Give some examples of evefs25v7x- forv ryday vibrating objects. Which exhibit SHM, at least appro7s -5 xvrffo2vximately?

Is the acceleration of a simple harmonic oscillator eve 0ied)5s+ev+iwqmc x)sh fn/7 r zero? If so, where?

Explain why the motion of a piston wxjx(ql3( p;e;og r1fin an automobile engine is approximately simple h (;3 exqorxl;gf(jw p1armonic.

Real springs have masb/i.y7jy 6ugrpt*c g/yekg 7 rl62(sjs. Will the true period and frequency be larger or smaller than given by the equations for a mass o gtyg/*p/2iu.rc66lej(s 7b kyr7y jgscillating on the end of an idealized massless spring? Explain.

How could you double the maximumgq;ok16iv *dsq hl.rj2 qeih f 2r8*2o speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, an30m0wza(*yblcg6t az d then is rel 6 w0a y*tzgb(aml3c0zeased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain orl.ziwc2v *0ck lose time when taken to high altitude?*ci lk.c20wz v Why?

A tire swing hanging from a branch reaches nearly to the 8tgtr 3usv +c6ground (Fig. 11–48). How could you estimate the height of the branch using oncu+3tgsvt6 8 rly a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake th h,kgsxuk vw9f ;8w/5be pan at a c; k kvbgxu58s,ww hf9/ertain frequency?

Give several everyday examples of res5m d 55, en5+xgp+wwvjw * .hadb4rbrsonance.

Is a rattle in a car ever a resonance phenomenon? Expla:eeu: gr)( ssqin.

Is the frequency of a simple periodic wave equal to the frequency ox)4e a4faow+jf its source? Why oa4+fwe)j4 xa or why not?

Explain the difference between the speed of a transverse wave +nmyq3j(yksxhb98 x6 traveling down a cord and the speed ohs9 bxy(y kj6+8 qm3xnf a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piaoi:zl9 z683o pp o2piww6xv5gushq: * no normally have wire wrapped wv: 5 xg28 qo*pwoup69 ps6oihizzl:3around them?

What kind of waves do you think will travel down a horizontal metal rod mr;pg4 jmj ) oze2)b: xb3e;(mr9pidnif you strike :mpmjor 4)dx)b2g;; jzr(b3 9em epinits end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decl0ffh.jq0 gw *reases with an increase in temperature, but the bulk modulus B is nearly independent of temperature0fw*l0jfg.qh , 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 travelr z)xlv6 ssy95/7ilcb azr9 s) sbl7 /cylx65viway from the source.

Two linear waves have th+ ;x /nc fzn+0gjvj gj3;p(nfje same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which trans3j f /jg(nvc jpn;;j+xfnzg0 +mits more energy? By what factor?

When a sinusoidal wave crosses thej gqcie zt2cm/9y6(2 qi4ask8 boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelemqtizqcaj6y8(4 cge 292 /s kingth and velocity do change). Explain why.

If a string is vibrating in three segments, are there any place nk4 1q.cr,mhvs you could touch it with a knife ,nc h1mr .4kqvblade without disturbing the motion?

When a standing wave exists oqwvzu516p af 7b-9nrs n a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy sw -65 z1n 7fbrqau9pvwas destroyed? Explain.

If we knew that energy was beinglk 3do ;+:h u6sdhai+o transmitted from one place to another, how might we determine whether the a:s +3;k+hdoiu6oldh energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude e0 912)wgao7oes fx0 q0ak x/ecvhaa+ 0.18 m, what is the total distance it travels in one peri2/ g vasceaxhw oe+)q0keo90a17f 0axod?    m

  An elastic cord is 65 cm long when a weight of 75 N hanwp(2u 3 awptyuoas2 )1gs from it but is 85 cm long when a weight of 180 N y21 o(p saupuaw3 2tw)hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into / x 4:rjjoj6 lo vg:kdt:*s.wkthe driver’s seat. If thsx4 6d .*towo:g:j jr: jkv/lke car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2 t)txr cxry// 2k0uc/n.7-kg fish hangs from it. (a) What is the spring stiffn kx//)cnyrc/tutxr0 2 ess constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is pbq ,4e1zw invu8j ,p0hung fj,pwez4b 01q 8in,v uprom it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in,t+v++(sytvlic( luhd.4 jc*b wn2cm Fig. 11–2 at times t = vmyljl b,uc+++thsdv2 ( wc.* ic 4(tn0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’r le2znmtxyu .5gqj1lk2l 61sab2 a2*s web. The web vibrates predominately with a frequency of 4.0 Hsrbg e *quljm11ay 2t 2lk 2za6x5l2.nz.
(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 oqn c t+ rjt2xus0hndg, 0w8g7x+(vy3spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to nxcdsg+ xu0n8 h, gy3to27(v q0+j rwtm, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibqb+3 s klk)q(srates 3.0 times per second with an amplitudess (kk)b3lq+ q 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 thz2-k,m ufrup 87bc 8dge speed of a SHO half the maximum valufzu ucdm, -b7g8 rp28ke?$\approx$    A

A mass attached to the end of a spring is stretched a distmeha:ra dx8 5*ance $x_0$ 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 spraj-6 wlvaoxe6:a)( :fuv2tx,g fw + cuing 0.315 m. If the spring is stretched an additional 0.130 m anduaf vwc):2oalw,x-ugfxv66 e (taj+: released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with springvpk 2e(d e*ok6 4xtalh xi;;a- stiffness constant k = 280 N/m and is executing s *6kxtp;ehx2ka4o iad -l ve;(imple 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 compress4uiz+kmur08db.j1y*i ns e -r the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. Wit+mbr e*yuj1i k-iz4.u80rd nsh what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless szfcc s, /g,(xv90kzysurface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rzc,v0g kx(s s9/cy,fzest 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 +f rj6r .g:pj sq qhjhseq6 hm23 .ji)6l.(wvtthe equation x = 0.45cos6.4t where x is in meters m6f3t6qhr: )+ .s(h qjpqh2ivgj.j6wre. j sland 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 SHnu1 :n lx/6hdmO half KE and half PEl:16nxh/ mndu? ±    A

  If one vibration has 7.0 times the energy of a second, but their frequenciesxuz *3jd wq2x+ and j x2 d+qwu3zx*masses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring oncs) ia)7 tt-bm7v2rf/ycjx n0 re every 0.65 7v)ryjtf txr-san7 m/) 2ci0bs.
(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 verticalni /7yxqk 2j,lxq-y2 h springs, each with spring stiffness constant k (Fig. 11–49). What will be the fx, 7l q k2yixy-n2/jhqrequency of vibration?

  A 300-g mass vibrates according to the equation x =k 3z1t5k ,bsthl/ 0nzf 0.38sin6.5t where x is in meters and k z3/1n,t bhtlszfk05t is in 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:+6grin f3 kkmv(brf( is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end ofxmp;3n55 b3b ad qim*9uo+t el a horizontal spring (k = 124 N/m) is struck by +io 9 qxmbml3b55t3up d;ean*a hammer, 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 tbb 8wfw, .84kt(ve j*h0phya 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) withk .e (,ftpbjt8*4a 0 yhwwv8bh 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 connected6l0 sp) v/xlm ,nrpt9j to 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-kg block7s km6uk+: gw(m or4oj attached to a fixed horizontal spring whose spring stiffness com6js(4g okw:+uo7 rkmnstant 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 a3a/h30 w0fx sfcmnq) v9dyi4k high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate t0 fsnq0f/9 kd4acvwi3 m hx3)yhe 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. Whajo maacgl +:c30u(t:ut is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make e)y9blu0oqcyr(j yxpv4 a 1gpt:h4oc9kjo*,+xactly one swing per second? (That is, one complete vibration takes exactly q9j4yxcyh: b)+,oopc 1j o0 t pk4*g vlur9a(y2.0 s.)    m

  A pendulum has a period of 0.80 s mqh5 qe(g9y:don Earth. What is its period on Mars, where the accq h5e:9dqmy(g eleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lonfrvg,/;u a+mqfv5 n2rg
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simplg1lh7 ivq (vc3o4i+eoty)d4ze pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is+ 3v4z)qt4h7 diy1 ec(i olgvo 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 cloca ,vueq+ 4mt9vk loses halvve, 9m uat4+qf a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the4dh3 e).t- xa2sjmgpv maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequenc j;col-k0 /rqz:jrpx+y of 2.5 Hz. At it is released from rest starting at an angle oo-c ;xk/pj+r0 j:qrl zf 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 pa c-etf2r)mh 3gss the bow of his anchored boat every 3.0 s. He measures the distance between two crests toe23) tcg-rh mf 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 speercu :8sl;l--* va frqa(qy y5egfb0.bd of 343 m/s How b*l b(q80 g-e5 af:r.a qufcl;r-yyvsfar apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 160k-sy6occ2) 4c x .qq9g giq*)th2atk 3iuq y;j0 kHz (kilohertz) and travel with aiqhqytk2gy4g i 3)jc9k-)x6uac o2cs;* .t qq 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 lond(r dq;w7 cf2zgitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dw/n. czhivs 96ense as the other. In which rod will thc hins9vz/ w6.e speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the tensf21 q1sko12cea15n b (zzpybbion in the cord is 150 N, how long will it take a pbo5z21az2f ben1b k1 s1cy(qpulse to travel from one support to the other?    s

  A ski gondola is connect qzmu0)ato4vr4i1od +ed to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the ga rqm vto0+z44 )udoi1ondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to 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 surfaew8o:nm qrcbz; sj.+7ae1/n uce of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean j1e/rba7;:cmu q+zne n.s 8wo at this point?    m

  P and S waves from an earthquakeqo7jy ns50mj3rx m44e:ru.j i travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the distuu5qre4io rmxyjn0 37 j4m .j:srbance 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 wavemza-kw ns 6+o2,3 uidb can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.5s a-3zn,wo2i bdukm6+0 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the int8,nl4 xxh9mz k5gu.gwensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two poingz9 4nkx.g5,8wm uhxlts 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passnq;ch5n xn(e;ing through the Earth is measured to be 5c(;en; nqxhn $ 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 zdq/v ;9; ieyb(xnf*rof the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the ad 9irqzvb y *x(;e/f;nmplitudes of the two waves?   

  Two waves traveling along a sttpp c-fn 3atq+z)ec6 6retched string have the same frequency, but one transportsft6+)zect -anqc3p p6 three times the power of the 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 totmqtsqxh 8;;p ;/3 gzpnal 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 KEqx tsgzmnp; /;qh8;p3 change?   

The two pulses shown in Fig. 11–52 are moving fe ru2 3f)jcor1 hfo:)toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a 2fe:ru)j)c 1o hfof3 rfew moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, whatkm(a - srby,4u are the frequencyabs,m- 4 urk(ies 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 unfi1: mg.h*y,t)7o hxo.t 3 sv3;jlq dmetf9aqwengered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only)s.7o9otg vt., wlxa;tmefh3:1j mq3*ehqdy two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string re)08s9thjenw hb tij,; sonates in four loops at a frequency of 280 Hz. Name at least three o)js0t ie8hjb9t;, hnw ther 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 frequenco7tl* (a7g/mpx-smx +sni (a fy of standing waves is 475 Hz, how far apart 7pax7( m /+g *f-m(tnolxasisare two adjacent nodes?   m

  If two successive overtones of a vibr6o spjd 2z xhm+ dola3w)xm+;3ating string are 280 Hz and 350 Hz, what is the frequjomw3m3la+; d 2s d6ozh)pxx +ency of the fundamental?    Hz

  A guitar string is 90 cm z)(4esw7ntvo 2ja6gf long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the t67gonafez(4s j2)w vstring is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suppccoj2hp) f .+nosed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to cc + p2hcfjo).norrect the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar strpr 0u c joe)px,4ivc:,ind4 w/ing is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 w,0:i/oen,xcvpd4pcju) i 4r Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontavpnba)x k c/-4l string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’sknp)bvc/4xa - 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 p hc2gu(6yeif h 1jn noavv9/nbk5)0)i ulley. If the hanging mass m is fixed at 0.080 kg, how many dif 5oa9 2v)01egib y/ch) ninnf jk6uv(hferent standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the rimu+mi(o0 joq 3ght frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produm0 j+(omo3 quice 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 boun5adlhsff 4-;ti:,zih n) dc: idary within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 47izshd-td)h,ici4al f :f5;: n $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach ah 1byx5.dw-xb n underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a .xbw5 h d-bx1y34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in wa;znwwv5) 4: sss yitv(jj.wn69 2fsycrm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interfac ny.()s2izjc 9w:swt6nsv swy5fvj4;e 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 earthqu/cv jy(aq1vh lx74kh/ ake wave strikes a boundary between two types of rock at a 3 k1/ 4/haxl(y7vc vhqj8 $^{\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 tol jb:,,(h xnbr the user’s manual, the dish has to be po b:l, b(xnrjh,inted 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 travels across the P2k4k 3urd c,n m4p(cv q.hf ag1wq2*74txlqtiacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approxig t2x( 2tqp dv1mu cr.4cqk al3i,w*74 qhnfk4mately 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 stiffness constant of 550 kN/m Find3sdwzqup i*1 8 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 (approximat*z1p 8isud 3wqely 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m belflvh. *vjr*r d9;40oxx/l katow, which stretches the net 1.1 m. Assh jk* 0lxx4fvadl o;r9t */rv.ume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a fre ;ptz*wx j-5pvely hanging spring. The mass then falls 33 cm before it stopst*5vxpw;p-zj and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at jcon-eag8m5 s du6*t,a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) o5t,c8sa6d e g ujmn-*What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace of 4.ohzt1ym (lyabout o zl1 .yyh(m4t1 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 coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of h1o;5 s(t3f6 . oase:ag yngysmw*0uj a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound em:nf1 sya ogga5( 0u.mjh;6tyse3 wos*itted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t w;8vwtzy +wg2phere x is in meters and t in seconds. Detw tw+8g2yzpv; ermine
(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 osa( e-hqw: kx+ ;kbs:xecillates with frequency f. What is its frequency if it accelerates at 0.50g (a) upward, xh+-e;:qxk(es a w bk:    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it s:(:h xt(/wjylj*stnv r3 lqd: inks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whil(dvw(: 3rn s:h:/x tl jyq*ljte.
(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 (vcqssq04l ; v,97ckjq 9sg/ ktb- y;joA).vko- g;qjjbcsl9/tysq4 79s cq v,0; k
(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 traveliszw8 )qo(wz6 xd o)-ukng 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 ratio8 -dkozx zs( wuqw))o6 of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of nmov kot-6/c1each prong moves 1.8 m16oo-nktv mc/m 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 o- 4 cph:zsd(qrf frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a ped-r 4 p(s:czqhbble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring thas 9fwfg4ij0jmr )m :1jt can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrationmws jf9r 1m:jji0)4g fs of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s -/zdv;:l aa1gvhte c6 — each one-way swing takes 1.000 stac : dle6zh1-gav/v;.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or c9xj+/jeqsg6fh8 e0i. 1 gvnxo ;rdex.an 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 th nhxe/f1j xd e9vge isro.gq+60 j.8x;e 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 stretcoh ;qb skg1;,xhed under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second o;h sqk;,1gxbpulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiq e+k3.k r:0v wmu c,sjs66qxigf0 nn6ling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum r,vgwxs.f60 emcnni 3 kqs6u:q60k+jamplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The ste5psp d uvlw)*o 2ex:3h8emwqb8s. 4 rwel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starpo 2.ed:w 38ehxp4u)8w* wml brvs s5qts 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 onqnf .7r6352 kbyle9.al sai luc p)pw3 a plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibratk.w3ei5u732l yqbc pla)a6r slnf. 9pion, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz