Give some examples of everyday vibrating objects. Whichf* yq/ /ojn )(.ipk)efv;ojr c exhibit SHM, at least approximat*p)y r/;ceqfvjo/ kj(.oni ) fely?

Is the acceleration of a simple harmonic oscillator ever zero? ,0g s* y,syaqqIf so, where?

Explain why the motion of a piston in an automobile engine is approximately si e1f05 qztw ,g);xunajmpxn;tuwjq e1 f,0)gza5le harmonic.

Real springs have mass. Will the true period and frequency be laf2b*u q3e80h z 3wqzncrger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.8 b 2w*c qqnh330fezzu

How could you double thej/c 0k6zlfz s, maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the//tqbx(ijp 7k1;k uv +me i01pyesj*q hook of a vertical spring scale, and then is released. Describe the scal+i bpekev (mi /y q*ts;1jx1up k/j7q0e reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when takt7q29.f jnhcfge g :4nen to high aqgf9h 4 nntf.j7e:2g cltitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48).*kssa1 m 7i2mf How could y*k mm1 7s2faisou estimate the height of the branch using only a stopwatch?

Why can you make wateri6 wuw u+lc*4m s0h+sf slosh back and forth in a pan only if you shake the pan at a certain frequewf+ c 0iwmsu+6ls4 h*uncy?

Give several everyday examples of resonance.xgt:6 r dpw4r9p g,;lp

Is a rattle in a car ever a resonance phenomeno; tvdyk 6js),yn? Explain.

Is the frequency of a simple periodic wave y3km4xns3wi *wb j( 5eequal to the frequency of its source? Whyx5j4e3si bykw (m3nw * or why not?

Explain the difference between the speed of a transverse wave bwauq5 t en501traveling down a cord and the speed of a tiny piece of the q50u1baw nt5ecord.

Why do the strings used for theg i+xfc rj;)7 +higj:b lowest-frequency notes on a piano normally have wire wrg7hcrg)b :i+ f+ji;jxapped around them?

What kind of waves do you think will travel down a horizontal metmmj; aa. q+x-v2*qg ky gk5yx,al rod if you strike its end.x2jyv5mmyg k*g+ a,x aqk; -q (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases wit. h1( oqahq ygktu792siij(j9h an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary w9qgi hij 9h kq7o.u yj(at1(s2ith temperature?

Give two reasons why circular water waves decrease in +xm5hx dni5 2wamplitude as they travel an+ xm25ihwx5dway from the source.

Two linear waves have the same amplitude and speed, and otherwise are identicx2iyf:6l/k wlii ge.m*dq5+tvv -r +qal, except one has half the wavelength of the other. Which tranx6iw l2-+f5*ml+ y :.tdieqk vrqv /gismits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of c :b n9lz-ce3m +wwo+bhord as in Fig. 11–33, thc+9+ow:3 ze b nlbwm-he frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could touc3k7s fuuab 6*nh it with a knife blade withou76b af*knsu3ut disturbing the motion?

When a standing wave exists on a string, the vibrativ*cp(34 :y1ofyg ogcxons of incident and reflected waves cancel at the nodes. Does this meanpyg1vy: *x(4 o 3gccfo that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, hqxt2v*bm1-d(-zdz 7 x vzenn- +j)kfwow might we determine whether the energy was being carried eq1xjw-nxvd*-d)z k7b+z -v tm2fz n( by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance:7w f b01ypb fk3dc4xu it travels infk 31y 4 fd7x:wpucb0b one period?    m

  An elastic cord is 65 cm lomv7gj8i t*g9n/ x0xdu ng when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic corx7mt/*v 9gndu g8x0ijd?    N/m

  The springs of a 1500-kg car compress 5.0 mm wt4 ,ryu)qjt l*wguj wm;0 v+s)hen its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequ0 uvt l+j) 4gwyrwtm)qjs, ;*uency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs frr1*7ml2 zrljg. /fnrj om it. (a) What is the spring stiff21jrjm rrglzf*. /7lnness 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 +qzf13r/ sgoo gi0-fq of 0.60 kg is hung frogiqzfo0 oq 3s1r-g f+/m it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 atlyf98y/. t ftq,l, mwo times t q t .yf/t8 9oymw,l,lf= 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 we)azfff -,s/j eb vibrates predominately with a frequency of 4.0 ff/sz-)a,e fjHz.
(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 0.88 Hz. When an5vo;m n-qs8q 3w gj.wf;z10w ,lhkvlu additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m? ;5l zv-;.q 0shv wjo1kg8wlqfm,n3 wu   kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with a gom42il eqlhxqd00 y(s rb;4m/ it.b7n amplitude of 0.13 m. Detemd qib;i42homb7.q0l0r syx g/e(4ltrmine
(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 max7 ;-w)xi.9aix ghjzrnh ( x/ucbbx) c9imum valuegu.hn ccb)xrxji(/hwx ax99b;)7 z- i ?$\approx$    A

A mass attached to the end of a spring is stretch88a posp:4)c3 im nh3yt.y m:fw jf;xeed 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 a7ny.v- ztq*-8arz0 b cp7kalt vertical spring 0.315 m. If the spring is stretched an additional 0.130 m andap t7v ytzqnr7-b 8l.*cak0- z released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached tm;ycyu:bi -lw+g /7 n l,j3qiro a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, iti;wj,m+i/byn q3ulg -:7 y lrc 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 s99umxy6 p:ukto compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball luspuyx9 mk6:9 eave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to oystqd1y hp .-0ne end of a spring; the other end is ypt0 q1s-dh y.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 a13fb aykmas)c .qr .4bccording to the equation x = 0.45cos6.4t where x is in meters ab .y3k4sm.cr q)a fab1nd 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 thldav+7tcr .k4 e energy of a SHO half KE and half PE? cl+4r7a dk vt.±    A

  If one vibration has 7.0 times the energy of a secon wqhdi 1d5v.ai9 cu-zo*)p/swd, but their frequencies and masses are the same, what is 9i) dc1.hwuio5wv- pzd/ s*qathe ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically haqvcf4g3w g6fe4:wi hxo3v6 4qnging light spring once every 0.65 qwvc6w f6v44fihqg:ox 343ges.
(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 twog6 ci5zhfld )dj :im-3 identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vi 5lmd)d-cjihif6:z 3g bration?

  A 300-g mass vibrates according to 0ypxbx9 x +3lvthe equation x = 0.38sin6.5t where x is in meters anx3lx+ vbyx09p d 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. For each, whahkz*5f2toa m3t 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 horizontal spring (k = 124s l bse w9(l.h23tx8ic N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determ9ht2x.b3e 8(wls cils ine
(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 stiff,p29z x b+vedifqg3 nlktx+lb--;vf /ness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from ixl/ e9zpq;-+tvl- gbx2f b,vn+ 3 kidft. 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 connecte,sqbgg1s z o(zns(e6+j;t2 eo d to two springs, 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 block attached to a o 2 sutx0 tv.idf+xdx68f,nm7fixed horizontal spring whose s7.dnt,o0utxfs i8dxvmf+62 xpring 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 me9/l ,mbl5em dvfwk)0s1ua 9jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched lenm/) l0vwemblfem9,as5 k 9 u1dgth 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 i9g7t q t-odt6-d7ngpixkp 1/kn exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to)(.)ae.dx rp fmyqb7v make exactly one swing per second? (That is, one complete vibration takes ex7 (dvmq ey).x.p) barfactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earthu54tq/;lr t9pv wp1gb. What is its period on Mars, where the acceleration of gravity is 4gv;qtr1 ptbp/ 9luw5 about 0.37 that on Earth?    s

  What is the period of a simplq 95zmz2rnu 0je pendulum 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* qd136kwoqbzbg1kp8;q i2fws,2jl/wo :bbp bob has a mass of 365 grams, and it is releasedwbbq1 owd61 32p8qk:/w2sqb* i,lok; pzjbgf 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 df.f3wttb/p1qnl * j)a length of 0.9930 m. If the clock loses half a minute pe *ldqpjb/t)1 3f.ntwfr day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxim 1saloz: /9xbmum 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 -k kx(kqmi+:w33bcvr 2.5 Hz. At it is released from rest starting at -wqbk3+xkvimc(:k r3an 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 warz9q sp3)hm d+c qog-5g38jkbve crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two cres bgr5cz3+p98okqshqm 3)gjd-ts to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz andncb7k/q* 5db x travels with a speed of 343 m/s How far apart are the wan5 cb*d7qb/kxve crests (compressions)?    m

  (a) AM radio signals have frequenciesg*60rmeoo,q4 d lhmn m5s*w8n between 550 kHz and 1600 kHz (kilohertz) and travel with a se,*5q rm mhol ng8mndo*ws 406peed 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 wavep;ts)mi erf+2ht ka71s in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have t crf 1da5(2hifhe same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be fr1 2(da cifh5greater, and by what factor?   

  A cord of mass 0.65 kg js nkx *n1zzqv .:,ox8is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travelzq s*,81 kx nvxjz.n:o from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steenngg.n;gwsp*d/d1 ;.ii s (fdl cable of length 620 m and diameter 1.5 cm. As the gondggfd1in/;gwnp .s(*din s.d;ola 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 of his ship just belbxg1.p k0r-h4j)vxd ;pl:dn /jqfmx .ow the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocea)kh bl d1.gxxqnxr0/-p vjpmf4;.:jd n at this point?    m

  P and S waves from an earthquake travel at different speeds, and this differ/g780*q ag h :arwd budekpc;(ence helps in locating the earthq:8pur*gka/bwhgc a7; d ( q0eduake “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 approximatehw7lm : gz 4vj0*ue2uud by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is ul2u* e0gu7mwh4:jzvneeded so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) th-j6 f;zr3uuxie intensities, and (b) the amplitudes, of an earthquake P wave passing through the Eart ;6ixuu-zfr 3jh and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to bbgb5h3 ( .3l6y kai,aw 0 sjgpsk.ee,me (e.g ymja3skag50.ksh e,w, 3i 6pblb$ 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 throc:l;fbi3 qy t6k0)fta ugh the same portion of the Earth, but one is carrying twice the energy. Whatyatb: li0f);cf q3kt6 is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have tq0 nl40 -ml-d+f zzieahe same frequency, but one transports three times the ll0 z-d + me-04ziafnqpower 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 g dnl5g14csiv(sz 8.k -/lvemtotal vertical distance of 6 1 8evvm54(g.igdln c/-zl kss.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig.h2e w6 yq 9ztd+qs(vld a)e+f- 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string-dl 2)es havq9f+(qyew +tz d6 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 fundamentaeeft4l; oz+x4 l frequency, what are the frequencies of the first four harmozxot eef;l4+4nics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequencyh7ehdwer0s ;5yqk0m * will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirdd 7rq*50whke e0; mhyss of the string vibrates as a standing wave.)    Hz

  A particular string resonates in fupg- /82u vnpomeh 3 /uy:xol1our loops at a frequency of 280 Hz. Name at least three other frequencies at which i8umgp pnux/y o h-v/u2: lo3e1t will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s rer53k5e-t0zzw o g;zIf the frequency of standing waves is 475 Hz, how far aoezrz53;0z- r g5e ktwpart are two adjacent nodes?   m

  If two successive overtones of a whm6sgbtz//cn*id(( vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamcs w(6zm /gdi* (bhtn/ental?    Hz

  A guitar string is 90 cm long and has a mass /xw xha 7z:mr3,p:u ciof 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 frequeh3 :7: /a purzxcixw,mncies of the fundamental and first two overtones?    Hz

  A particular guitar string is sunvz-9 f o/pd3gpposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shoudzo gf/ pv-39nld the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibr14q fv.ftw 4ebib* c;ni4v j;kate at 200 Hz, but it is measured to vibrate at 205 Hz. By jknbw4;fe4.4*ii qvvb f 1;tc 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-amplitude mv ,ntrn5d2. 3x5evdffechanical 60-Hz vibrator. The string’s mass per unit lengt ,d3v5ne2rnd. tf x5fvh 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 str12biwttgujh7m( 0k9ring may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how manybt 2wij0gkum7h (tr 91 different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right freqpm u9sz+; 5xbp-7b evouency, the water alternately rises and falls at each end, remaining relatively calm opzp mvb e5b-ux79 ;s+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 traveling at k.0 v9n6y2dnr1 v s iod1inq2dmb nov0), 8km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident810v6,d bqdivo 2nr)n2 ndomvn1ysi9 angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocit.r6 c .b8atto(qytv -n79ud g2.xnpkty changes from 2.8 m/sgottr 2d xk-pcn79a6.yb8t n tqu. .(v to 2.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when itm:ho;w9xkmx4 y f3* li hits a layer of cold, dense air. If the sound wave hits thel:*xm9 mo;f ykihw4 3x 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 beiwg69nf p: 8jwtween two types of rock at a p f9nj:8g iww638 $^{\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 71qlrh am*oza-7 x)lkph1*gt user’s manual, the dish has to be pointed in the direction of the satellite, but an errorm*r1x77la- pzk)h*t1a lhqg o of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Paci;b4e8riz wfpo , 0 auwy2kt ce50fxk6)fic Ocean. As it approaches Hawaii, people observe p54fuf )rokwye;x ,abe2k0t0c6wiz8 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 has a spring stiffness constant o -ip4 x (x-ppjp ulg6za y2o(;,tn5apqf 550 kN/m Find the maximum compression of the bumpalu(xgp5 ntppy-p 4;-xqi( poazj,26er if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a wsmh bd * -c7fnt/ h.okw,tq0hd(s6z-l indow to a fire net 18 m below, which stretches the net 1.1 m. Assume toh/*.fslsq6k tchm w7zd(n th0d,- b-hat 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 on the e0 ;5qcv+m/f :uhmgdl wnd of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of tmwu:5;mqc +g d h0l/vfhe oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compres4v8clmbs j q,)j2i; czsing the spring 5. zvismbc)c 28qjj l4;,0 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 justytf qyq.sg0w :rt a0(7 the right pace of about 1 step per second, the coffee7q 0yrw0a .(t ytqgf:s sloshes more and more 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 3vgovil4pr q w ap0*n:o/3t+oj4 ,kw. s3-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency v w/a,po ovn ipo gqjt+*4r3lw:.ks40of the sound emitted?    Hz

  A 2.00-kg mass vibratp ),rcsgwkv(y )u uqx 9*z2l2;a+lxhwes according to the equation x=0.650cos7.40t where x is in meters and t in seconds. Det*29y(hu)), swp;xcvwxurzakgl 2ql +ermine
(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 wi+j 7cdj8 wfn5tth frequency f. What is its frequency if it accelerjt+nd7 fc w85jates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg/gysf+ l*. ekx man stands on the raft, it sinks 4.0 cm deeper int *xefk.gyl +s/o 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 musicj((el )uae+93k 0 l(hpum93;l l yixgnwde0lkal instrument are tuned to play at 392 Hz (G) and 440 Hz (0 3l(9wu e;lek gd l9m(nye)ihlpx+ 0 lauk(j3A).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord o k1cn :tk(ck j)xtfup3rd64 .wf Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section 4 tun)j 6wc p:(tkf .1ckkdrx3versus 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 tij5u8 st.bmpn2w3bm v+p of each prong moves 1.8 mm to eitvbmsbn528 +p.j uw3mther 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 6 2z 6nmsvz*xscycles per second. What is the maximum amplitude with which the end ofzn *sz2v6x6s m 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 2nar( vw+ 7uzfk(lf6xto a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the reso2f6wfu r(v(7zxl +ka nnant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-wabfmv4n(zoht 1usm)odlij :kem: u4-u0/ p: n 3y swing takes 1.000 nj1- h:03:pnsdv( 4zmbuokfui)t:lu /4mmeos.
(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 oscillate8i.hq+x6z )dj) gxg kew10tyo in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Lex+6)8 oeyg qx i.g1)htdk0wj zt $l_0$ 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 p tw8, zxe:sk ez 1ofpu**f2ag)ulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first mzz:x)*e *gfs2,ewuka1p8 otf eet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffdwo+w1w4lc bm*sa:i (ness constant k. A penny of mass m is plac*+w(mawl :ocsiw 1db4ed 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? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 22pv l 8nk.b5 zhq3 qn2cho(y/v( m(pnhv hqvb z q8n3c/5yo(k2. l 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 the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a p .u+)tkecv 9c94(kqas wiw c9rlate as 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 vibrating on a spring, estimate the frequency of this vibration+sca9 cwc.i9u4qkktvr e ( )9w, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz