Give some examples ofgr22fcreho)2b- yl4n n yp h30 everyday vibrating objects. Which exhibit SHM, at least approx2gly hrh 22renb)yn4 pc 3-o0fimately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where? mbx 3,i2vxm,d

Explain why the motion of a piston in an automobile engi-1 hi dxra 7u27ou/a.)r jmwrzne is approximately simple7r1-.7mdu 2raiarjz ho xwu)/ harmonic.

Real springs have mass. Will ezb+w5ugq, u u ek22p1the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless sprin1wu egbe, +2qz2 u5kpug? Explain.

How could you double the maximum speed of a simple kx; nbsjn4tst: zb9 sg4ww (as;.ku7(harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hvpd1) gf0i0z g pj7r*kook of a vertical spring scale, and then is released. Describe the scale reading a p10d)k7gg0v*zprjfis a function of time.

If a pendulum clock is accurate at sea level, will it gain 8bfg6yu9 drk(0ac pg5gez5 z/or lose time when taken to high altitude?czb5ru(g / 6gegpz y 50ad9kf8 Why?

A tire swing hanging fromr -9goth *zziyb0k l,b(:njq6 a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatch?h t,9b60lyzj :g(r*bo iqk-nz

Why can you make water slosh back and forth in a pan only if you shake yc9y+64pnfqa7v2o a rthe pan at a certafryoq a497pva2n+6yc in frequency?

Give several everyday examples of resonancezchs( m:)uayj- wn.1m.

Is a rattle in a car ever a resonance phenomenon? E 6 ftiot;f9m 36pjk;waxplain.

Is the frequency of a s(m9fc)8jsverv-u9lu06 w7y*hya z-suop v s8 imple periodic wave equal to the frequency of its source? Wwhp9uy9vsv l sz8a -*s 8vr0)-(emouufcy7 6j hy or why not?

Explain the differenlic -rl j.ct,ar59lj0.e:fjfef 8 /sece between the speed of a transverse wave traveling down a cord .c tf.s/ilrf 8e0rlc5j j,l eae9-j:f and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-freque* k4.vlh8xi/(bvpoba ncy notes on a piano normally have wire wrapped a8 a* p4vb.hkbvx(o/ liround them?

What kind of waves do you think will travel down a horizontal metal b t3 yb2fpd iahj0-;9jtw/*burod if you strike its end (a) vertically from above and (b) hor h -fbpj* a b/i39tdjy0;bt2uwizontally parallel to its length?

Since the density of airx5kzzo u ip61. decreases with an increase in temperature, but the bulk modulus B is nearly indepuoi6z 5x.p1 kzendent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in ampjak2ug+nt7p * litude as they travel agtp2ja7* +nuk way from the source.

Two linear waves havg92*t+ ..m7yugl 8uymm rkmma e the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factor? r8 7lmmm9.y*kya.gm2gu+ mu t

When a sinusoidal wave crosses the boundary between two sectdgn uoj m d(d4+m-.s5fions of cord as in Fig. 11–33, the frequency does not chan+.sd54fd -n(udmjm goge (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any place,k mm8d:b ye9sc4s4 tts you could touch it with a kbt4tmy dks4c8m: se,9 nife blade without disturbing the motion?

When a standing wave exists on a string, the vibrationspf .zd4 v+q/li of incident and reflected waves cancel at the nodes. Does this mean that energy was destrl q4. f+v/pizdoyed? Explain.

If we knew that energy was being transmittcsn cft325q*r ed from one place to another, how might we determine whether the energy was f5r c cnqt23s*being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.j4v1(n dof2 neuo-hf- 18 m, what is the total distance it nj-ofn-42 fhedu vo1(travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N ( u*l cs9w1mbbsit(0qhangs from it but is 85 cm long when a weight of 180 N hangs from it. W(*tlbwsi0c1b qsum( 9hat 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 glr-f 5qt0ch 4m38dqhzets into the driver’s seat. If the car goe4dfcz5- hh lqt0 rm38qs over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm wut6n l9b- ,cbwhen a 2.7-kg fish hangs from it. (a) What is b 9-tcn,w6bul the spring stiffness 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 kg in c7m:ds;nn6ti) yc; is hung from it. What is its frequency if onlysinc)nt; ;yn dic7: m6 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fi rnma) j6.::nj/ lj sop)aqli7g. 11–2 at times t = 0r:nqao6m)j) sn j/ il:apl7 j.,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 we 6d:fltt,g2 wjb. The web vibrates predominately with a frequency of 4.0 Hz. dftw: 2,gjl t6
(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 vib7fgxy e) 5/tne kn0/styu rr(-rates with a frequency of 0.88 Hz. When an additional 680-g mass is added)5 -y/ge 7(s/ uy0nrknx frtte to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a s5wzxwdq t )6yi*87bte6 v-duu pring vibrates 3.0 times per second with an amplitude 8u7w)i yz5w ttuxdqb d6-ev* 6of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from eb +f3b,fa2s scquilibrium is the speed of a SHO half the maximum value?fbafbc s 3+,s2$\approx$    A

A mass attached to the end of a spring is str b u)j bea:daodiw8-9(w)ve, cetched 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 0.3e ktxnn:3p h61s;u 8dk15 m. If the spring is stretched an additionalpk1e:ndt8 us3kn;6hx 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring*c-2 mpoasj,h with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium posphsj o-* m,2acition, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgu-r.as6vbcw. i++i7m ,izca ftn 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave th.6+-7fi, i+itwcb a rcszmva. e gun?    m/s

  A mass sitting on a horizontal, frictionlesz.c.fbx dt5:xs surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is requi.tfxcd 5zb: .xred to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where rmsg 0-vku2rn-aq 1w7 x is in meters and t is ivwkan -1gm rs2r 7-qu0n 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 g8n*m:umt+9rwuc ) vt a SHO half KE and half PE)*r8u untmgm+v : t9cw? ±    A

  If one vibration has 7.0 times the energy of a sej09.m /zmqn eqcond, but their frequencies and masses are the same, whatmqm ./9eq jzn0 is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every 0e6jykkp1xhp ,/hlkensz p* 7757s i3 o.65 s. 7k6/eo shnjz,i5 plhp7ykx* p 1 ks73e
(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 815v hpmt(1:irqb zek uq2tp6supported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibratz5(p mbh 1e86u 1i:rqqtkvp2tion?

  A 300-g mass vibrates according to the equation x = 0.3qgz0 25akmkf4a g(do2 8sin6.5t where x is in meters and t is in seconds.q( gom22kz 50 ka4dagf 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 an c :*ct h5iritnm(p:5td B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end 5c d u,6c,bhypof a horizontal spring (k = 124 N/m) is struck by a hammer, which5b,6cuhy ,p cd 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 spring stiffne/s*i(gh lg r,ezh+ zs5ss 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) (l 5s/r gsg+,z ehz*hiwith positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two spr lj0z(h/x7l,z y 4xi wnka2xx*ings, 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:x5e:8w ahvaohzx +, k attached to a fixed horizontal spring whose spring stiffness ka:8:zxhxoweha v ,5 +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 bo(zwtz ;lj( ; fu):ibfrom 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 rez b; ()wb u;i(of:jtlzst 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is itlzkm wj/x7c(v,0;pyx (bf 7 czs
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swd9sj/bh,w(/txj xg 4 vbwly7 ;ing per second? (That is, one complete bv,wxtw xh l;yd/jb74s 9/j(gvibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wh y1b0ajb:sti4 4j3 wrlere the acceleration of gravity is about 0.37 that on Eail3j 40wtby4sr bj:a1rth?    s

  What is the period ofii ;5 ,p*8bnf)iug ilkb lao*4 a simple 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 bob has a mass of 3;cxq vho6a w n:1y(( ipiuyn:+65 grams, and it is released at +i(w ;xa (cph yiu ::1yqnn6voan 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 se6gm) cpvif. bi+ 8oag0cq) .a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulu m .o)s 68gacgiip)efcqb.0+v m? shortened by    mm.

Derive a formula forkxuzq:u;4sl 3 the maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz.y5zf y d *qwvb1l5y, yk9vtk2* At it is released from rest starting at avbty y9v15*kykl 5q2 ,* dfwzyn angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boatqc yo(7v)xt2xsbyc*fzjk1:l58ph p9 every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wavqob1hyjlfx5 )k cvyp:29 (sc*7zpt8xes traveling?    m/s

  A sound wave in air has a frequency m* zn)+8amd 2khz51 ed(luaqtof 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressionsdm28nu tdh* 1 5(k+leaza)mz q)?    m

  (a) AM radio signals have frequecbdva7 j3.7c2zs 8)1ddo9sfro ou5 u dncies between 550 kHz and 1600 kHz (kilohertz) and ufz uvr2d91oas38.so75b7o dc j)ddc travel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal w;fo2*yo+*1 qrwakp graves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as s;: lx+c 8 grmes*vku7the other. In which u*l:m +8kgxc;rvess7 rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 ik7 6fcwvtv2:/ut 22xnm o iz5m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from ck7iuxiv/ot6 wt2f:z2n 2vm5one support to the other?    s

  A ski gondola is connected to the top of amzpe r*1y o,h: hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to r*ro:eh1m,py z eturn.
(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 below the surface of the seail fr*c im3a tyf,2*hsz6y s-vfil* (*. He hears the echo of the wave reflected from the ocean floor directly below 3.0 svlia,6**fi-rs ifz* cts2 3m(*yhfly later. How deep is the ocean at this point?    m

  P and S waves from an w.ith5sy hi2ss/49w kearthquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance iw.5w 49 i hss/ktys2htook 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 z hw4fnvpbo4)b .vae:3*qqvjs y /z2*be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is neede2s wn/ovy.peb4fav z4 b3j* q)vh: *zqd 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 amp*7n/if) nr6fksm l-1zoared9 litudes, of an earthquake P wave passing through the Earth and detected at two po es nn6-i/9fkrr mdfl)o71z* aints 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through tql2.os3e(uo/ 9e tt nxhe Earth is measured to be (ot2exl t.u ns/ eq3o9$ 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 samelsbo+fls -,j-pnpg /* portion of the Earth, but one is carrying twice the energy. What is the ratio of the -gsbn-f,lp+pjl/ os* amplitudes of the two waves?   

  Two waves traveling along a stre96 11h.s aag;q/ lwlgzwvt0dptched string have the same frequency, but one transports three times the power of the otherq ht zasp61;1dvga./ llww90g . What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total vert o-wty7fquk )96l0qn cical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease-clfo7t0u6w nkq9) q y to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (kmj)vwp:zq+ dr0j z,3a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a fe,+zwrqmk 3:j )zj0vpdw 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 fc4tyg1s4v3yl d7o (uhundamental frequency, what are the frequencies of thecu47hv(to 41gld y3ys first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what i s8:1bz -sd* p trg/5hskl8cofrequency 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 az5bssp-i* l rkt8o:1 d /8hscgs a standing wave.)    Hz

  A particular string resonatj-p.yh he;mofgk 1 +m3wut(0l kt 3d+jes in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it willjkg+-fd+; lhkmte3 1 h.omwuy p 3(tj0 resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If (7i6t q3,ulj 1 8 rqjvwbd1gow5dl3pfthe frequency of standing waves is 475 Hz, how far apajw3rd5wq 1j 3, d bl6u7vilqf8tgop( 1rt are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whzslq4xp/k:i :3ma3 o mat is the frequency of the fundaz4: i:kpm3qlso3/ axmmental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dz*q/ xavvh4w5f w,vx 1istance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N ax v4x 1vqzf/w,*wh5v. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hr// skpy f+n jb9rq2/y xj.c8gz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are, 9j/sfkr8/2brxy/ .jcqn+pgy    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measurjb aeu 6llz.z.8r0e/ ied to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased byu86.l0az e /i rebj.zl    %

  One end of a horizontal string is attached to a small-amplitudeb43h +ats.(w,je hd/)fula;1pwtla b7dg rs 2 mechanical 60-Hz vibrator. The string’s w/ asp)e;,32f7 awdhrld.bs t gtljb1u+ (a4hmass 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 bei -qupy0gmz k n5q6:h( adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cmqz:ymug 05p( iqk- n6h and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency, tp.)ps3 scz: . l9wci sq40g m-cn6uecqhe water alternately rises and falls at each end, remaining relatively calm at the center. 36psg90mquclq- wcsz e)4ic . s.cnp:Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary sp3dey9 x)b67px(tefg p/6kd within the Earth between two kinds of material. If it approaches the boundary a)gs d( 3tk6pyexb96pdpx/7 eft an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf”,/ l6vzd tzfa6 where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests zatz /6d6,vflmake 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 lrxs)x iv gpu5v c 7r7t60x)o+sayer of cold, dense air. If the sound wave hits tv+rrv)x c 5t6g)s7i xxs07uo phe 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 between two types of rodn,ee2a).x3i di(/1uad ak bgck at a neda.b eu),/kx2add( i1g a3i38 $^{\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 manual/h m7p4 7zuahh, the dish has to be pointed in the direction of the sp7uh7/zh m4ha atellite, 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 trg* l qh;fnrm*)m93mb7:maptc5g/v j havels 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 knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see strandedgg ntm mbvl*)7qa*;hcpjrm 3:/9fmh 5 fishes and boats.)    min

  An energy-absorbing car bumper has a spring hpo-7g9ey g+x stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mas e-yo7 +hpg9xgs 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 18 m belo:pcdms i +7j8q5 sj:pcn.6sbl w, which stretches the net 1.1 m. Assume tha s6:+ncpspsdclj7b ijq8 :5m.t 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 placedw2mz2er,l1bp on the end of a freely hanging spring. The mass then falls 33 cm before it 2, zl p21mrwbestops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a hmf 3q55+qh- k5gou 7jyiwu:peuge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the sp-+uog: i whk7ufm5yp5ejq35 qring?    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 (diy urq7 dwl 6lnl3f5i2i(z, 9qtameter 8 cm) at just the right 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 coffeeqyz9qfli6,i3ld 527r nu tlw(.    cm/s

  The ripples in a certain groove 10.8 cw9l;5 h3/9be p3svmy8asbty fm from the center of a 33-rpm phonograph record havaf/ ph 5vy sw 8;9bsyelm3t9b3e a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.nc wf23x41 z:.d.pkz txi g0nf*(rlsr40t where x is in meters and t dpf01 ( *4snzg.krilxfxn 3tz:.c2 rw in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if it accelv+w(n e,tth :cerates at 0.50g (acn :whvtt+e,() upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a656 bhy(jqe byr (fg;l lake. When a 75-kg man stands on the raft, it sinks 4.0 cm6rgb5 b6;ylfehy (j(q deeper 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 atd - qtskr50g(gi8r1hb 392 Hz (G) and 440 Hz (A). s1bhr5- kgdq80gr(ti
(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-parxd0f oz s)*v3ft cord of Fig. 11–33. Determine a formula (a) for the ratio)f*3vz x dfs0o of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and tcvl1e jvpu(95bgr6 -j-5 jgd fhe tip of each prong moves 1.8 mm to either side of j f91j ubpvl j-v -dr55(cgeg6center. 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 frel3:x)f l)8o g;q mnypwwnm;n 5ug89gs quency 1.5 cycles per second. Whum wn n;sg3 fgy mx8o8g5)l qnpw9):l;at 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 ring th .w8ffndg6k2bz) iru *at 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 otiw.8 f 62znuf*bd )grkher free.

  A “seconds” pendulum has a period of exactly 2.00 8(uab9qd2 vuw0 s — each one-way swing takes 1.000 waquvb89ud 2(s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or can 3xc:t*0t o mebswing 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 whaco:*ttmex0 3bt 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 sh r6toov 93(vatretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulsesat v 69hovro(3 first meet?    m

A block of mass M is suspended frofq8g( 3uws5- cby pg5nm a ceiling by a spring with spring stiffness conbw3g- 5(s8fu pyqg c5nstant 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? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at thl 5kuy:urta.9jk*w+02 kl saie junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. Whatu.5a l*jik09su:+ 2akw rlky t is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a pla+ w.ad ohpy3s;z/j* aste 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, given that the ss /.opa a+dz;*jw3syh hear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz