Give some examples of 0rlk41) w:bc txp+ oy; mvzxf4everyday vibrating objects. Which exhibit SHM, at least approximately?cx;btpomr: 1z44w+ 0kfxly )v

Is the acceleration of a simfl(ys9 h 16oknple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately soog5,*0fj2ltv a0l ipns sh50imple harmonic.0o* , 5 nlpvjl0t2sig0fh 5osa

Real springs have mass. Wil.a4an wmcio5, l the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Exw c.5,a4oimnaplain.

How could you double the maximum speed of a simple harmonil 5b8bww7z4q gc oscillator (SHO)?

A 5.0-kg trout is attached to the hoo*i,fub 1ks5-qx,knh7x 0p -hxx yi 5dpk of a vertical spring scale, and then is r p*kk0x q57fps,di,h hx-yxxu i1-n5beleased. Describe the scale reading as a function of time.

If a pendulum clock is accurate9:a;yavw 0plldln 2e( at sea level, will it gain or lose time when taken to high altinaypl9wea:; vl(ld20 tude? Why?

A tire swing hanging from a branch reaches nearly to the.8cietnkqzt/y9 w 4f (tfs1(r ground (Fig. 11–48). Ho8q(fn4f/.1 wi(szt t e9tkrycw could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pz 3qwj t/)ud.uan only if you shake the pan at a certain freqd/wt3q)u.z juuency?

Give several everyday example e)rdaq) vx5k +a:n/mvs of resonance.

Is a rattle in a car ever a resona,nt ;nrc6 ll,ance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its h(h,.fuvdrq *source? Why oh.q,*vh u( dfrr why not?

Explain the difference bsys 68)*a9 lej w(dkwxetween the speed of a transverse wave traveling down a cord and the speed of a tiny piece of the cord.s s(a6* yk9jlxdw )w8e

Why do the strings usedhicf e5n7do .u6r*iz2 for the lowest-frequency notes on a piano normally have winei. *d5c iuoh7zr2 6fre wrapped around them?

What kind of waves d+ yq x7p3hcdbti (pd *xf.2hcp+mh2n7o you think will travel down a horizontal metal rod if you strike its end (a) 3.dhp7xht c* p+hdb2m27q yc+f(pinx vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the bulb mdl 4ilwp i4iymjf ;ss ux*m/q:5dk7( /2qu;k modulus B is nearly independent of temperature, how would you expect tquyks4i4*smp:b w/j;/2 im xf;5(ldqldui 7 m he speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude 21 z)wf)b g;fk l2qwqoas they travel away from the sourcwfg2 o k)12wf) ;lqzbqe.

Two linear waves have the same amplitude and speed, and c/4 kgf0 z2os,i u;icootherwise are identical, except one has half the wavelength ofg c/f4uic2k;z so,0oi the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as6 jkng v4e-f8q in Fig. 11–33, the frequency does not change (although the wavelength and velocigj- nk4qf86v ety do change). Explain why.

If a string is vibrating in three segments, are the)w)jrm y-wc x+re any places you could touch it with a k yx-jrw+))cwmnife blade without disturbing the motion?

When a standing wavew74x-q7ob iak 2hoyp tw9j*- u exists on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this meak97 7t ow*2 4a-o jqi-whybupxn that energy was destroyed? Explain.

If we knew that energy was being transmitted :g42mhdh g.pffrom one place to another, how might we determine whetherg2:hg fd.h4pm the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoyoerde8kg-5) uq-f 7mes SHM with amplitude 0.18 m, what is the total distance it travels in o7e -d5qk o )gf8yumre-ne period?    m

  An elastic cord is 65 cm long when a weig/j n92e ew4r+ 7plsnplv :u)kmht of 75 N hangs from it but is 85 cm long when a weigh 74juw /vl+e 9mnelrnkp2ps:)t of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500m0s+d bq6m 8lcv2sk,r-kg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what w6+2bm80svmlq c rds ,kill be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What-y 6vy z+gs ms7,s3qhv is the spring stiffness consysqs36 v7+,mgh vsyz-tant $\approx$    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 0.60e1 5a(fnayga * kg is hung from it. What is its fre y*a(1 nfag5eaquency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig8xs th0a1a. yt. 11–2 at times t = 0,t =s.x0h a8 ttya1 $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 web. The ) aqg z1 xkyg*,47yfabweb vibrates predominately with a fre)gafy 7a*bq4g,1xz y kquency 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 vibra4kxh2ua l0xti+o,svi )1+rpj tes with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What04uarps,21itj+v i+k ox) l hx is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per secondpmj6+qxk -y/ v with an amplitu/j+vq-ykx6p mde 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 6eo0a4:4b6 ji xun / 6muzf p,gbk4sroequilibrium is the speed of a SHO half the maximum value: s/x z6 6b4r gjf4em60oabik,o4upun?$\approx$    A

A mass attached to thsfr; d5 h;sk; g+d.5aaze/n )nk9gr xae end of 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 stxre 1,7x4 zjtnwe.6 xrretches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take ,je1ztxrr6 nx.7wex4to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg i r50-m i/,dbb98n+n-d e q tbshypg)uas attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it i9y rn g08-ibbd,+5 nph)uq/a bmt-eds s 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 80.0ncyi anbjh.r02v29w2 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gu n9jv nah2ci2b 2yr.w0n?    m/s

  A mass sitting on a horizo0, b9aoqn5r:ny e msu1ntal, frictionless surface is attached to one end of a spring; the other end is 9sr1ayu qnoenm0: b, 5fixed 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 vibrates according to the e iaz i)(b8u-tid3kf o5+d9 ; fjxrkl4pquation x = 0.45cos6.4t where x is in meters and t is in )-tdz9d k(8f3ipx jao;b l i+ rf5ui4kseconds. 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 isg668t(i -lw dm;psqpz the energy of a SHO half KE and half PEz6i (dg;6lsqp8 w-mtp? ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencieh jlilp(98f+ss and masses are tfl+i 8 9ps(lhjhe same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging luw-m ckb46tazq1e* :g ight spring once every 0.6agmzw:e 6 -qcb4*tuk15 s.
(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 vertical s1op ql m0v z(+(3wgljgprings, each with spring stiffness constant k (Fig. 11–49). What will be the frequqlgz31j( vp 0+ (gmolwency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38si2 s ncm-zu;7fen6.5t where x is in meters and t is in seconds. Detezus mf 2-ne7;crmine
(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 istkh; 0ia.quj h9 c*/q/wbskp4
(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 horizov2m 4fgaxfc66:l9y bg0gh x0/xig,mqntal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m6ig chxfvl 9xy4fm gxgb2q0a6 g:/0, m/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 stv+wjopvp6:4m ;yjr.q ;k.yc7 0agrqyiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass0;. 6 kr;p7g :qqjoy+p va4jwmy.c vry passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springsa9bf1rvk eiwe jy0a-*)7q 1d)br ps7l , 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 bloc h y0 v:pa3f1e/h z1c;dzatwl2k attached to a fixed horizontal spring whose spring stiffness constan1vf ; ep hw/y2tclz0:3h1 aazdt 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 ma; f gxp,vzs;: hui/vutxi( of (jeown,rr-., 5ss 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness con(;oxz.iv /u we,5shfig-r n:x;pr,u,otf (vj stant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What ixjabmw u6 fmc,;)/ y1xs its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactlydx lnpsx2z ;oh ny-1vc3 kn52( one swing per second? (That is, one complete vibration takeyspnv3; ln5c-k2zdon hx(1x2 s exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its pe;6u rk t-p 2m:m)gqc)hf:i(f1mm (4dlmfpz frriod on Mars, where the accelefzu i t ):f4m)cfk6-m dr(m(pg2fmphmq;1:rl ration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pey(i gz+3r-di1jryd tu 88e;d tndulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum icbrlp8)(w nl f.is5 p3s 0.760 m, the pendulum bob has a mass of 365 grams, a s8fipl b 5r)n.(clw3pnd 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 n77dv1px e:jka length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of th 7dnp ekjxv71:e pendulum? shortened by    mm.

Derive a formula for the maxim,vnx bbzj6 ;3 o z7xugx2i8j(u yb/ks,um 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 954,r(uf 7 wuq neffjl,qukkt9 47ji f2.5 Hz. At it is released from rest starting at an angle ou k7, 95n(irw74l9uf,qje ufkf4tfj q f 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of3zm:()( o1rihru3 bib sy7muc his anchored boat every 3.0 s. He measures the distance between two crests to be 6m1(cozr:mr3usb(3i iy) 7u hb .5 m. How fast are the waves traveling?    m/s

  A sound wave in air yrl )/(ih ds)fhas a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crest yihrf/l )(s)ds (compressions)?    m

  (a) AM radio signals havk ,jm88h*ep/lw xet4y9 4jvmc(+x ukbe frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a4em* /pkwvkje xt4 bl+m 9cj( ,x8h8uy 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 ppi9 rs 7x 6h-qkbi*.alongitudinal 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 dense as thee0 a(. dv;crau other. In which rod will the speed of longitudinal waves be greater, and by what factac0;ade vru.(or?   

  A cord of mass 0.65 kg is stretched:(7pkt iq/q-5c6rox4. ah;ho,jqr5 j j bc dky between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one suppc.c -:qhbj j j(/o7x4;rkdi p5hkatqo6 r y,q5ort to the other?    s

  A ski gondola is connz f;eg/ 9-ahteected to the top of a hill by a steel cable of length 620 m and fz/ ae9e;-tgh diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to 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 ua x49i+snm5i6 ktrbr+ch-) nof his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocea +6-st mrnicbxk n+5u9h) ira4n 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 different spd r0kbc6f7wlb)b( 1b weeds, and this difference helps in locating the earthquake “epicenter” (where the disturbancebdbrb1blw7 k6c0f w () 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 b+i,d7x zii -p-bh6t ;magjvn/e approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: v76,x +thdbpga- z /ij;nmi-iSet the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes;+azo4ve k0yt , of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km ft a+;0zey4o vkrom the source?(a)    (b)   

  The intensity of an tih)z-c4j1qe earthquake wave passing through the Earth is measured to be ihtzj14) qec-$ 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 frd7la)o j-6 w/9zrczb)aig w(o equency travel through the same portion of the Earth, but one is carrying twice the e(owjd wb 9gacr/6-oza)i) zl7nergy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, b, lgz3t,l1xscn g-w:w ut one transports three times the power of the other. What is the ratio ol1gcsgz3-w,l :n,twx f the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total v jh-ylb*a* 9twertical distance of 6.0 cm, from theb* ltyw a9*hj- 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 moving toward evkwwm 7k d;8(keb29 n-svob/p ach other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few mo sdk-8k9v;bnmb wwv/p7 oke2 (ments 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 fb+:4xdek2( hr bax a,q vtigacw:f3.0 requency, what are the frequencies of + ca, bwf2d h04k(q xae.xt:avrbi:g3the 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 wi 8b- d;wt1zox3bmxfjt dq7mu8,mqm ,,ll it vibrate if it is fingered one-third of the way down from the end? (That is, only twozdmo1bwj-,,tm8 d3;x87 muqxfqb t m,-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a fren+0z o6 um5mkxquency of 280 Hz. Name at least three other frequencies at65kmz o0nu xm+ which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves hmj3mfx1a0s qal2 j6z -d f+ a6vh9*gmon a string is 92m/s If the frequency of standing waves is 475 Hz, how fah j2amdvl-*ga6fxs9fqj 6z 1am hm+0 3r apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280u7 . wbp1zt: 6wbqo;cw Hz and 350 Hz, what is the frequenc :cq .ut6powwbz w7;1by of the fundamental?    Hz

  A guitar string is 90 cm lo-o 0i*vr khy.tng and has a mass of 3.6 g. The distance from the bridge to the su*vtro 0ky.i -hpport post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar strin):vpsb0d bz w6g is supposed to vibrate at 200 Hz, but it is measured t0bzpsv wdb6 :)o vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposoy.xvfegm3.et 1 aezyk-0( c5ed to vibrate at 200 Hz, but it is measured to3faxt0cekeemy g5y -o1..v( z 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 smalarqddxp4 c*ov f1q cw(tl* :ix8(x05nl-amplitude mechanical 60-Hz vf* q51(woq:nclv 0dai8dx (x*trp4xcibrator. 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 th j)uittb2aw39o+,a d5rrq-zke pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5i9-qtrb2ka)t+ ow,zar ju5d3 m?   

  When you slosh the water back a qu4hb+tuql 9jm23 -kmqp0 dg8nd forth 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 Hz9+q lbt djq2 u-kqumgm48h0 p3. What is the speed of the water wave?    m/s

  An earthquake P wave qa yn-27skr 1ytraveling at k.0 km/s strikes a boundary within the Earth between two kinds of materiala72-rsnk qyy1 . 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 chh-mxqg/72ei -qm o 9vi l27pahanges from 2.8 m/s to 2.1 m/s If th2lx/ e i7h97gmi-qm2o vp-h qae incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when i):e1j tkwbw+dubd0 6nt hits a layer of cold, dense air. If the sound wave hits the cold aewu6n b)k:+01 db dwtjir 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 on q+ c;p. +q*vuod91 g zsbiwvut429ha boundary between two types of rock at ap1uqs4i t oodh wg+9+9u*v;zv.cb2q n 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 diam jrrt c5 t8bi28/t6 .qqa7gv+o l6:suzby pz1veter. According to the user’s manual, the dish has to be poi y 8 r/vpsz6rtl.j8qo27ivba: 6 tgz tqc+b15unted 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 P 9ug zxninogr;t /7 8j7.vfme2acific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do 2r7vfjgom.9zg7e;n tn/8i x u 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 h8r m5k)ffd23uz xxa8has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.8z)xk 2u5fmf hda8xr3]    m

  A 65-kg person jumps frlk,f ya16y w+dom a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the nety6,1 wfkyadl+ 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 freely hanging spring..cz ozh,g( 3yx-r4fdf The mass then falls 33 cm before it stops g fr-(fy.xzo4 c,d3z hand begins 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 (Fig. 11–54), compres,2g nt/uwbd 2 02vzx nnlmua5,sing the spring 5.0 m. (a) What is the a tx5 ugm/nbnwvl2d0 u2,,n z2spring 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 pac17 h;yoevi 7 r-ithyl5e of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig7vihr t1-7 lioye5yh; . 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groov32hvk bal x5w-e 10.8 cm from the center of a 33-rpm phonograph record have a wavelhb5 xa2wl 3k-vength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equan arb.z*j 1h +i/e)udf,jt 6jation x=0.650cos7.40t where x is in meters and t in secon1,+uj z6jba rafd h*.t)ej in/ds. 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 frequent4s 9z*hst) ,m vel) 7t-qefkncy f. What is its frequency if it accelerates at 0.50g (a) u)sl z,9tnt *q-ek)7 mstv4efh pward,    f
(b) downward?    f

  A 220-kg wooden raft floatk wv94r y;o3uhs 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, the3rv hy9o ;ku4w 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 9spnz7akcd7 9 play at 392 Hz (G) and 440 Hz (A). n 9pzks97c a7d
(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. .5lwiyg 8tv /tqs e8n611–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the ligwln gise58 8.v 6/yqtthter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong movesj0 k c1wfb:uc4k4m5ru 1.8 mm to either side of center. cwu ku54f0r:kmc 14jbCalculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with sitfa,5i rl94 i s(ju8kimple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrat rjf(i,t8ii9lk 4a5use 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 thh pd;ta*dlr)d .yca9 /at end is attached 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 rapcd 9y/.)d* hal dt;the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takesfci+c(*dtla+tdm 55 z+dcnk * 1.+lf+dz*ccdci tnam* +55d k( t000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical w( ,rghk96edub. 9mxarj k y++direction or can swing as a pendulum of sm99kbxmar6 .+ (re,g dkw yujh+all amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pulse 5xgbm72 gvis2 1t+gaa0nk0e xis generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where wg1vg 2m07aaigk5 +b2e snxt x0ill the two pulses first meet?    m

A block of mass M is suspended from a ceiling bh a t-vx;1gv4ry a spring with spring stiffness constant kv x-t1vr;a 4hg. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg cagb68mt -hahh1j03u x8w2tdp.w6fn7. hnarfk r at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car-8hf3ampw6rkx28h6n 0ad u1 bj.twh7g n.f h t bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (whichjgjr4xks 5gayj2;1 /k1s9gms also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus kg1kag ;s1sjs5j g/jmr9x 2y4 (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz