Give some examples of evel 8lfowh5g3:l ryday vibrating objects. Which exhibit SHM, at least approximaf3l o8:l5lwg htely?

Is the acceleration of a simple harmonic oscillator everhh fu9 ,xw7zv 07r4ypc zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximat+let fxq(h es:tfn;166 +rgxrot c1) uely simple ht x6xrq6cht+l1 :e;1rtf u+g(n )fosearmonic.

Real springs have mass. Will the truedx2)u,tsz ;no period and frequency be larger or smaller than given by the equations for a mass oscillating on2)tuz, do ;nsx the end of an idealized massless spring? Explain.

How could you double the maximumjj73m+snu5cn7)xw5:ds at tm speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scavbwjv8 *8 *::vesnxnrle, and then is released. De*jn:8 *:n vxbvserv 8wscribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will /sbug7 oq1cgjd,8agti 4c/ytx3g)f;it gain or lose time when takenqf );gxojtg b/a,8ggd/suy1c3i ct 7 4 to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48).8lr7: y*o9fzn7wcf wo How could you estimate the height of the branch using only8c*:l f7ryzwf o7w o9n a stopwatch?

Why can you make water slosh bav((de c-pu:gw) jb+o lck and forth in a pan only if you shake the pan at a certain frequency? cdw(-j(u) v lg+:bpoe

Give several everyday exa,hdd6e6tjb9r0 gti 1m 5jv0 h );grugjmples of resonance.

Is a rattle in a car ever a resonance phenomenon? Expju99pdk rul-3c5 txk -lain.

Is the frequency of a simple periodic wave equal to7x ipdagfdz, v:.r/v1x)px/ d the frequency of its source? Why or why notrvxa/ , :ppdz71 .xv)gfidd/x?

Explain the difference between the speed of a transverse wave travej d:km 9wjp1qpm qr*5u)(3ashling down a cord and the speed of a tiny piece of t(1 d: *q 3rmwsm5jpaqku)jh9phe cord.

Why do the strings used for the lowest-frequency notes on .8k5qdcr: bf 8 ocd*xia piano normally have wire wrapped around85.k8*q:odfr xdcc ib them?

What kind of waves do-zkl.0v9qa dbxck*8u you think will travel down a horizontal metal rod if you strike its end (a) vertically from - q .c*vlda89kbu0xzkabove and (b) horizontally parallel to its length?

Since the density of air d( , cpa ((uh yb.(bj4g/ifllqrecreases 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 air to vary with t,c4.q( u(pa ryjl/h((flbbg iemperature?

Give two reasons why circular water waves decrease in amplitude as they travet8br;qm1: he 4y7fdzk/. tjxul a 8u/jd : rxzt17fqyh.;etbkm4way from the source.

Two linear waves have the same amplits nd;b,yeab+s),d yy( ude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factob ( dsbed yyy,;,)+sanr?

When a sinusoidal wapflu4g7,8etk:1 spprgxs4p; ve crosses the boundary between two sections of cord as in Fig. 11–33gxk1rp8tsg :p,e44l;f p7 sup , the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are u92t25l o g9 oymqyaf-there any places you could touch it with a knife blade without distur2al-ug 29fyo59t ymq obing the motion?

When a standing wave exists on a string, the vibrations of incident and rygo5u 9-p35yrghys r9 4j5 ii1prdb/eeflected waves cancel at the nodes. Does this me9gyoh- g 1/5i9rpryiy4 5edur 53jsbpan that energy was destroyed? Explain.

If we knew that energy was beism d5b (9q*.nl fmbqe0ng transmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodies) om d5bn(qs *m .9qeblf0r by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the totale9qlvj *c ux e2/etsaa4ux4 c,dc3e.5 distance it traveua,s ccv4le/u 34 2*.xq eae5dtx9j ecls in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fro)sh(p 0 +tss/y4egmeu* ,ygfom it but is 85 cm long when a +* ),seyge0 u4/p( osmsytfghweight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets i9 )s+li*p wtkbg oe,:ento the driver’s seat. If the car goes over a be +biog,wk es*9tl :)pump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.68*nzflqo. r hv6k/h s, cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffnessql /*hv.r sfn6h 8o,kz 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 frequeuk5yf urv,q* )34rqkgh-v bk6ncy of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequencq34fr byvh,uk 5kqr-6kuv)* gy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating tcj4ww/: me2 xihe position x of the mass in Fig. 11–2 at times t = 0,t imw: e2w/jcx4 = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 prf*u z4/q byqub*9 k4hbedominately with qb 4zybk4u/u*fbq*h9 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 sprg n39iioh/ro,ing vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0./9n,hg i3rio o60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 tim*kwv ew4b. 96 9 pbswgr;h8jwoes per second with an amplitude of 0.rskgpo *w b.ej ww9w;h84v69b13 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 an. hca5(q2 u5spl)lp.yhv -au SHO half the maximum value- 5p2lnplauhy s.v)q h.uac(5?$\approx$    A

A mass attached to the end of a sprizph)bcm0- v4,e yw8e ing is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg streml / rlctvzj .*n8r5(stches a vertical spring 0.315 m. If the spring is stretched an addition rrz5* 8(ljl.n sm/tcval 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kgu ix2 9 :y0fy8uvml4to is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When thoyiu9fxvyu4 lm2t8:0 e 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 sprk.chl)o wtr7d)3c fl :b 7a8zzing of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what 8lk7zchl)7.c)dtw br 3fo z:a speed will the ball leave the gun?    m/s

  A mass sitting on a horizontlcf4 /ws(z x(s0 hq-kgsqo(9e al, frictionless 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 the spring compressed, the mass experiences a maximum acc(qf 9h(0z ke- (wssqso x4cl/geleration 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 = ch a(n a/-e-5vxk(*u s,wlhg x0.45cos6.4t where x is in meters and t isgsvh-, -a5n (c*ha/( wx xeulk 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 halfs)y .:3gbutjyki m).w t,gou0 PE? 0kuowi.j, ).g :3 gy)ybtutms±    A

  If one vibration has 7.0 times the54olby b sj2)f energy of a second, but their frequencies and masses are the same, what is the ratio o5b j)b oyfsl24f their amplitudes?   

  A 2.00-kg pumpkin oscillates from a verticall4jrf f xn)c:/us)e *ryy hanging light spring once every 0.65 s. c/:sfnjur*4r)f)e xy
(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 paral9j.qb8zg j0;un c7o sdlel vertical springs, each with spring stiffness constant kn8 g9oz0 7qc usdbj;j. (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t whekqr)mpr2 85jlmn -z-nre x is in meters and t is in seconds. Determinn8m j-pl5 rr)z2mqn-k e
(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. r:ha-s2 pf em)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 1 /jo)o 0 dwg3djdjs0vrest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, whichj wvd d 3oso1jd0)0/gj gives the mass an initial 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 springs- 5w9*lxrhx7dyg m v* stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at xlw-mg 97r yvxs5*d *h
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with sprdy 357ntw/hws7c q:m y*pk*jzing 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 fyup7i t 3(t vsj3w mzl);3*fkvixed horizontal spring whose yp3*37w;jt f3kvzuvi) l tm(sspring 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 hig (h5ecqa5g g sy86szf/z35k zgh 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 length of the bungee cz5a6q czh sg5sk(z/efy58gg 3ord.
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 60 s. Whot;mq . kunn3/at is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simpleqzi (yas6;tlk8 vx1v0 pendulum be if it is to make exactly one swing per second? (That is, one comp8 zi6t1slxy k;v vq(a0lete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s onrrgv9geu(80xj h6;rl Earth. What is its period on Mars, where the ac;0 l r8(geuj6g 9rxrhvceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple penduqugvd guye*5 ccv(-52lum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0a)9 h tce *z1eav74e*xnr/x md.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angxzher ) *t*e1ax ec/mn97av 4dle 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 pyiqcigw 0g 3hs ;s15g5endulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust 53qgcis 0g5g1h ;wys ithe length of the pendulum? shortened by    mm.

Derive a formula for the maximumx 0velo*hg ,4d 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 frequt6,: ebv5swxqnt (et9 ogi65f ency of 2.5 Hz. At it is released from rest startinb 6tw5tge f6t5ios e,:(9qvxng 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 anch /) u,3z:qzk)jmkkuw kored boat every 3.0 s. He measures the distancezwq: kjukku) k3 m)/,z 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 a vfp x)jvs ,1ddy3c.7dnd travels with a speed of 343 m/s How far apart are the wave crests (compressioc17 )d. j,yd vfsxpd3vns)?    m

  (a) AM radio signals hav lahip)o,2ugz n21 zd;e frequencies between 550 kHz and 1600 kHz (kilohertz) and trav2zd1 uoa;z) gp,n h2ilel 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 longitud2xv rs7*gedc*--vfab inal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elakffo0z9cn+ 2coxjr8mrsa3 p8f:6xcu7zl 8 e1stic modulus, but one is twice as dense as the other. In which rod will the speed of lonf0n9zp:ocf xsx7j6u2o38 8 1e 8fk carmc +zlrgitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If;ds ;k45-ocrrrw hb 3y the tension in the cord is 150 N, how long will it take a -rrd3s o ;bcr5yh; kw4pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length fb /x ybw8k 9ty,f(t;a620 m and diameter 1.5 cm. As the gondola comes to the end of its run, fx89;b,tkyw/(b tyaf 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 thex5, imhkgee4n,cvq8r 3i,dm4 side of his ship just below the surface of the sea. He hears the echo of the wave reflected from trv,4 4 ,i8knie,5mhq 3ecg xdmhe ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquakerwy ywa2r1o6x 1vdn;6)mz(o q travel at different speeds, and this difference helps in locating the earthquake “epice a1od)6vwno yz6 qry;2wxr( m1nter” (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 sinx 8wr;bk ,sxz nk6o 36.w6coamusoidal transverse wave. Assuming r,komo.xca8w6s36 ;6zxk bn wa frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, andsq,c;)*lw l fh,h33wi6ai j aa (b) the amplitudes, of an earthquake P wave passing thro)ail6wwi3fcaj, h *lsa; h3 ,qugh the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave pasxd n0uxw8g0q og40yxm3 / snj3sing through the Earth is measured to be 4gx3jgu n3dm 0/o0 yx0nsx8wq$ 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 orv )k hv+5alk8drc we500 y0zsf the same frequency travel through the same portion of the Earth, but one is carrying twice the energy.lhc z 0+yr)0 wadk5rs0v85 kve What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same+*ppv69(yr-fadkv8k.b njipbvc 59o frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two waver8k+ idppb(c-v n96ko*vpy9f. j5v bas?   

  A bug on the surface of a pond is observed to move up and down a total vertica ja)t 70o w;myr+3ohbbl distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factobar+ oomb0h)j;y7t3wr does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward1 9 gr5xnb1 tg5bueu.t each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a f1tg9x e15btubgn5ru. ew moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental a):zt;a0cxrspj 1 md8frequency, what are the frequencies of the fir)amds8 rcja0;pzt :x1 st four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what8gktsf )gax3( frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as gf)3agtx 8k( sa standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Ht0r; qq* vsh6- dy;ulhry;p y 8+icba.z. Name at least three other frequencies at which it wilqi +u6rt.h0qpycday *r8hsb; v ;-ly; l resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string te8 .yhi28aenyc +wi* 2mk*gm is 92m/s If the frequency of standing waves is 475 Hz, how far apa 2i.8+amcytew 8hng*ky m *e2irt are two adjacent nodes?   m

  If two successive overtones of a vibrat7 rfunx+mw3r9ing string are 280 Hz and 350 Hz, what is the frequency of the7w9 fxnr+3 urm fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from theg* qc(* mzj 8jb6u3qxd:qdy h1 bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and firs(jy83 qgd1q 6**hubmdcqz :jx t two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured np 8 2e0warpp wd75:sxto vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the th s w:appx 7end8250rpwree frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is hrpw4 m74o7(-lhjlk d7li u*vmeasured to vibrate at 205 Hz. By what percent should the tension in the strirjhl ( pk*4 4wlo7md7hvl7u-ing be changed to correct the frequency? decreased by    %

  One end of a horizontale120roudh7k* d u3f7 v0gwdkh string is attached to a small-amplitude mechanical 60-Hz vibrator. The stkdhd0rg o3 7kwd*v2 uh 0e7fu1ring’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 the string may be adjusted by mokj 0ko r(z;dxvtftr01zdp9ii: s 0f*3ving the pulley. If the hanging mass m is fixed at 0.080 kg, how many diffdz0s0idv tfikkop*; :1 t9rz f0xr( j3erent 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 rig 8ptwylpw1y: 9ht frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wav 8plwywy19pt :e?    m/s

  An earthquake P wave traveling at k.0 km/s si/ebp f.nfu5 xj 0*h)dtrikes a boundary within the Earth between two kinds ofxfd5bif eun)/* p0.hj 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:bawk3k , tqmwqwdub, x0:d/ 4 underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m4q,k bwm, t ud3/qkwdxa:w:b 0/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 it hits a(a7 hdbci4 y1j layer of cold, dense air. If the sound wave hits the cold air bhya idj4 (17cinterface 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 stri(;)jkkgllr5 pyn5 n +tkes a boundary between two types of rock at a lk)r5(gkyn;tlnj+5p 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s manua.rb2 g 7c+p4tdoyjy/u 4iz45 wlmbn *bl, the dish has to be pointed ymn2 zwg 5prbi.d44j7l+obyub4 /t *c in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h trave31 +bzy vn k;gn*k:dacls 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 the absence of knowleg nyb;3+k kdvczn*1a: dge 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 stixb;zl go 4usb(+od1k-ffness constant of 550 kN/m Find thez xu+o4ld;(bkgo -sb1 maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net t9tq(u dw)2dk r7:dys 18 m below, which stretches the net 1.1 m. :qw72d s9u)rd ytkt(dAssume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass the bh *yp:yh+s2 x)6si-ffx:lgp t 4zd7 e+p)iwpn falls 33 cm before it stops and begins -*dhptf4x) :p6) bywpi+ y+l:h2se ixsg fpz7to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of )k2hq6a7ghz x* zz 3fs22 m/s (Fig. 11–54), compressing the spring 5.s6hf7*zagqx2)z h3kz0 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 o +yktlqq7 ; 2os43:rl )qesvpcf about 1 step per second, the coffee sloshes more and more q3; k4rlcyoe2q vq7s) lst+:puntil 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 10x/gm gl+bv ,su 3r:thm6(z lg).8 cm from the center of a 33-rpm phonograph record have asrl/+6gg3xgm h : v u,bztml() wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according 9ujekp g 5i eus:10vb3 n-kour z 0o1o;(m;ihxto the equation x=0.650cos7.40t where x is in meters ajnx1gp3e h 9u 1omi5(kvi;s;ub-k :orzo00e und t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates 1ov +5 9)flgcg +evcajwith frequency f. What is its frequency if it accelerates at 0.50g (a) upward, +)9 a1cf gclv5 ovgej+   f
(b) downward?    f

  A 220-kg wooden raft floats on a lakeme sww;whu0/ohf;:j1*ub p2e . When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the w;1/u uh h wm:wo*fpes;b02wejater. 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 kngg s:-2f dj6-4e5idu lfho.n7lw k4instrument are tuned to play at 392 Hz (G) and 440 Hz (4 lngwn-s.d i4ghj kelf:u2 df5ko76-A).
(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 rbgz5 -3k,ausme+t i g,lh;5odown the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the s,l; +i,eh-o5sma 5gu bgtzr k3ame in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong moveh20jk 5.lva xks 1.8 mm to either side of center. Calculatek k25va.lx jh0
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simplb60ns 1//0-rwd.dlrd ezy mcve harmonic motion of frequency 1.5 cycles per second.clr1mddzs/ 60r/y.n0eb wd-v 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 attached to a rinvu z*c sn : ezt8d ez:74j(s65s.cyphig 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 tds: z(6c.7z *5hs4ueczvnj8i ype:s free.

  A “seconds” pendulum h2. h-qdzpkewfi ip 3)rng87 wjar;/t1as a period of exactly 2.000 s — each one-way swing takes 1.0003-e1a. )if pdrni2/w ghtqz8r jpw;7k 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 springwhw uo*, x92z6 8wutwk can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but nwh ztwou,*62 9 x8kwuwot 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 stretcrig):f 0n sb+thed under a tension of 255 N. A pulse is generated at one end, and i)gsrb :nf0t+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 h pyaspem;d* zbg0 q;xdxt2..ix0u ;)spring stiffness constant k. A penny of mass m is placed on top of the block. Whgmb.dt;x*q0x;pd ayz ei ) .ph ux0s;2at 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 1b)may,,fbdmq 6agz ;7200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bobq b; 7amay,, zmgf)6duncing 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 sx9 pm5yf/ihy0cvg3;9hx m m h3hown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, 9;3mxxmv3f0hcg5y9myh ih/ p 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