4ej 46vba(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 frequency6b bjlt. ji).q of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency j. lqbb6t.ji )if only 0.38 kg hangs from it?    Hz

Construct a Table indicating t(qhx zt /j0:yv. w4tx 7u. uh,zpr*ngohe position x of the mass in Fig. 11–2 at times t = 0,t =t:/ u(n zu0pxj4,h*qwohg.yr7xz. vt $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 predzp;uv6 bfvz,,lav y7c5*pe -g e8 6dgmominately wicze8dv76a*pfb 6vmgz ;lveg, -u 5py,th a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a -(9u w8bxpef khx(-n)-fsu lgfrequency of 0.88 Hz. When an additional 680-g mass is added to m, the f(- b pkhw--g 8une)xsuxffl9 (requency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the kra4pz; 9lh y9a;5e tiek0e2qend of a spring vibrates 3.0 times per second with an ampl0;elez 2ia 94h t;a p5ryq9kekitude of 0.13 m. Determine
(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 peb y, ilnr.qntl*2.(maximum valui* bntl (n.e,p.2 lyqre?$\approx$    A

A mass attached to the end of a spring is stretco8j00oqox- 4xb. gwyh hed 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 stre/8f7ddv 2i x1 vwprtg icny-(-tches a vertical spring 0.315 m. If the spring is stretched an additional 0.130-nv/( wid cf2ix dyt1rv8-gp 7 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring witb18 -li (xymvwh spring stiffness constant k = 280 N/m b -18 ywilmxv(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 nx of(oflj;/hp-uh6a+m r/r*a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed w ;6lp-jho u(hfr o* mr+ax/f/nill the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless s6:cjxwcnd331h/qll e2 ris+e urface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of workce +nrw lc6j1l exiqsh:23 3d/ 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 accordin yn-p,ysr.,m 6sd:uche:k2ynvcf6cd p,)9 cqg to the equation x = 0.45cos6.4t where x is in meters au ne-cph6,yf,qv. s 9,2d6 )s:ckmd r py:cnycnd 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 equilibrium is the energy of a SHO half KE and half P225 lgd ux8elsmz0 c0qE? ±8xd2q clu0gl 5emz0s 2    A

  If one vibration has 7.0 ti g1g g5jwzi,n 31x0c-nfgor.imes the energy of a second, but their frequencies and masses are the same, what is the ratio of their amplitude jggo1x51,ri-wzcf g ni3n0g. s?   

  A 2.00-kg pumpkin osc. papldx apvf3t/ *0ry3 9cfm2illates from a vertically hanging light spring once every 0.65 s. .aax3ftdf v9pm p02c* prl/ 3y
(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 -i c: hfjyd*58pys3 u1o21+giuwcrqhidentical parallel vertical springs, each with spring stiffness consi +cug:2 usqhy-hfpd3 jyr ico*w1 185tant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equwk5i5fszb -1gation x = 0.38sin6.5t where x is in meters and t is in s-kf5wg51 zibseconds. 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 q exiky3:2ks2and 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 horizonme0wsqpet2- )ku: 2cj tal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determin 2:skeqt)uw2e-p0j mce
(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 sh0w7mx ft 2*oetiffness constant 305 N/m vibrates with an amplitude of 28.0 cm whe0et72* xhfo wmn 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,j .zb,n o2/ dqpp23kyh-cyre) with 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 6z) vga2gupll qh*v;.block attached to a fixed horizontal spring whos*azpq;hgu2 6l g )l.vve spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge.nbsr2 i(t* xm0 After reaching his lowest point, he oscilnb2m rs0xt *i(lates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly(ylvrt a4 bm:kiq: b:5 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if i - b.;vwbz4piit is to make exactly one swing per second? (That is, oi-w4ip.v zbb; ne complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where (lwv*).eh/ v ,r,jwtka sy9xg* x z.lrthe accelr vaw xj 9.tswlgkvyrhl* z*e/.(,, )xeration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendul0kbt9 k ss,dv)yy-v9pis2, fgum 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 3hl5u+6ps2 y ou65 grams, and syu2u l 5+6hpoit 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 0.9930 m. Ifzm8yj ft+g5.g q :n2xt the clock loses half a minute per day, how should you adjust thtn5g : jqfx.2g8+zmy te length of the pendulum? shortened by    mm.

Derive a formula for the maximum spelppe yt*i:g 9s. x-lo(ed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released8ez;j*8depd)5 /sxx oo - b8 ;fvyrqu+1tnvlj from rest s/5 dre; o+ ut)blj;oq8xn v-*v81zxjedsyp8ftarting 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 boat5z.8:l e:s rqsea2ew-ntor a fq3+v.o every 3.0 s. He measures the distan zrt2e qa.5ref l:a8 :.osnwseq-o +v3ce between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels withl6mh*oal g ;uch+yy 80q/b5fb a speed of 343 m/s How far apart are the wave crests (compf;gl8qb a5hy* +6m yhu/0lbcoressions)?    m

  (a) AM radio signals have frequenciez:nj+zw. tby8 yx 3zce)9 kqjxc7 t50hs between 550 kHz and 1600 kHz (kilohertz) and tracb7y+t)znq x38x 0z.hztk 59ce:wjjy vel 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 in v x08hc1;co(q (yay*ua,1rucdv8lqv
(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 th;evr 3;j/c swobe2jy7 -mjx; we other. In which rod will the speed of longitudinal waves be greater, s;xcr 32/-vjo;jw7 ;e jbwemyand by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the tensa+ p /kxnuv9d9ion in the cord is 150 N, how long will it take a pnud9/kp+9 x vaulse to travel from one support to the other?    s

  A ski gondola is connected to thm7ip,imj9r (pm8 ed+xe top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a mi(8ji d7,9p m+perxmwave 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 sid6l/u 8tbpyc d(vgy. 7 ;nnb*ahe of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean cy n;un/7tyvb8(*lhbd p .ga6floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travayutit zve7 c)*fpk) 9;jgsu nh(l0/ue x09,zel at different speeds, and this difference helps in locating the earthquake “ep9u g lhef9snz,/0p;)t( ku y)z7iauj0xet*vc icenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by x.lu+ej gon9l(/rj h*a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actuallyn/ j(o xlj.*gr h9eu+l 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, a-5js dy+qke1lb4ao :ind (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at twoyq- d1e+aobki45 :sjl points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through thhf9n9e9av y.ve Earth is measured to be yf9.9v nea9hv$ 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 f hu0( sih-jy.rf ir88prequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes orr y8h. 0ifhpj- s(ui8f the two waves?   

  Two waves traveling along a stretched sdtsv0:/) hdy vtring have the same frequency, but one transports three times vh)ts / vyd0:dthe 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 c8p a 3h9g+;cxy fyo)2ue/w qbup and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as ; epxhy+qyc uo9 g/ )w28afbc3a 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. u9q dc;0yumob--nmg7bd byuko. ;80y (a) Sketch the shape of the string at the mbnmoo7-by ;g u.qcdyu-ub80;m9dky0oment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates)dinhve e9q lnzv9 :2+y44 gwe at 440 Hz as its fundamental frequency, what are the frequencies of thdw9v4ie 9evnqen 2:+zl y4g)he first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. Atua/iw/4/ 1yo(w k lbdqx,mc3z what frequency will it vibrate if it is fingered one-third of the way d(ac4yqmk /wx,u/31 zwoibl/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 akt9e/cphb9 z(t a frequency of 280 Hz. Name at least three other frequencies at wb /c9h (9ektzphich it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/v7 bb 9zm)wn-bs If the frequency of standing waves is 475 Hz, how far apart are t- znmvbb 9b)7wwo adjacent nodes?   m

  If two successive overtones of a vibrating s4d y5kie,d0yt0hj ;zn8mm u60 fop:notring are 280 Hz and 350 Hz, what is the frequeeydnp6u,40 my0j0io5mhzn ko:8t d f;ncy of the fundamental?    Hz

  A guitar string is 90 cm long and has akma 5t (3 kbc(t i0g-btt1qf4mw7yq(r mass of 3.6 g. The distance from the bridge to the support posb53 tt(b1wtmfagyi 0t74q(-kk mqr c(t is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, blg7 7og lt,fen,4 zam1ut it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?Somgzo71tg 7la4 ,lef n, the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is kklti2k,8t-* sj j3qzmeasured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct kkjj, s23zik*t -qt 8lthe frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude 93v* sr(jmstslz*io .mechanical 60-Hz vibrator. The string’s mass per unr mi*9*szos tjs.vl3(it 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 lengz n*h4:dkbhz( k klj/h,28npn th of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 p (:jbnl k8 2*dzhk,/nn4 hhzkm?   

  When you slosh the water back and forth in a tu+;9ciwm1 wx q y4/nausb at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the ceqw+m1ysi nx au4w/;9 cnter. 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 stv;/cip3 tyqm f22 0obtrikes a boundary within the Earth bet3t0of ib2cm/ty qp;v 2ween two kinds of material. If it approaches the boundary 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 velocity changes ffta jr/-q+w6.tlhs t 3rom 2.8 m/s to 2.1 m/s If the incidenth/stfaql. j+6r-3wt t 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, dense air. Io,x5ebo/iok5zqn )z+xuh uby;;*e+k f the sound wavun xy;5z)ek + iz5q* bbxohe/,+;ukoo e 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 b6zj0d;f8/p gyw kr1sbetween two types of rock at a 30kgzj y68b1srfp;wd / 8 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s mx ;b/bq6h3sivanual, the dish has to be pointed in the direction of the satellite, but an error of abbs vqi;h/b63xout 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 t;fcpz;g8 -z4esx 8vmou5vpa 8 he Pacific Ocean. As it approaches Hawaii, people o8uecz; po8s 8vp-x4z 5gmva;fbserve an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper har 4u tqfumz+**xq0a0xs a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi mxqt+f0**0x4 rqauzu /h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire n(7 7tv,p5sv ,;lb lg zvcmr+ b( x7bmmcnuxr8.et 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, and7l7vsc(m 8b.muxbz +r5 x;lmt7(,p v cbng r,v
(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 enl6o(b zccjj/t*s5 ph6d of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillatchj/6s(c5j6* o tlz pbion?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. ;j3zq vsslo+ s27ojr 111–54), compressing the spring 5.r 3;+zsj jqo27vo l1ss0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace of awg 3)bk)b7kmr bout 1 step per second, the coffee sloshes more and mo)7rk k)b3bmwg re 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 gr-j,n lc8 y-od 1lsb-groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength ofr, -dc--g8s byl onl1j 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.6ts,wo)nlg -1 pmql64+ucyvl)xu(5 e r50cos7.40t where x is in meters and t in seconds. Deternt m+ q(eg6l,u oc4x-u )sr5wl)yl1 pvmine
(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 witvh 1qd:0)tjhu(dj 0g5st0 tn5rnyo* ah frequency f. What is its frequency if it accelerates at 0.505ny sqjdu 5h gt0h0ot*tajrn1:)v0(d g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When 0oo u/u*onvm.yz l3c4 a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, 0y4o z.l*3/u m uvconothe raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 4omngp,+gv i l a1+)n0e40 Hz (A av oieg+p0nn,)+m1l g).
(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 stretchedgae5 nkq em3tqq,3a+ 6bdzi; 6 two-part cord of Fig. 11–33. Determine a formula (a) f6z a3eb6 q5,a denim3k+gqq t;or 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 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 frequebjcel,r n .g(l( fht6;ncy of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center btlrfj,;. (c6( nhgel. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates withv4* d e.o-cvyl 1ge-fl simple harmonic motion of frequency 1.5 cycles per secondv1*e lyvfcg .edl o-4-. What 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 attachedrxv6 er(hz *z2 to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other f x6ezzvhr r2*(ree.

  A “seconds” pendulum has a period of exactly 2.000 s — each og:tg2vgtx( 3one-way swing takes 1. (v32tgxo:tg g000 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 oscill g2v8mf g7-acege04d hate in the vertical direction or can swing as a pendueh v4e7ggad- 0fcm g28lum 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 of 255 N. A puls l85qe2eqzia.* p jui86om/ nhe is generated at one end8l/uj *zi n ap65hm2qe io8eq., 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 ceiling by(i twk-ozp 2fegv pd+.2n1r6 i a spring with spring stiffness constant k. A penny of mass m is placed on +dvi1 pkpi2f(on t- wg.6 zre2top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The mzj mcnpw ee48c+ ta1.s*+v6ft7yv* zsteel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of+*cvp .zt8w 6cmvn yzmetj1 +7a4*sef the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which al2l)h;i dn9zfj so 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 vibrating on a spring, estimate the frequency of this vibration, gifnz 9hj i2);ldven that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz