Give some examples of everyday vibrating objects. o c+r6k 8h ud;/ zah,ua(pzw*xWhich exhibit SHM, at least approximate8a* o(khxc/upu+ r ,zd ;6whzaly?

Is the acceleration of a simple harmonic oscillator ever zero?)c +znjx6-:*f cwazkl If so, where?

Explain why the motion of a piston id7j 3t,pt/kuk,b2av g n an automobile engine is approximately simple harmokvt2 g3 ,,jpbad7tu /knic.

Real springs have mass. Will the true period an gs0;c9qb.qt( ucwv ;cd frequency be larger or smaller than given by the equations for a mass oscillating oncwqcut.;( s0 qg9 vc;b the end of an idealized massless spring? Explain.

How could you double the maximum speed of a( z c 2w7 *p(o tfr;b7hayl1:k(uvcewl simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is ar rt/2/gx:nareleased. Describe the scale reading as a functiox/rgnt 2a a/:rn of time.

If a pendulum clock is accurate at 8:syjen.w 4ysk ekw lps7:2 k:sea level, will it gain or lose time when taken to high altitude? Why?:y.esky:p kwkejs 7l :82wsn 4

A tire swing hanging from a branch reaches nearly to the grou :lsiw*tt:wgw8o i; 0hnd (Fig. 11–48). How could you estimate the height of the bri*wi;wtls w:ht:08g oanch using only a stopwatch?

Why can you make water slosh back7: lqeofv3 dqj 3hqkxs/)eu ;xam3o97 and forth in a pan only if you shake the pan at a certain frequency?s f3qh xmv9lq)x7 o;/ae:ku37 oq ej3d

Give several everydagpqtro d 7)dm798if9 an1hn 3jy examples of resonance.

Is a rattle in a car ever a resonance phe o2 or+sc*)xrrnomenon? Explain.

Is the frequency of a simple periue,5h6;y4 ul(xc) fuli1 d z:u 8xewvoodic wave equal to the frequency of its source? Wh65u i)e1:ll(uhx ;o8 yz4 d cfuv,xwuey or why not?

Explain the difference between the speed of a tran0d kk9qwt)l/asverse wave traveling down a ca9 dwkk )lt/0qord and the speed of a tiny piece of the cord.

Why do the strings used ri9u c* 0+(sawzwv:hh 1qunydgv ,i/.for the lowest-frequency notes on a piano normally have wire wrapped around thema /zqd rg(0ui,hcvyh.:un1wv *i+sw 9 ?

What kind of waves do yf zyz(ld z:g +t 0b m0que3:wlh+-ssf)ou think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel slydtws3 f0: uhlqz-(fez+)g+m0zb :to its length?

Since the density of air decreases with anpu0x6 av,umu .o44y nk increase in temperature, but the bulk modulus B is nearly independent of temperature, how would yxa6m4y0p,n.vuu4u k o ou expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitud bc, zd9uab+m j-:1x5v0hlxffe as they travel away from the s,0x -l+:fd1x5cuh9 mj v bzbfaource.

Two linear waves have the same a4ysx;b.4rbp4d, cmc omplitude and speed, and otherwise are identical, except one has half thsoxc4b ,cp br; 4m4yd.e wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundar q mv,wc6z3fb zixn;, 0-y/bqky between two sections of cord as in Fifq0z /;,cbxq-mn6w vyki b3 ,zg. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating :nquh(9 jo. nrnch4c9in three segments, are there any places you could touch it with a knif:q(c hnn4c. ujro 9nh9e blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incidentjs3wy9iejy 81 and reflected waves cancel at the nodes. Does this mean that jwj y1 y8eis93energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how miwunm;+2r8 1ktxenqt, ght we determine whether the energyq ,wex1k+r8nt2 unt;m was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance )gvl p1v2fuwyw a /v1n bl-8l5it travels in one p pvl125-fl gn/y1uv wv a8)lwberiod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs frgzb bxg*c :vg6w)e68lbaj(,u om it but is 85 cm long when a weight of 180 N hangsj:)6a(u, b6g ggzbxvbwl8c* e from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0g;ami sget86 j f5u)(y 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 tsygej mf6a58 )g(;uivibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) ofp25-to21iznq0hid tc3h d/uj - bi1What is the spring stiffndu5jcn hdtizfq 10 /b-i1t 2i-23opohess 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 0.60 vx*a:491ju 0i g,r fr)nl1 nylf ag+fukg is hung from it. W ij yv ngffu,nf )l x+:1agr4lru1a*90hat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. :jdln:i*63hn; , *x.dnp fycdkf ul3 p11–2 at times t = d33k6ll uxfp:n in,y n;f ch:pd*. jd*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 caught in a spider’s web. The weblc8rp 8l wf;k7 vibrates predominately with a frequency of 4 8 7lpw8ckf;rl.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 frequency of 8uherwl 4l5w (/lb5 wg0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is thewrb (4l 5lewwgu5l/h 8 value of m?    kg

  A 0.60-kg mass at the end of a spring vibrate5 d3o ruf;l2o-guio)qs 3.0 times per second with an amplitude of 0.13 m. o)5 o2i3l;u- fgud orqDetermine
(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 equilibriumm8z01j.c,rj 2dckl )axkn-wa is the speed of a SHO half the maximum vala1 .jznm xc0jc,rw2a)8d k-l kue?$\approx$    A

A mass attached to the end of a spring is stretc lw 4ljegasbgk, + vez10:uc1/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 stretches a vertical spring 0.315 m. If thhs *w5hx0*illm5i :g se spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibsl 5m0h h*sgw:ix i*5lrium position again?    s

  An object with mass 3.0 kg is attached todid4va wb59936pum en:cc/b e a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from itseb p: bdw6m93ea4 ivc5c 9dun/ 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 compre- zvsmd3u7:p2ci.f f zyr-op+ ss the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the balprp2 d.my -z fcsz7ui-:fv +o3l leave the gun?    m/s

  A mass sitting on a horizontal, fraopk5:2;u: c8:y -aijqzv,dvy th0bgictionless 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 spring by 0.12 m. If the mass is released from rest with ::v5;:k8vpch 2 -,jgo ai ty ydzuaqb0the 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 whem8k32 7l;wgc q/nxc pnqw4 9wvre x is in meters and t is in seconds. Dete2lcpk37wn9/ 4x wn;qvgmcw8 qrmine
(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 enq:swf :u *f4hdergy of a SHO half KE and half PE? ±q:uf:sf hw*d4    A

  If one vibration has 7.0 times the energy of a second, but their frequ,okr)o2 z-wuv encies and masses are the same, )u 2 z-roov,wkwhat is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging ligp:hc zsv:*;5f y(9ls py;yzkx0kbnj. ht spring once every 0.65 s. f9:(lk:zs *p;k c 5hxzn bvyys.;jyp0
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertvq) +6( whklxpvw 3yt.ical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequencl h6.w3v+ wptq()vxy ky of vibration?

  A 300-g mass vibrates accordingmw)l ekq/t/l;u.;u x a to the equation x = 0.38sin6.5t where x is in meters and t is in seconxm lkleq)w;/ta ;u /.uds. 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 eicdy 6 v2c l18.mkvy/uxamples 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 rest o 1g f*pg8a6tx9kmbdc9 n the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initim1dxb6 tg9gcp f* ka98al speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates withelk)d i-eg w onv05o(- an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive veloci el)(k0wg5i-d n-v ooety 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 spr 4 ny-:pddyo,kings, 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. *sbh:p2at mj,bbm 8j-600-kg block attached to a fixed horizontal spring whose,mat hjp8:*bs- mbb 2j spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reachi6x.vx,oai jp8e 8zl 3iqcb+ vz*+ y5afng his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He vy+q3p *.8xi xeol +68aji,fzzc5 avbfinally 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 inr0g96e s3h1 ji9g17qksmo of f exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum /e-).*zi *3ov pt jud-k nzvxrbe if it is to make exactly one swing per second? (That is, one complete vib vzit.o3/v uz*-n rkxe*pjd) -ration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its g 9ojru/69d wcperiod on Mars, where the acceleration of gravity is about 0.37 that on Earth?ucd j9 r/g69wo    s

  What is the period of a simple pe /xbua34 nt;crndulum 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 c)fx3x+fjgw6 *4meg km, the pendulum bob has a mass of 365 grams, anckwf4*3e f g x)x+g6jmd it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 056e(: vgyko+ s(smf ke.9930 m. If the clock loses half a minute 5 kgs+m(6k ye(:ofes vper day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxim10/ 0 dt6pji8dmhump :z *shugum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At bkj+ h*lvm4)fvt 9dr. it is released from rest startingvhml4t*f.vb) k 9jd +r 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 jb,0zizib(zy)p8b a*that wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crestszza(bbb8jz p0) *ii,y 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 with a speed of 343 gqs-,;xrh;cn m/s How far apart are the wave cres rhnsx,g; ;cq-ts (compressions)?    m

  (a) AM radio signals have fre,g1kl+ /wtzy zl -5nczquencies between 550 kHz and 1600 kHz (kilohertz) and trzc1l-tg +nz5/z,wyl kavel 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 n i h:371upk;p3)ynq3vcdfn hur 1h 6mlongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same ela1dsgxj91 + rawstic modulus, but one is twice as dense as the othxg+wd a19j 1rser. In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is strf: 4.xwxe p85y iuxq2retched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel f25wqrup e8 x fi:.x4xyrom one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 62jru o+ja ,h2h wj67q+r0 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a w 2rjuhqj7ho+6ajrw+ , ave 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 shipw cch8 esos;2- h2 p4q)s7a0u0g1pnd7be iqa l just below the surface of the sea. He hears the echo of the wave reflected from th bh) acnp2es;1h00qeasd7oc usg 48 -l72iwqpe ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at diff i.y jikv p9s 8(gyv0pt8k6+g :msvtv3erent speeds, and this difference help0gi t j:sk68tkvm9ys+vpv3.i p(8v ygs in locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoida8hky*e,h3xtwn c b v3+l transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquwk33,xny vh*b8ec + htakes, 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 amplitudes, of an earth1+b2o:; y8fh ocqtx lm(lex a)quake P wave passing through the Earthc()+qlohxl2 ym:e8;f xo 1b ta and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake waror/x;0vg j ;tve passing through the Earth is measured to be 0r t;/ grvoj;x$ 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 through the/tety. k /b *mbw0m8kz same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplib /bkekt /0ty*m .8mwztudes of the two waves?   

  Two waves traveling alonjx. +9h4n:p7r ztgk9w+k hkafg a stretched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two waves? ar+z4kh+t9k.97 xw p:jghnk f  

  A bug on the surface of a pond is observed to move up and down a total ver))vh+c6 plfq stical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to)) q6 shlcvp+f 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) Sketl(u( g 7udw+mnch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few momlgu 7(uwn+md(ents 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 44irkk foo40q (cyp(2j50 Hz as its fundamental frequency, what are the frequencies of the first four orqk(2p j(0i fkco 54yharmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 sws.:fy+db(o Hz when unfingered. At what frequency will it vibrate if it is fingered one-thb(yswsd+.:f oird of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates.hly7t07nj ky)qi - n( ug xl8f0uf xnnd2sj3; in four loops at a frequency of 280 Hz. Name at least thre3k -2ds0ij;7gtxlf0 uu.7y fjh nqnl8)(xnnye other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standnhf 65y(u,jcm*irx .q *x ,zy-bp9wh cing waves is 475 Hz, how far apart qz,w5hx(jyhiyf.*,c upn 6rc*bmx -9are two adjacent nodes?   m

  If two successive overtones of a vi)c yr0iq 8 py-r5.bokwbrating string are 280 Hz and 350 Hz, what is the frequency of tikq)wypyb.5r- 0co8 rhe fundamental?    Hz

  A guitar string is 90 cm long and has a mass*rxud-yi l ,2t of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 2iur,- txldy* 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate ak+u 7 l:5z 4nuvpz/pli,lk)zst 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should ts7z5k+l /z, zn4ukivup)l pl:he tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it isdk iqa3fc zoo+gk1 b4h5h, z0dwk3kb 7s9-nq: measured to vi7 3b io 9d3w fqzqn +kdsz:a c4,hkb1-gk50ohkbrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small- duulacaz 6u3) ; ;uf-7w7azxg(qwg.p amplitude mechanical 60-Hz vibrator. The strindzaw -;gu 3f)luag7ux7;(.ap6w czuq g’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of tha9 vsk3+ub4(k 3dqriee string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave pattere ( rvuq+kdk3ai4b3s9ns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the watev o(,j3o va+dub-. kyfr back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, rema +3ovvo ( d,uy-kba.jfining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave travelin o+yx6oxa 7).0v w3 ,qq7iabb2mv dhibg at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary atab+ v 7 )dx ob2 qvhimq63ab7o,i0xw.y 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 “shs ;z2fc2vgse51ibppi : z47vkelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crest4 zb1z sf: sgkipp evi7v22;5cs make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm (doxnc4orn*6hau- j,r,8bk 8,acle gair when it hits a layer of cold, dense air. If the sound wurg-j 4*(brdaa,nl 8co8ex,k 6h ,nco ave 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 bounns a63iiiz7b( dary between two types of rock at a 387s i36b(ini za $^{\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 manualdqw+4a1xa/md zid, s0 , the dish has to be pointed in the direction of the sat 4,wiqmd/1s0dxd+ aazellite, 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 25il :eeg 0 )gkb8n.eg5x:a ctk v3tk84z0 km and velocity 750 km/h travels across 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 theggk 848cgtiel:a0 xet:ke .nb z5)v 3k 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 stiffness c nu *7.q++jslpnow(.rj3l/iw(isqpc onstant 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 (appswn. nwo+ lqii37(urscq(+pj.j/ *lp roximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a f(nm(a70ta lojm. zf d,ire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, and,zad 0m(t.7lan (omjf
(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 place:fxiubq hz a c3)fmn(bri :k5-a7v6p*uyw:r6d on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begf :rcv*n i-wzpqa5:u6(b3 fk:u6) yrmbxiah7ins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 1)xqyll/xn*(hlcdj9 w +80ld x)k o/dd1–54), compressing the spring 5.0 m. (a) Wdw xll j+(/d x8lc)o0qhxd nl 9d)*ky/hat 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 ri.zu25p s/kk cblc+o -eght 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 in the cof/u b.elk-c zposc25k+fee.    cm/s

  The ripples in a certain groove 10.8 cm from the center,se x8ygvpsgtd p/81; of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency v/p1e88;pgx,gysd stof the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7 /yg idqle+5 c/7zz ao.rj98sb.40t where x is in meters and t in seconds.75 a. sj gcq+9dl b8/zreiyoz/ 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 if it accef9-q.jx5e2lo- if ezilerates at 0.50g (a)lo-qfji-2 ie9exzf5 . upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a7yosxw 1ulq: * lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deepex1*ow:su l7 yqr into the water. When he steps 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 392 bwroq dbl9 z(0s1:c,o Hz (G) and 440 Hz (A zr: bo,wclds90b1 (qo).
(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 trave pfls*jd y3u*8ling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speed j 83lspdu*fy*s 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 -fyb5j..ye0eqm( n aq 2/ fchhfrequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculateaf.mnq(02hyf-y.b qc 5/ jehe
(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 mot7+mjs tin .p90ebw3y qk -qok7ion of frequency 1.5 cycles per second. 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 boarp 3k 7 k0qen-9.wjt+qbysimo7 d during the oscillation?

A string can have a “free” w+a6lz uf* ekntlb*9.end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations owf.u l*kbnt 6a *ez+l9f such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takbd 8y8ylo lj-7es 1.000 s. j7yd- y88 lbol
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical di/w0/ y frth808xpxvxsy g4x0frection or can swing as a pendulum of small amplitude, but not both at the same timsr04 wy0 f/ghxpf8x/x8v xy0 te. 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 /.;uakz otxmqv uvp -h32.q9v 255 N. A pulse is generated at one en9mvxpuh t vkzaq/2.- v;qo.3ud, 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 a spring with spring stiffnt h 1:j1ba+jxuess constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (h uj:+at1x1 bjAssume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. Thens2 p cqi 5/5s.mws 2bqdjqc97 steel crane cable is 22 m long and has a dn/cqds.75sqmc 2sjq bwi59p2 iameter of 6.4 mm. A breeze starts the car bouncing at the end 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 also gihg1z7 :x2k ixm) db(pcves the dimensions of the block). You push itb1c:2()zi d pmhg7 xkx sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz