Give some examples of everyday vibratingt2b72g*c,8b r bek* 0zzirha d objects. Which exhibit SHM, at least approximatelkib,r2 g d7*htcbbaz r 0z8*e2y?

Is the acceleration of a simple harmonic oscillb9e(cvo . p8wikw y55lator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine k 14bs(ehu21yt : o hks6-qjycis approximately simple harm2qss h: hc4tubk 1o-jk1eyy( 6onic.

Real springs have mass. Will the true period and fre/.xhpaqt, m5b hpl4 3nquency be larger or smaller than given by the equations for a mass oscillating on the ex,b4hla.p q/mnt 3h5p nd of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (Sb9a 2qhd5tmtt3a8d v(HO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, qmtrtrgd)v.jc0s/-y7k you 2hf o57r2; e h6 land then is r5.y-6 jt dvtryoqrech7/)og;2urmk2l7h s 0feleased. Describe the scale reading as a function of time.

If a pendulum clock is accurate azcv hv w8b7k+/t sea level, will it gain or lose time when taken to high altitude? Whycv7hzvwb8+ k /?

A tire swing hanging from a branch reaches nearly to the ground 76g1bmfth /w)fcumtqd8d ( a,(Fig. 11–48). How could you e( hw 1fm 7bq8ta6,u/ddmfg)tcstimate the height of the branch using only a stopwatch?

Why can you make water slosh backolo1 vo v-3st1po ii48 and forth in a pan only if you shake the pan at a certain fre1o1tvs8l -3io ovo4piquency?

Give several everyday examples of resonsd59 7fjpg;m gance.

Is a rattle in a car ever a res zmm. lx(z(bi2(e( yrronance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its source?wu fy,8dq6 cdopf9y)1 .b 2rmv; uxk8u Why 9k ybw6p81c of, dxuy.m8);r2u uq dfvor why not?

Explain the difference between the speod4 )3pgae;gzk w-d0zed of a transverse wave traveling down a cord and the speed oz;pa0)g3 dwd k- ge4zof a tiny piece of the cord.

Why do the strings used for the lowest-frequency 9wl31j dh4p pg n2 n4pu.v*jernotes on a piano normally have wire wrapped around eg2wp4 4jnjnlp3 p1hd. v*9ru them?

What kind of waves do you think will travel down a horizontal 9- sbmtq78;e38yk9ptv foxjd metal rod if you strike its end (a) vertically from above and (b) horizontally parallet-jm 8x vo 9;qkfsdpy9bte378 l to its length?

Since the density of air decreases with an increase in temperature, but then ,5)ljo/ akvu bulk modulus B is nearly ilv/ak5u)jn o, ndependent 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 amplitude as they t4s5e mk:vby--lj tn q1ravel away from the sourcs4-qlj ey1-m v:tknb5e.

Two linear waves have the same amplitude and speed, anxnt6g1r ,7a trd otherwise are identical, except one has half the w6a g rr,7xtt1navelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectionsv*dbu gu0.g. s of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain wg vu..gd sb0*uhy.

If a string is vibrating in three segments, are there any places you could tou:l0kzxbjd 9x52kkj2 tch it with a j0xb l92jt kxd:kk z25knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrat1esl* d9tyh3x8(m; pxbnv kz:ions of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explainyh3vblp(m: ke9ts; x8zx*n1 d.

If we knew that energy was p,zkt8w4.k (ml 4pwk obeing transmitted from one place to another, how might we determine whether the energy was being carriep4tklz 8 (,pwomkk. 4wd by particles (material bodies) or by waves?

  If a particle undergoe6 q4z gs(p/xtls SHM with amplitude 0.18 m, what is the total distance it travels in one p/s(lzg p64xt qeriod?    m

  An elastic cord is 65 cm long when a weight of pqs ;28buq+ku 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 e8b+2uq s k;pqulastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drivp5qp./q)ptcd.3 e amsbv2 3vr er gets into the driver’s seat. If the car goes over aqp dv3e5pp/q )b3a.2 smct.rv bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs froz)qqu3u *nc 4im it. (a) What is the spring stiffness ccu*3 n4uiz )qqonstant $\approx$    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 vibraerkn/09 qta *stes with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs fromse9rqn tk a*0/ it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–ai+*hf q1jx2wm* lyj* 2 at times t = 0,t = 1w*2 + *lxiaymjhjfq* $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 c*va aupry7-9 .0wrr odaught in a spider’s web. The web vibrates predominately with a freq rw uyp9o7 vr*a.da-r0uency 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 ohcsef)es)awd -i 1 3j2f o-t;jf a spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What))-ajfi jte 3s21dhw-;scf e o is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with azk 2+toxy.g/ qah jn.(n amplitude of 0.13 m. Deth2n./( jqkt.oax+ z ygermine
(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 maximum v;wu jaf(dy3- lji5*qzh,+gjo alue w;jfa*l-uhj, ji(do +qgz3y5 ?$\approx$    A

A mass attached to the end of at04s)/l,ettxkn5.y9r fv/ 3rp+l qdne km6kd spring 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 stretches a vertical spring 0.315 m. If the spring i3j*sz 8bn+ nhjc.tiz9s stretched an additional 0.130 m and releasedinzn3s 8j ch9*.+tjzb, 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 with springxnrp x / +7nwntnsl8j -pa4f)* stiffness constant k = 280 N/m and is exe n*nnsj4w7-px/rxnp8fa+l )tcuting simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m (1pfs;p6f:(r7 *v :g8rmhntyqjzamt to “load” a 0.180-kg ball. With wha:nh* v rm7at(mfp:6 1t(sqgzp fj 8;ryt speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, fricp1 hmpd .hrr35tionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 m1 ph5h rrd.p3J 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 according to the eq*0-)v i pdu 06n.c9rvvlhgbfruation x = 0.45cos6.4t where x is in meters and t is in seconds. Deter06bugicld0*9 )v-hr.vn fv rpmine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and half PEj* a8khhc t5i :i/dqp4?:4ii5ca/h8 tk hpqd *j ±    A

  If one vibration has 7c99ucywhsl4yo5 3l d9u+lvji:y 8kd -.0 times the energy of a second, but their frequencies and masses are the sa 9lo4ckijus ydcu w9l5+dyv- 8y39:hlme, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a i)sifmdp 9kwu.; ugu j 6f8w/h 72l:levertically hanging light spring once every 0.65 sui .w:/eff 9lk; g27w p lj)8uhmi6usd.
(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 n -hp -w1n.p y(+/zr8yqzojglv*ikg 0supported by two identical parallel vertical springs, each with spring stiffnen+l i1 -n 0p.v -ryz/gq*y(kozpjg8whss constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equ744m/qu(kng (mj2g q 6 /qvofpl yyp-uation x = 0.38sin6.5t where x is in meters and t is in seconds.u q4y-l 4qgfjp(7uy6mqmo(vp/n 2kg/ 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,/d6gzb wjqbgwb+; u1sm.wp30 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 resf5ah5hb rbe*b5c-h w3 t on the end of a horizontal spring (k = 124 N/m) is struck by a ham5ch5hrb 53e *hbbaw-f mer, which 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 stiffness constant 305 N/m8-e1 fjj;sgq:j/ to ly vibrates with an amplitude of 28.0 cm when 0.260 kg hangs frefs /qy- j1jj8: lgto;om it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spr s/p( xxzgd.n*ing 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 fixed horizontal spring wk2cq8ep cno2bv+c0w:6yhi)rhose spring stiffness c2:q 8ocyn 2ic0 pb)v+hewk 6cronstant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reachinkn /b1vedi(u5 g 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. Cvb(nde/1k i5 ualculate 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+ f c4poz0bzz(m-qq:i exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make e0w/rx7r . wv1kan2eef xactly one swing per second? (That is, one complete vibratiorea .x0k v1/nrww f72en takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What ib4f m-hc0l1v7eb)r7(hsw( kwzx c +acs its period on Mars, where the acceleration of gravity is hvfbcse (zw 0kh w 74r c7-+a(xl1m)bcabout 0.37 that on Earth?    s

  What is the period of a simpleq(vr 4n2j pus, 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 penjfc lu+b6l)8 wdulum bob has a mass of 365 grams, and it is cjb+l)lwu6f 8released 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 cloc4)ghwf8 bs-qyay o,g)tl1flbbagrm:g ,w 5)+k’s pendulum has a length of 0.9930 m. If the clock loses hay+l ,ab8)bawhg qgrobm5 -4wl1 :f y)gst )f,glf a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximumer7.,h gkriz:l 8 l4fb speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At idi5. 6o)o kxont is released from rest st.k 5o6dxo)n ioarting 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 wr * 2t-vic0y,w+drpkr ave crests pass the bow of his anchored boat every 3.0 s. He measures the yt cv-dr,+rwpki *2r0 distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels withqsaq7(z;oo y q) *iti4 a speed of 343 m/s How far apart are the wave crests (ai z4qot 7y is)*;(oqqcompressions)?    m

  (a) AM radio signals ha r-o9djs6fm j;ve frequencies between 550 kHz and 1600 kHz (kilohertz) and travelm6j r d;sf-j9o 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 htnv- 9/;b9y vx5e2ian x mis8of longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same e+qffjj cwtsk9g1s,3 nb5umzv- 4v++ plastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be 3 -nvu1jwz ,jsp t+sgmqv+f4k +f 5c9bgreater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppo*ve.lz0 qb27p3juar h rts 28 m apart. If the tension in the cord is bp7u zh.qj2*vel3r 0a150 N, how long will it take a pulse 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 lenx:93hfho2g /z7s l fuzgth 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 hx o7: z3h2l/uszf9fgit 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 below.dckc. u; 4ogcrr)+muk6 wgo ( the surface of the sea. He hears the echo of the wave reflected from the ocean floor )m coor.wkr. 64cu(cd gu;g k+directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at differjj u e(o+qfpltv2 w1 0sc r7ln-+p))au 8:rgkbent speeds, and this difference helps in locating the earthquake “epicentef2 :tu)p crw+oqnkbjgse1)vpu- l j(0l7+ a8 rr” (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 blu/l) tf2rj13h ;wzfoy a sinusoidal transverse wave. Assuming a 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] uf1 hzrfl)32w /lto;j    m

  What is the ratio of bf *(mkft:+40fgml /,u7cirvpla aj)(a) the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the sc(if fv )m:r*maa0jtb f7,pullkg /+4 ource?(a)    (b)   

  The intensity of an earthquake wave passing zb vtosibm,k /z:17v0 through the Earth is measured to be 1 , bbim/ ovtzkz:0v7s$ 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 samdgzh0xp0t 8,ve portion of the Earth, but one is ca z0tp,vd80gxh rrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched sixa8q(af;2l h kjs t 3;7a6eh4hay;cctring have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the ts q iyf8jht72ahch;3x;e (la6a;kc a 4wo waves?   

  A bug on the surface of a pond is observed to movel 49r0 spek7anh d2i(t up and down a total vertical 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 factor does the bug’s maximum KE42 irl0 dp7eatskhn 9( change?   

The two pulses shown in Fig. 11–52 r:ui bu ;kpxe;;,i0lware moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–3;,;0xiwl k be;pui:ru 6a, 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 vib55k7pa1han r 3xbeph3m oz4ha8u3 nl-rates at 440 Hz as its fundamental frequency, what are the frequencies of the first7p1835nurhn-ap lh ko3mxza 3 eb5h4 a 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 frequency wigckeli5z (+,r ll it vibrate if il(z 5,er+c kgit is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates b-ng; sda:mp ql6*qgli m9y8ni.pb-9 in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will r*psm8ap;ydin.- ggln:lm 9 6i 9qqb-besonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on)e 2cei5ipa2)n0v yc n a string is 92m/s If the frequency of standing waves is 475 Hz, how far ap)2cvny np5icei0a )e 2art are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 20arnc8(7x8kk mp0fa *r) btub80 Hz and 350 Hz, what is the frequency of the fundamentabc7an0 0r*ka)8k p t(mubx8fr l?    Hz

  A guitar string is 90 cm l3hk7 qiah4h 3long and has a mass of 3.6 g. The distance from the bridge to the support l3 3hi7hqk4ha post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it isd( iwzis9sham43 k8*ye,w q )k measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So thkd)34q w*ae ,h wiky(smzs8i9e three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to6vtelh:9 -lqe vibrate at 200 Hz, but it is measured to vibrate at 20he-te9 6l:vl q5 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-ampx 059sim5 aikhjbhy-:b2)jg x litude mechanical 60-Hz vibrator. The string’s masmxjbki:5x2g-)i y 5bh0 hjsa9s 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 movingz0 xj5)pw 3saajga2i0 the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patters0 aga 30i)zjwx5aj2 pns 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 freqg/v+ y2uk; gz2;sues q,zq5dluency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose thu zqeg2qgs+;s5 lzdv2k/y u,;e 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 within the Eadajq 2pr 1 s/fj(y4x4srth between two kinds of material. If it /aj2jrsqd4yp sx1( 4 fapproaches 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 under0 7m*1f t+ffmx8vswsz water “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests m 0 s+8*fxwsff zmv7tm1ake a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense air. I(vg mbmw-2 s66nh t(laf the sound wave hits the cold air ina2m t -hg(m6n w(slb6vterface 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 5 efkccnd 8-r)two types of rock at an-k5 cre 8c)fd 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 )wq5fr-fv,bw ae-m6fthe user’s manual, the dish has to be pointed wf65mr -bv)ffe a,-qw 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 travels24*(xp;fz fsxasje4n 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 pf(z ef*x24ja;4nxsstsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper ha b8 prb6l a:kyjuj sm90:xk45os a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Uurkj:6mab8b:o4y9 js5xp 0l k se conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretc2l) +/h2qsdtf 1m cnnk* ukct0nb6rv*hes the net 1.1 m. Assume that the net behaves like a /r m0n )t +s vcfkbk2hn2c*6u1qnt*ld 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. Thm+2yc*d,x ebl jnx* (hb0;o pve mass then falls 33 cm before it stops and begins to lovpecb;h0,*x dx j my2*b (n+rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a hrfw 6y 3sj *0.khsm(dyuge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness co6* d3kj yrys sm(wh0f.nstant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace of aatnw-baa a b1:e2 )l3wbout 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the spa a wwtbaab1:n l)3e-2eed of waves in the coffee.    cm/s

  The ripples in a cer-kugr.bm yq 0ocog6 ;3tain groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelengthogm 0urb ;6-.cogy q3k of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the eqm-sifr fvw7do+n4hd 17xtnq;s1f x ) *uation x=0.650cos7.40t where x is in meters and1 )h4nrtfx +*- 1x q7f7o fvswsi;dndm 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 with frequen3rh7u/+s xupccy f. What is its frequency if it accele/3 +crus7 huxprates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floatr6dnzvprrf) /2ef(f ; s on a lake. When a 75-kg man stands on the raft, it sinks 4.0 c(pnr);r e/f dz62fr vfm 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 pl6q ;x51qcenhuay at 392 Hz (G) and 440 Hz (A). e 1c nx5hu;qq6
(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 ofaue ae/3 7r uon(( 65eersgkf/ 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 ths ku/ re6rnag/ 5e (eu7e3a(ofe 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 fq6i/5)jxxny lrequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side ynxjl) 5xi q/6of 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 s).rwsfz.cj6 jb-. ykx imple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the endyrx kw.zb f6.js-c.j) 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”bw /lj 2sn9fbfa/ gz54 end if that end is attached to a ring that can slide without friction on a verw sbgfzn9bl54aj2f// tical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exav:9 wlfz)d.(/ taemgn ctly 2.000 s — each one-way swing takes 1.000 s. afd.z nev9(wl:gm/t )
(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 9w10inc /*tm n1 ywpbaa spring can oscillate in the vertical direction or can swing as cnipab/wt1m*wn 9y01a 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: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pulse dg6 e aj)/ b0oa6+ylagis generated at one end, and 20.0 ms later a second 0j+a/bydg6 ago)l a6e 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 wq -t13-. lb;q6sspuxg ifs ct,ith spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny toslq;x.f1g-i s bp,c qst3- t6u just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at*(+ i5d enwbxr the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A+xe rdbi*n (5w breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also 35ztzbd /lhbey) ::txgives 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 vibratio zex):b/zb :lty5 3htdn, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz