Give some examples of everyday vibrati-vdhfdb wp3645 e)2mhpk2xgx3p)b 2 g atpj) ang objects. Which exhibit SHM, at least approx3hp5 pp)p keavb-d 2dggwh))mtb2a x62f3 xj 4imately?

Is the acceleration of a simple harmonic osci5ye( * -pcg.pc hryc:-xg,zkpnlb v (/llator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine ifyt(9v)nsh lz*bxz;)o t9 /fls approximately simple haoszty9vl tx)blf)(9/zhn*f; rmonic.

Real springs have mass. Will the true period and frequency be larger or sm*3 -y1usgx lu mo.gci+aller than given by the equations for a mass oscillating on the end of a3gguc*s i.+o1- um yxln idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHOqbv wr+.qsc9nys0+h lppfpt3 n ;10 0o)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then isra.76 es2f cox released. Describe the scale reading f7arcseox 26.as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose timenw,vhpm .s 6no4h(k3b when taken to high (,kn 43w ovbphn sm.h6altitude? Why?

A tire swing hanging from a branch reaches nearly to tvw p/su ;j.mvpi/ 2t.mhe ground (Fig. 11–48). How could you estimate v.w/2u tpjsm piv;m/. the height of the branch using only a stopwatch?

Why can you make water sloshlj4y9bi2wel 3pyo. bwakii. o u5w,7 2 back and forth in a pan only if you shake the pan at a certain frequenc,kiwo uyw3 liw 9j4il.. eya 2opb72b5y?

Give several everyday examplvo158 b1d/uf yt( wllles of resonance.

Is a rattle in a car ever a resonancqg;k/j epq3a/rbgy+ ptqer+vz80(: ie phenomenon? Explain.

Is the frequency of a simple periodic wave equal to th7gjm:jc ;yf ,5if ikf.e frequency of its source? kf;:5m. ijg ,j yf7cifWhy or why not?

Explain the difference beb+;. mq t8clea vx19+k djg.mstween the speed of a transverse wave traveling down a cord and the speed of a tiny pie+mk9l sv am c.eq+j;b.1t g8xdce of the cord.

Why do the strings used for the lowest-frequency notesdq,0-bgn2 s ,, wckjvr on a piano normally have wire wrapped arw2, r,q-jkg ,b sn0dcvound them?

What kind of waves do you think will travel down a horizontal m/xki 97h0dn8p lwyhm 3etal rod if you strike its end (a) vertically from above and (b) horiz 3yid lmhw7np980h/kxontally parallel to its length?

Since the density of air decreases with an increas90g f0ovx w(l-t )aqnue 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 twv(ux a00flogtn9- q)emperature?

Give two reasons why circular water waves decrease in amplitude as they t4syak abw y1p*frh5 *ig+ps/:ravel away from the sow:* /aapb+ gfry5i hy1k4sp*surce.

Two linear waves have the same amplituddckq wy(2g 3(n9is:-op ;esra e and speed, and otherwise are identical, exs-r(i owp(n; :ae923dy gkqcscept one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave cs, .;fs lb+428tgmkb*io:h rko,jjvy rosses the boundary between two sections of cord as in Fig. 11–33, the fgbjr.yh , of;*l2k+t bks:mo4 is,8jvrequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments,qf,paft4 :x8 j are there any places you could touch it with a knife blaptqfx 48ja,:f de without disturbing the motion?

When a standing wave exists on a string, the vibrations of incidew/mt/r wdb4 0hnt and reflected waves cancel at the nodes. Does this mean that energy was destroy/rwmb0/th 4wd ed? Explain.

If we knew that energy was being transmitted from onuvio dwd;c .8:4t0; qttwt7o we place to another, how might we determine whether the energy was being carried by particles (material bodies) or byvq47dt:td c.0uowo;wttw ;8i waves?

  If a particle undergoes SHM with amplitude 0.17gg -u hm7ywz)8 m, what is the total distance it travels in one peri7z h g-wuy7gm)od?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but ige;s:-n7. c0z uqfh36rufekbs 85 cm long when a weight of 180 N hang73.gsrub0hqfn:ecfu;z k6- e s 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 ygb as;k/* g snw39+b-nyddi0 when its 68-kg driver gets into the driver’s seat. Ifd0gb; s 3nnwyg*y i-sb9/adk+ the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm wg)fox opew) v 1iw1 l(+ 0l2(uwaskn*hhen a 2.7-kg fish hangs from it. (a) What is the spring i0swpw1( n hlo)wfalo1v *ue (+k xg)2stiffness 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 wit,gjm n4rn4ma )h 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 4 ,j4rnagn)mm hangs from it?    Hz

Construct a Table indicating t6 h 0fcxi)ofd7he position x of the mass in Fig. 11–2 at times t = 0,t = f xi6ch d7o0f)$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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,foq5jza4( nwt;da 4;r9 qvzz web. The web vibrates predominatet,nwfrz;v ;q z4a59 aoqd4j(z ly with 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 spring vibrates with a frequency ofqy9r/ vtbm12pyq,iqh7 *tq o+ 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value9yqyq1vh7q*/ +,r2m pbo qitt of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with imh2y (kb i,40m w-tlyan amplitudetmi (wyh-yk 04im2b,l of 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 equilibrium is the speed of a SHO ha1: mfgpbp1ji2 lf the maximum valui2: pm1 pbgj1fe?$\approx$    A

A mass attached to the end of al69ym2 n8t/ s3k+zhiwh7zfki 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 i,)if /sb+ta ee*ci1r f.h*:tqdu(ha m. If the spring is stretchesea i)/ct * h:f+brihdaf.*qt(1 u,ied an additional 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 sprimnz u)/a;6p(a uv ne-gng with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its eq(n guv;m 6apeuz-an/ )uilibrium 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 .jhl; kb3mt-l 80.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what b.lmjtklh3 -; speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one .,ov;il.2w 4f8zs ejoi5 dy qcsq-y /tend of a spring; the oq4i /;y qt8w.jd -svc5if. oly sezo,2ther 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 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 vibra;gcjn-ccip0q: hjp2kl3:l0 d,4 q lmxtes according to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. 0 ic,0 cp kg4jpl-2;j:llnd3:c qxmhqDetermine
(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 equilibr8ljpl;2-ym. m)c g w9vb*d perium is the energy of a SHO half KE and half PE?j8vwp*) ;lrbmypd.-9eg m2l c ±    A

  If one vibration has 7.0 times the energy of a sec)g1ac r 0swno/ond, but their frequencies and masses are theg1 )sw0nr coa/ same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a e/edtnx+m xv791+jcfvertically hanging light spring once every 0.65 s. tx f1xen7cm /+ved +j9
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel verticaeobyqc;97t 5nl springs, each with spring stiffness constant k (Fig. 11–49). What will 7bt nc5eyo;q 9be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x ifiey y,u 7kmu 2qux1/(s in meters and t is in yu fx,u(q1uy /mik2e7seconds. 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 andq*c.-fxial(xk qs* u 3 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 n3uamrd d2(8,fzkc y vn(iu0o2mkl5 6end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/skka( (dr fnz82ldvm36uciy o u0m2,5n 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 st1/cw: uloe(c 1+ crgzsiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equil:1(lg o cs c/1ue+rwzcibrium 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 t)pijdy4)ido ) qd ne+nqbp82 *o two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-pe:ogup k,n0h;)hp (;.mozjokg block attached to a fixed horizontal spring whose spring stiffnepoo)jp m(;0e: .khnh;,zg upo ss constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching his lbwr pim4a px 5(u0y .u5z.x9liowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to resryau.5 0u.(z 4xx5lw9mp ibi pt 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 u;5umx:u *btb. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pen 95 aj)lw*y7 2cfom0vp xrw e.ld*xxr8dulum be if it is to make exactly one swing per second? (That is, one complete vibrationll5m. px*rwx c2 r870yow9 *xdavfj e) takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. 2 n.n,kq.cu ahWhat is its period on Mars, where the acceleration of gravity is about nnc.2 qhak,.u0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lpphbv5rx 8dc e/,80)1ibme yxong
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760b flrwe 938 i:dv+zzyl(+tr 0 u9-rx+qcf dh9h m, the pendulum bob has a mass of 365 gr9r3d(u+tb fr-ilhfy lq+ zr9vzx89w 0:+ecdhams, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock lo6krh6ttlf + 7ises half a minute per day, how should you adjust the length of the pendulum? shortenef 66ti7r hktl+d by    mm.

Derive a formula for the maw:di ts3zh(4p ximum 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 it is released from t8dk1kk5yj+sjs -f f.4 kmn-wrest startingyk.f-fkm jd5kj +kt-48 ns1w s 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 b /rd5b3m yhf1;u 6flzonqr2u3 ow of his anchored boat every 3.0 s. He measures the distance between two crests u3hu frnbz2;6od 31 fl5/yq mrto be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a y 2q2+1+ ( ppxpz 3uhkao4 m(uwuniem0speed of 343 m/s How far apart are the wave crests (compressions)+zm(p(wq2k n3u2upepi4a xh 0u+ 1omy?    m

  (a) AM radio signals have frequencies bl wv4/yv4om- hha 3.ztetween 550 kHz and 1600 kHz (kilohertz) and tra4o wtvhh3.l zm4-/vy avel 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 c 1+;i d5 cyqtrmo4;;ad*yzwtwaves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is w-p.bu2hvddc- n 1 .vnl.jh+stwice as dense as the other. In which rod will the speed of longitudinal wav.hhnc 1 jnvd+wd--v bp us.l.2es be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the tens 6er wthf9k ;;uy)2/xxi4xahrion in tw/h k rra4t 29 ;eufy6ix)xhx;he cord is 150 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 ys7sd*lu;p t aq 9b4db4(ufo; 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 pul *(busso a;47dlb dq;tf4u9 ypse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the s n31yn*t,y t nk, 1beg80nwgnmea. He hears the echo of the wave reflected from the ocean floor dirn 3nbtyny1 e8k t1n*g0 nw,gm,ectly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this diffd *;x:w u17ah p8rux8 mtjml7oerence helps in locating the earthquake “epicenter” (where themh*1;d7x8r:p 7jmu8tw axo lu 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 sinusoi-pm/qdt/: 0i2,sqo7,nda pd vr1 ni;up rdri 8dal 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? [Hinqt1r,u2i d8-:i ;0 d rp7d,oqvm n/s prida/pnt: Set the acceleration a>g]    m

  What is the ratio of (a) the inte*tm 9sgp fdr.4emw4vratc8,r x*s-h-m t*2e x nsities, and (b) the amplitudes, of an earthquake P wave passing through p*t xr sr m 98.-*xme ,r4 dhs2ac*tmfg-4wtevthe Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measui++wzh : xsq9kred to be zw hq+: +sixk9$ 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 same portiock21ij :sz* vkh+r+mpn of the Earth+k2 vzhj rp:k m*c1si+, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the samej9h .tcp8rv,-bmb j5 y frequency, but one transports three times the power of thpybmbjh 8v, jc 5r.t9-e other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total srg; rcdy4b:k-;*d o1 rlhu k-vertical distance of 6.0 cm, from the lowest to the highest point, d rry*- rbl 4d;hkk1c :s;uo-gas a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each ot1xp,t:3jj xy v sm;f2cher. (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. 11–36a, at the moment the pulses pass each other, the string is straight. Whaxpv j 1cf3:,m xjsy;2tt has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its f b2slanf-;kp ku9 (+ j5971ntfcdx8tmmj)wtlundamental frequency, what are the frequencies of th fjlbft 8)t92-k(7sn1tx pa+jc u;mk mdlw9 n5e 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 frequency eqi6k5 g hj p;h-t6r*mwill 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 a tgi r6 kep5q *-hjh6m;standing wave.)    Hz

  A particular string resonates in fx, 0g2mlt2 xoo:-: (pfg snga9gjw2ihour loops at a frequency of 280 Hz. Name at least three other frequencies at which it will rjpo mf x02 lwg (x:t-ia9gno g:s2h2,gesonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequencyu f3k7em7ukl; of standing waves is 475 Hz, how far apart areuefl3um 7kk7 ; two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what rmkz)1jl6 kgoje:i 9k kfl255h: wf*p is the frequency of the fuho2e9 k1k:lpjf65l kwk z)m:fjir*5 gndamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance )cka3g e1(no afrom the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies(gk o1a e)can3 of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but 7 13ul0gtqisx 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 asq10gt li7x 3ure,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hzpg/a-jnng . :w, g,tfh, but it is measured t. agw ,n ,-n:tj/fgghpo vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60-Ho3nd) dgm8cq.rf3:+ sx en a.ov(fm*fz vibrator. The string’s mass pe+fmn: oq(mfro .sde.xd*8vc3 )f3ang r 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 moving the pulle( ft -96y+gilghlp3mmy f)j-by. If the hangingm)fm-yp6( fj+y bt-g h3l igl9 mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forthwqy9 jhk7.c(dpe;r (t in a tub at just the right 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. Whayw7hpq .(d;k ce( 9jtrt is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary wick g)- 1mefd8jthin the Earth between two kinds of material. If it approaches the boundary at an ie8m djcg1 -fk)ncident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the vele3z 9dl *yzp6v5h c(zxocity changes from 2.8 m/s to 2.1 m/s If the inc*hypdvx96(zcz3zel 5ident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in /t0/l*mv;6z eyryk*y/qa v sll u(i s,warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at anll*vsav*l,yyek(0 tuqsmz; r / 6 /i/y 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 stv: p.+mojug)q8r b 4hrrikes a boundary between two types of rock at a.r) mgu vh+:rqpjo 8b4 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 fi nou10gzf0vks7n 90)dtpxt;- ) fdidiameter. According to the user’s manual, the dish has to be pointed in the direction of the0dn)1ito pt7 iu)s9k x0fndg -;0ffvz 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 wavelengtiz85gea89v bf vx+ gw;h 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to s+ga i;vev8 w8x9gb5zfafety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car mthj :i +;6h ync9yw65bjuq7ebumper has 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 (approxicyh5b6;m nh te79+wj:6q jiyu mately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to jnwg+lu bgev4o6h, q *4a0jgu8ne4g ,a fire net 18 m below, which stretches the net 1.1 m. Assume8an446 e un4ueh gbq0l, +gvj*oggw,j 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 (9t gip;s xjqyk+3g5cthe end of a freely hanging spring. The mass then falls 33 cm before it stops and begins;tgj9pc( 5xi+q3 gksy to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fi0h ziq3 (cq7ez.4jdg ig. 11–54), compressing the spring 5.0 m. (zje zi3q (iqc07hgd .4a) 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-rvx0/:zr1 e j xr 7oeqrhka597ae :uf just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over ther ehveef:7 5u/:axz 9j1ko qxr7ra0r - top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the ceddp62hgc6g 2. tt8nkcnter of a 33-rpm phonograph record have a waveln 2p62.t8gdgdhck tc6ength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to3sye)ne 3g ld3fm9ht, the equation x=0.650cos7.40t where x is in meters and t in secs3n3egedm ,9)l h3 yftonds. 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 f2jx);afndpx 3 . What is its frequency if it accelerates at 0.50g (a) upward, fnpaj3dx2 x);   f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stanbb .95vy,gko dds on the raft, it sinks 4.0 cm deeper into the water. When he stepb,bdo .5 k9vygs off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 Hz tke3 89knu:uzm+ /ecc(A).3eucnk z98t/u mc+k:e
(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 e oc:3 kv+4*njra wq6dl+ ke8b1 pv7xxtraveling down 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 same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the kx+plkv74*8rndq6a:31 vxj+beec wo lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tfkevq5w58uy1 ip of each prong moves 1.8 mm to either side fw8k1v uye5q5of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequeqdmg* xv 7vw7t; b4lnw ht(4:fncy 1.5 cycles per second. What is the maximum amplitud tvh7l4 qx ;(mb7:twwg*f4dn ve 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 -1ik1cxcf kxp qh+k,2to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string w xxq21-kih+c kk1pcf,ith one end fixed and the other free.

  A “seconds” pendulum has a pervp*(kp.02u 8cqw vowyvda1u 6iod of exactly 2.000 s — each one-way swing takes cvv*dkwyv 82 wuo6pu10.apq(1.000 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 theb 4; x- wg4gmq:of1znn vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscilzwx1:ogngn; -m4 f qb4lations 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 123m+x/ nea4h vd-3gb:x s g is stretched 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 oppoedn4sx+hmagbv /-3 :xsite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spjtp y .m rrz5vc 6h2/lrn0m*f e9lzh9,ring with 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 to just stay on t9,m 5c*z nrfz0rlyeht lrh6j2/ v9.pmop of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkixvja 5f* ab81f: ztesd5ia84 yard. 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. What is thef 1v:*j585 zedf aiias8xat4b period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as *35i: n6i 6rjmz*4ez eunemvcshown 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 vn6m e**i uzenze435icr6:vj mibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz