Give some examples of everyday vibrating objects. Which exhibi4 5nuld19w2cxnvd( 1 dy.kbkqt SHM, at least appr.(5kkcn9b2wdu1 qdd4 ylv 1 nxoximately?

Is the acceleration of a xx24k r87a kcbps:sxe4 2r8gy simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately s ;6 fbb n8iyp/zhxo6mcokq)d,xd7e)1imple ;,8yxd1ipd) 7f /b6ozek6 mcbnox h) qharmonic.

Real springs have mass. Will th6l vng njj43tkhuuw*/,vvn3 2 e true period and frequency be larger or smaller than given by the e njl4 j2,uhvkvtu*g/wn633nvquations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the :dgu3+ px:n)tdo srx8maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then o5+jwj zc5aci87)lh u76aqw yis released. Describe the scale reading as a function of tizacaih l6)cj75+wuyw 85 oqj7me.

If a pendulum clock is accurate at p9 hxuomhdi):58; h szsea level, will it gain or lose time when taken to high 5i p9)h;ho 8mu dshx:zaltitude? Why?

A tire swing hanging from a bgx5jrg5 r aho2fb+7psq72vy 8ranch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of thera2s+xyg2pj55 7 qgr7ofvb8h branch using only a stopwatch?

Why can you make water sls8*fon4kl;d6ji2r hf osh back and forth in a pan only if you shake the pan at a certainffod6;rsh4ki8l 2*nj frequency?

Give several everyday examples of revh83 rcx nr+9ts/ a9rnsonance.

Is a rattle in a car ever a resonance phenom-yvmm+)5m b9odf ferp q/v *1senon? Explain.

Is the frequency of a simple p;/+ed -uc or dj(xs)cseriodic wave equal to the frequency of its source?;x(oddes -+)j rus cc/ Why or why not?

Explain the difference between the speed of a transverse wave tc3srz8+b pt9x d lak9)raveling down a cord and the speed of a tiny piecp+)a 3cts8rb k 9z9ldxe of the cord.

Why do the strings used for the lowest-frequency notes on a pia zb2l/ s ky4kiukhq ,u,vag9n+ka; 9k5no normally have la,hy;nkg4/,kusk2zk +ui v5 a kqb99wire wrapped around them?

What kind of waves do you think w85tic2nox,d35nqkxi f2 ld(mill travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parall5f 8nx,2m (23lixcdoqdt i5knel to its length?

Since the density of air decreases withc5o;oytu2u w, an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in ai,ut;ou2o5ywc r to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as thdu p.rob m1eh7 da3(prs2aw* f1n4 bo3ey travel away frb s4 rd2 au*fbonoepp1(3 d1m.rh37awom the source.

Two linear waves have the same amplitude and speed, and otherwiseuup(fcwc : l+,k0 2czl are identical, except one has half the wavelength of the other. 02k c +ulu,pfclwc: z(Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as )lkn:rj6 sl2ktx ;w8i in Fig. 112ns6;i:tk )l8klx j wr–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could tdv +1dqb9c-b hkzyy*of30 4 dvouch it with a knife blade w1 3 kdfdcvbv -hzd0+bq 49*oyyithout disturbing the motion?

When a standing wave exi5yfondl8 ;j7hbdk u:o4n*4hlsts on a string, the vibrations of incident and reflected waves cancel at the nodes.:o8fl5* 4d4nk ;yjb7d luhnoh Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmittetbecx3+ v6do) p9 +7x.nkulpyd from one place to another, how might we determine whether the energy was being carried by particles (material bodc7p69x++ etn xvyk dplou)3.bies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the totalz vo j)syn6+c oox3r, qu)bd8. distance it traves6ozyxou q))on c.vr83j b+ d,ls in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cm 6fnscza 43rn1long when a weight of 180 N hangs from it. What is the “spring” cr13fa n6s4z nconstant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gn440 fs j*fmojiw /p(dets into the driver’s seat. If the car goes over a bump, what will be the frequency on4o*j/ (jwi0sdf4mp ff vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fic 5 k8b(wv9rqqil0fw9sh hangs from it. (a) What is ibqvcq5 r09 wf9w8l( kthe 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 whegx( ec97(f,zoky6tk bn a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hayxfkb,e c(6 z(go tk97ngs from it?    Hz

Construct a Table indicating the position x of the mase;mz b:4ja ezqw1(ux8s in Fig. 11–2 at times t = 0,tw 1ezzm qa;ebxj:u4 (8 = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 acr);77u nrby;ahx t zb- uf5v0 spider’s web. The web vibrates predominately with a frequency of 4.0 bruv; )ay7-0urt fbch5n;7 xz 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 frequekmy 2pn4w.g:k0zo9oq/p m *znncy of 0.88 Hz. When an additional 680-g mass is added too m0*n9: .qkgzn2pkwzpy4mo / m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibratht ,x;q 6.8et lzoza5jes 3.0 times per second with an amplitude of 0.13 m. Deterq.;ez 8t, t 5o6ljzahxmine
(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 equilibrijt+zsuqh -7c gt1pg86cje,b4sl8)jvum is the speed of a SHO half the maximum value s zp+81 ejtctugjs qvb8l4)g7,j- ch6?$\approx$    A

A mass attached to the end ofk ;1rab v),wpi8 rij-t f hjskc04es27 a 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 verti*qy)yyk1zzk hr* tu3 .cal spring 0.315 m. If the spring is stretched an additionaq.y k1 )tz3ukzrh** yyl 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,4re-ayk+ wyz d dr+/m attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When+e+my,-zdr r 4dy/ wka 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 top746 +l khldoh compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With opk6dh7 + hll4what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one enraw28v 9slrp iga4i*j;*am-r d of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed,ag warr-9**rpslmai2i j; 8v4 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 xt k+i+l-u qp/epc-a*a is in pq/- ua+k li *tpa-ce+meters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO hkqo)qlt03/ dp rsus ,1alf KE and half PE0 sl)3t/q, kr 1pduosq? ±    A

  If one vibration has 7.0 times the energy of a second, but z-:rxs( b,k) plrjg 8gtheir frequencies and masses are the same, what is the ratio of theirzgsl g j:rp)8bxk( -r, amplitudes?   

  A 2.00-kg pumpkin oscillates from a 6gyjca( otzf :gi9sxuk *cg5q/ 5 ii9x2e+ez*vertically hanging light spring once every 0.65 s(c*g zyu2te so9ci *x+g6 jix5a:kz/gfqei 95.
(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 sups 2e d 5az0+n1jaub vb5gg/u5mported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the jg2a55a dn/u+b01v5submz g e frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5u(6xl3ut yy8ot where x is in meters and t is itu8y xy63(lou n seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what 3jbze9bg/ x9, f*bpq yis
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k v is;:,eumdd r;ni;2p= 124 N/m) is struck by a hammer, wdn,up vi s ;e2d:i;m;rhich 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/m vibrates wiv4hkw l ).9*fcv9mh ahth an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity a hch)lv *a 9hm9.4kwvft
(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 spring stiffneuyq2k.rxw -so i7fht* a;l(pae4r 6a8ss 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 bl 53/ tkgr;+zp -shef,tphz, p zp(ak7xock attached to a fixed horizontal spring whose spring stiffness constant if hz-7,pttxakgkr(p ppz5h ze 3/s+ ,;s $ 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(z: ff(c8ebc w his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rfzc( wceb:(f 8est 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. .n gkmh,dx 5v/h ,h.tzWhat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly on l)al/ jehimi(uq: 26u q4cgn*e swing per second? (That is, one complete vibra2:) /miiuelh (qjq a4cl *6ngution takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is8xn5 q( q3c4z ibu4iqx its period on Mars, where the acceleration of znq4q x8435xci( qubi gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm loecao8 a cgx(o o3 0vh8coy/,3qng
(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 jmudzb5p75bu/k06 t5j8rmt p 65 grams, and it is released at an angle o5md7pu6put8bkm /r5tjjb0 z5f 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 losw2lq mz-1h*cw2;zueqf 7qmy( es half a minute per day, how should you adjust the l -cmw qwyq(h1m7qu ;*22lz fzeength of the pendulum? shortened by    mm.

Derive a formula for the maxiif2ifij5 /)s8 d evy(scdx/,d mum 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 5j;8jvjsy tp1nninz+pw6q1jn ,z*v . is released from rest starting at an angle of 1*n5, yz+ pt 1q;pv js8in6j1wjn j.vnz5 $^{\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 hvg41cd g2 sne,is anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wavesc engg,142svd traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and traveltraeons ) 3ppv3c72 9ks with a speed of 343 m/s How far apart are the wave crests (comprvc)anope 7pt2k s393ressions)?    m

  (a) AM radio signals have frequencies between 550 k y je0cvtbv/4: h tn1*.6kisuq/2pax jHz and 1600 kHz (kilohertz) and travel with y4axvvkc 2 eu0js/*i .6 qb1jnp /:htta 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 l,fya1pt 3,vqft+s1p fongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the bpw et9 hs- 7g,vqm2 6fqlkpd1n. u1 w/tk8)ctsame elastic modulus, but one is twice as dense as the other. In which c1kupqnv /t8,kdw m w1bqp 7-9e.gs 2f )t6thlrod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betwil ck*6dz.6b4ab2mucepi , q8een two supports 28 m apart. If the tension in the4kii6cmuc b8p d6.*az,bq 2el 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 a steel cable of leng i:ioq4lj :.0fck(n vjth 620 m and diameter 1.5 cm. As the gondola comes to thqiolvk :f.ni j4(j0:c e end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the snbm/igh9 +7 wrurface of the sea. He hears the echo of the wave r7w bh n9im/r+geflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at differ/ l0py5e(mzx ot0-qhv ent speeds, and this difference h- lopq50t/hxvz0ey m(elps in locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated bo589i id iwt35ygpb38,z tbfby a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of 39o3b,i8d y gtp58 fbbizit5wfrequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensr lx*bq2a/4y;:uq-mb3xn*g au d df5b ities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected a5-*fa/br43bqag:lnub ;* x2uddxqm y t two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave e/q agh:3 u3sjpassing through the Earth is measured to be jq3u3h/ age:s$ 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 /a hhgh:tvj q70j -,uf5qc1a-h* jzumportion of the Earth, but one is carrying twice the energy7- g0vu/1:hhhuact qfmj ,a-h5*j jqz. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the sa9as mffew wfq.ojh (i8gi 8+3)me frequency, but one transports three times the power of the other. What is the ratio jf9os(hii).wa8+8fqw m fg3e of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a thela py4 (dr+wq 4g7 ptdj-y+.otal vertical di ehyq(p p+d4tw4 -drg7jy+.alstance 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 KE change?   

The two pulses shown in Fig. 11–52 are mdn3s7r(d 8-mq k urkh9q:a(m sdcs;x x :8ic.koving 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. x m8c3m :98(ad7ur :rksqns-( i;skkq .cdxdh11–36a, 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 vgv 1pbki /m 1/-+stysz4chbq* ibrates at 440 Hz as its fundamental frequency, what are the frequenci+1vb ibqh1/-*/ ym pkcstzs g4es of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingerevf n* 76pbv fdiez i)c-hc795hfed x9;d. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the str h fhpn di9edcffi79)7e;cb-v6v5z *xing vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name a g25xcvs )z 0ja3mkb5i:qf 5qjt lek5gi ): 3q52b5svxzqjf0 jacm ast three other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequro;ikh8zxb. i7 jq71j ency of standing waves is 475 Hz, how f;jzo1 7x.bihji7k 8qrar apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 2qwkn-rfvd;6 gcu/ m)p t46okc9 r :p:c80 Hz and 350 Hz, what is the frequency of the fundament/pwugc6qo- d k nrp 9cr:f c;k:)t4v6mal?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g.*3 ls;jmc y0nhng-odj1xoxb a56e: 3q The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones? dql;ox -no0 y5as3bj n*m xeg: 3j1ch6   Hz

  A particular guitar string is supposed to vemk c e2:gai,,vjw vab8r5t73ibrate at 200 Hz, 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 frequenc,j w tvkibm v: aagr3872c5e,eies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, b:ph.ca8t43qgp(d bf b4;xm .b v9va ixut it is measured to vibrate ath3: vb8mxg9aa4bt q.(dcx4bp.pif;v 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 sszr-+wur*0vzmz4 z v p,60uvgmall-amplitude mechanical 60-Hz vibrato6u z+4s0*vv,rvwrpg m zzuz0-r. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pujr-1ckt- ( fwnlley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns mawrf1(tj--k nc y be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back aj,y + kxozf9a c8d-o)bnd forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relativ y,)fkxdo c8- o+ba9jzely calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 k/ y61 nib0lv 6z x9:ctp0azdnwm/s strikes a boundary within the Earth between two kinds of mcwp6v9tnl/n0 1 a6idz 0x:zbyaterial. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changesuo j1 e-2mz cz6xxqi+.gww94r from 2.8 m/s to 2.1 m/s If the incident wave crests make a 3 i6ec2u+gjxw.z4q w-xo91 zrm4$^{\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, dense8 lu zttgt+ud707uz0*heoz v. air. If the sound wave toz .gh*80uz07t+evzudl ut7hits the 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.qq buc812j c k/po8r+slwag/ rock at a 38 81ku l// pqswbcc 8+2qgao.jr $^{\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 thy+*xagily(eh .91x to e user’s manual, the dish has to be pointed in the direction of gt (e x91.layi oxh+*ythe 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 vo( o*hslf3jm4k l.w1p 3zlk5velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, pev3hp* . 1 (wskl4 koo5zmj3fllople 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 stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness0u2s ;i7n- w,nlqnq.jjp6 cw ifks..n 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). j, qji2-;cnwpi fnu. s.sw70.l qnk n6[Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a wind4ye4lg4fd (zj)j/x h,kms.iaow to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behlfj4y4g a ie.k ,s(/4hzjd m)xaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. n lfp2wg 7;8zhThe mass then falls 33 cm before it stops and begins to rise. Whafpgn 7wlz;2h8t is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 14.(h6 tclzj wo1–54), compressing the spring 5t6lco4h(z. wj .0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diametyqt k7nzq)r98c 4/7pw xak,pt er 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 coffe7cq/zrpt 84x ak)nq 7pyt9w, ke.    cm/s

  The ripples in a certain groove 10.8 cm from the ceno sov3mm(aw5* arys,4ter of a 33-rpm phonograph record have a waraow s35v s*ay4 (mom,velength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equat7vid /8 z+.wx niyvw2iion x=0.650cos7.40t where x is in meters dwiv v +z2y7.8/inxwiand 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 frequency f. What is its frequency if it l4h0tx nix fr9 37nc*xaccelerates at 0.50g (a) upward,4 i3xfc0lxhtn7n9* rx    f
(b) downward?    f

  A 220-kg wooden raftfom)m; nr0t. o floats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whilofrn ;o.0 m)tme.
(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) andnj38pfb 8ren2vtm(3 rn r1aory 5p38cv nt)+s 440 Hz (A).jr233c 3+ 8nty bfnopv5ev(r1an)rt 8m8n spr
(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 of Fig. 0btq;jxon/g)+ uj fw6 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 b0fxu/ +wtn;gjo )6jqtwo sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong movesaxtjn tnn v, 8fp0w6g(uj 50d* 1.8 md,fxwv0pj6taj u n508( gn*ntm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cycles pef 7hf*vm.tr8o9g p4 pcr second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed thererpvmfp h9.go*tf8 74c (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is a9*,l hfr mkat,ttached to 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 with one end fixed and the other freet lm*,h9a,fkr .

  A “seconds” pendulum has a period of exactly 2.000 s — each olh 1-ajfk,.ob knb2b5ne-way swing takes 1.001nl,johb2kf .bka-b 5 0 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 osci8/h)zf.ogd )c.; gob* 2e y2hcq1irm cyrg*yhllate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hintg d r./mh*y8oc1)rh h ;y22i*)fqoyg cbzgec.: 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 strsjcwg ;g :f2bezd3w:o sc629r etched 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 thc9zsbj 2:wdocse :2fg; w 3rg6e two pulses first meet?    m

A block of mass M is suspended from sdffxwhd-o 4z;1*z,atig +v oe1 :t9ja ceiling by a spring 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 thi *4 oed1ajftt+w;s 9vd,xzg z-:f1hoe penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at t-(lc.9rbv alt ,kxip)6i b 7rwhe 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. What is the period of the bouncing? [Hiniwc6)9 r bi xvta ,r-kll7bp(.t: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which ap4 l( 3utc3f(ogvwe,slso gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs backcwt4 g(3e ,fvp3u(ls o and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz