Give some examples of everyday vibrating objects. Which exhibit SHM, at leax9v2lc b mo jv2/as3z7st approximaljbz2vsoc7a3v mx/ 9 2tely?

Is the acceleration of a simple harmtc;:nsf 69t-lzmg f+honic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile 3;b7.cibn ym y qwgecr)4 me4t(m- 3thengine is approximately simple ha4r;cc-itym qgn4m)b y(b te3w 3.hme 7rmonic.

Real springs have mass. Will the true period and frequency bedh5t: hn05 /zw 4+hvg:k gedmj larger or smaller than given by the equations for a /dg 0wd::vhetkgz4 55hmjn+ hmass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillatokr l,2q*kj 6wh0sh8akr (SHO)?

A 5.0-kg trout is attachexy b 3gn zhl:9tk4c:x/djfh79d to the hook of a vertical spring scale, and then is released. Describe tlxgjthx7 :c z9fh9:ny4b3/ k dhe scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gainh ( hb+jed0.yps.8qfo6y wy(p or lose time when taken to high altitude? Wj e.p0hhfws y 6(+ypyqbo8d.( hy?

A tire swing hanging from a branch vp 1srh+d1v04wo anjdby7z26reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the brans 1vz2 w16+jdb a4ohry7p0n dvch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake thifady.y- +5:rbb3 gsi 7bohu7e pan at a c7f+bb:siy3y 5 urhagoi bd. 7-ertain frequency?

Give several everyday examples of resonanc)m22 o1 li2yzxepv vo g8o,fx2e.

Is a rattle in a car evervlh.1wgmga;zvn5 f(3 a resonance phenomenon? Explain.

Is the frequency of a simple periodic wb z-;xq7pw/v wave equal to the frequency of its source? Why orzw q-;v7x/bwp why not?

Explain the difference between the speed of a transverse wave 0uosb zwvl1)gylvle;nou-n1i 9 ./7 jtraveling down a cord and the speed of a tiny z1 ybw;e)l0uovolsl ji n1 n7-.v/ug9piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano n1wj l extzto2,5j3 o5pormally have wire wrapped aroelt , wt2xjj155zp3oound them?

What kind of waves do you think will travel down a xr28dj+l-w*mg;wl5jfn i7b n horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally param25 - gix;f7lwwj8 rb*+nd jnlllel to its length?

Since the density of air decreases with an increase in temperat nbhd*0 wt)*l,(efo mdcfwh48ure, but the bulk modulus B is nearly independent of temperature, how would yo8 w4,wfn(d*o dmc ht*e0hb)lfu expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude ( h9geu rx0fd h*tuk- e:2; 8ghdq3xrjas they travel away fro e:du0jg8h9q;k(u-fehh xdtr3x r*g 2m the source.

Two linear waves have 9/tc+dz b,j fr jm( )iq)4tfpwthe same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what fa jmd 4+/b ,tj9ifzqr( )c)fwptctor?

When a sinusoidal wave crosses the boundary.hnaywmn.v1 1cy l6,a between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velo.y,n chv.1lyn w ma61acity do change). Explain why.

If a string is vibrating in three segments, are there any places you could +u9bhx:6 3neqj fq;h btouch it with a knife blade withoutjb9bf6 queqxh3 +: h;n disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and rfxxnk3w mvb ,f3do, /o0r h*2seflected dv 2mx*o ,o3rf fknb0x3sw ,h/waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one placeo* q5a;nzc/t vyg l)f: to another, how might we determine whether the energy was being cac;tq)z *g:an/fvoy 5lrried by particles (material bodies) or by waves?

  If a particle undergoes pgkg:+. r8v quz x+ll)xo t0m7SHM with amplitude 0.18 m, what is the total distance it travels in one periodl0 +qgv.u x)z78mx+:pl tgkr o?    m

  An elastic cord is 65 cm long u: chybw9b 2/bwhen a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of th2 9buwhc b:y/bis elastic cord?    N/m

  The springs of a 1500-kg car compress 3dwg(nwn lo7q8er;/: v/kw f d5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what q ow:78/wf ng(rek dw d3vln;/will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish ha*a0 fnvfh(;6-.u( fejeevif6r qns 9bngs from it. (a) What is the spqr(*(f;-j6.9nfhue0 fs a ibv vef6enring 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 vibrz,e8o2cx**yech--u7 fj7 o gddu,h 1kfry 7qtates with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. uh,ye cj uz**q2xy177or- ct7fgddk 8,hf e -oWhat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of t jape9*4 v b m40npl21ur9erkthe mass in Fig. 11–2 at times t = 0,t r *ea14vkjn4btpurl mp02e99 = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 spidei1p*i 8/ujmtgwo dqo 61 c1;ozr’s web. The web vibrates predominately8*qoi11w; md t c6jguiopz o/1 with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz..gxt8iako;gw8 r +z m: When an additional 680-g mass is added to m,tmx zgrgk 8:8o;a.+iw the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second w;yuz,p0ra)omp w 7d x-ith an amplitude of 0.13 m. azuw)x7,0prm y; -odpDetermine
(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 e;k uen-focvp 1rwhq1)6 gf) g-quilibrium is the speed of a SHO half the maximum value?rkf hnfcvow egq;p1))ug-6 - 1$\approx$    A

A mass attached to the end of a spring is stretc duiehl-fw32j.6q. o ehed a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical sp+ tx iwa -iwm0:uth7;dring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equil7: 0ixtmah; w wt-iud+ibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with *9xqrim i -o(2hh-v*22rtbv jo;b ep pspring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the obje *he-hb( 2 vm2*qtrr-io2jv;popb xi9ct 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 toc99 qmzq2a xip4d 7+zv compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball.+ixmpq 9 4z2 qzdcav97 With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, friction1zlc7 c)8v3 x ssmsloh) (ds-sless surface 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 0c)ss)- 7lmsd1oxl z(83 chvss.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 equation x = 0.45cos6.4t where x ib;w67pdzhdw 28sqa qins4 x8+ s in meters an8b w7w+ 8q24had ;i6pzndqxssd 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 encm) /uhv l5- tkafe19jd.k9 lxergy of a SHO half KE and half PE? ±ll ).fxktuhk5 ve cd1ma-/j9 9    A

  If one vibration hasgbr1,m29ei(saoa:y h 7.0 times the energy of a second, but their frequencies and masses are t2,1ha:yrms goiba9 (e he same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscil+u ozwm,m gvf1x 4ai:f lnd028lates from a vertically hanging light spring once every 0.65 sz2a:u,ldni8fg mx1vfw 4o+m 0.
(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 identicayz8xs jfjpv2s0fc -30l parallel vertical springs, each with spring stiffness constant k (Fig. 1jf8 vj p 0z2cxsf30y-s1–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t fg70w l3b- jv4vnnn +bmj 1r-pwhere x is in meters and t isw + fnr7ln--bbm vp vj041gjn3 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 y thk004xv7*8atxpmq each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontarh ks.w +y,kg lx+mg: )nzb)p+l spring (k = 124 N/m) is struck by amgg bkls) .x )wh:zr,k+yn++p 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 3,u)m ackisfx0cz 2y7 q8d6d8 etf(7pu05 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) with positive velo8ytp )uifdf7,zqke6 m0dux7c(s 2c 8acity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffn51 j vni r w2ltoij03e*u/nqgv87d9w vess 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 0.600-1rel+ ubkdvm-.*kkwu0dls+ u8uk hq3*ts8j5 kg block attached to a fixed horizontal spring wh tqkw3kv*ue0hsd 8suk+ dr1k um85u l*l-j b.+ose spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps dfa nqfj en7f -9fx)18from 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 stiffnae9fdx-8qff)nf7 nj 1ess 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 v7/ 2(ftl ;f ww+mebpfwdu/qb 0ibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly or.g-pbs (qf-17 xdyv hne swing per second? (That is, one b x1d--7q.h v(fgr pyscomplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where theheh kqsvbniwm(3 dti+ *5-8(e acceleration of gravity is aboiem- i* 3(qb+s8ntvkh hwed (5ut 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lona(43t pwr w1w fdrkfdvd3,d1)g
(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 mi9xk8i ga i80a mass of 365 grams, and it is relei90i g8a8xkmi ased at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock los7.i v g3.iau+lgf 14 .glcdtfses half a minute per day, how should you adjust the length of the pendulum? shor3tulf. . 1ga .7i lsif4v+ggcdtened by    mm.

Derive a formula for the maximuw;bvwed/)lb- m speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released )vyprd)m)2 y xfrom rest starting at an x )v2 y)mp)yrdangle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave creb ,5iay1 8lqm8vduyh2mzran3 dc/ )8 osts pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travelii lo3zy1c88 rha ,mv /d)yqd58mau2bnng?    m/s

  A sound wave in air has a frequency of 262 Hz and travels x oolw2.01pclwith a speed of 343 m/s How far apart are 10xpw cll.2oo the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz an ,skf q5yb19e(b(q6 litay: sxd 1600 kHz (kilohertz) and travel s a x(15te6fl:(qb9,yky sqbi with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in . 1g izhq2yhgk)cy+(a nq +n/m
(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 the:l hhr4yktrr toaau- c jn48+(zi/7: s other. In which rod will the speed of hcrtra/ 4sz:j t-k+:u48 nyl ha7oi(rlongitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If t g e,sy)a:,niqhe tension in the cord is 150 N, how long will it take a pulse to travel fris) ,:y n,geaqom one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of 0ipp7e akht86btj16*y1 ctlm length 620 m and diameter 1.5 cm.eatpcp bjt0i6* my716kh8l 1t 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 of his ship just below the surface of the sea7)erjt)a+id * is7jl5ufa py7. He hears the echo of the wave refr5e+ s pyjl7*)7fu)aiajt7d ilected 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 atmyh(1f+) yku j)+vpzd different speeds, and this difference hd 1 vmpj ))(hkfy++uzyelps 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 by a sinui9kq i6h/wrmt i k:(-qsoidal 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 t6 -iq hiwq:9mr/kk ti(he ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the h1w4znr ,2c5g 1trqy e0ql )unintensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth y)5gw14nrz 0u2q1qeh,tlnc rand detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquakoo++,pv -ge445hul2v,mcltxx ), nutg k 4zpme wave passing through the Earth is measured to be + n ,p m4m5 -)u2kxg4,glpou xl4+zohv,tcvet$ 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 portion of th*sv27)ri vzlbci:j 0pe Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of th)*l b:0rji7 2 icvsvzpe two waves?   

  Two waves traveling along a stretched string have the same frequency, but d;;i/kreuj*cm a+)ksone transports three times the power of the other. What is the ratio of the amplitudes of the two waves/iakcrjde k;u )+s;m*?   

  A bug on the surface of a pondt u2,kj z0q/( cg8gdqd is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a u/(0dzt ,kgcd2 qj8g qwave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch the s*0jyg76x q+jv z6m7:lw j dhbshape of the string at the moment they directly ovez x: q6s7j0hmjly6j+ b*wd7vgrlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string veu z v:v9y;v6wibrates at 440 Hz as its fundamental frequency, what are the frequencies yevuvz6:; vw9of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibra 2af/c ynf2ka ,lzr, 3mpdri h2puk;..tes at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way 2 3r2hdp zlfan2a/i.p.,fk ,myr;uckdown from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a fred:ifn.:,m cz hquency of 280 Hz. Name at least three other frequencihc:zm.: i fnd,es 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 r 4xqsw 5h-c ko--+tpffrequency of standing waves is 475 Hz, how far apart are two adjacent nodew5x-kf h-t c- psr4oq+s?   m

  If two successive overtones of a vb2xjg0 w t94dqibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamental? 409jtd gxqb2w    Hz

  A guitar string is 90 cm long and haqi h4c; 5 rrqdr4cz29zs a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the stringqzc9h2i d4 r4;rz5 crq is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it br. 1mvdom fn ./upg-z5:kvr/ le/b, uis measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correl: ob.vd1geu /mun-z//,.mr5b vf krpct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, butl.l -y nbz1hy64l oppi5o80n w it is measured to vibrate at 205 Hz. By what percent should the tension in tpz6 bl w 0lli45pnno.1hoy-y8 he string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitv uhtj9sx-f69 ude mechanical 60-Hz vibrator. The strin- 9xvsh96fjtu g’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 anm9.22xb wt hudjusted by moving the pulley. If the hanging mass m is fixed at 09t un.22 hbmwx.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back a6iqic350qkzjamz fgbs/6 x -q v46+rend forth in a tub at just the right frequency, the water alternately rises and falls at each enqzbk gx5v-s04 c6 3i+6ae qjf6i/rzm qd, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary withex:j/du a8bare6 -h-rin the Earth between two k 8rheea6/jb-ruxa- :d inds of material. 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 “shelm8y:kwq+k l +ck hcb88o+-m unf” where the velocity changes from 2.8 m/s to 2.1 m/s Iy +8nmwc8k:lk 8 qhm-okb+ u+cf the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travur+rte.vil ( 8arex 2qw46z 7xeling in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angr2ie rex +wq4rlv (a.x7u z6t8le 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 betweeniz 1p8upofapibh sd.5/ l.*) apm6gq: two types of rock at a 38 mlu5.6ha.p ib 1aq/fgzp8s:dp*) p oi$^{\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 the usergtd4tlm1 1 7ac’s manual, the dish has totac1m7d g4 1lt be pointed 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 ke(e31ix6v*u -y z hx0fz is-mtm/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the s*zi e-v yx- ei3z(1mtuf6 x0hshore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constante j2ti: jr:s.x of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wartx :2 s:jie.jll at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18b+8fu kn 4+g9u+ qujhu m below, which stretches the net 1.1 m. Assume that the net behaves like au+9b uqh g +f8kju+4nu 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 e,n. bx2k0yyzrk6 ezq,nd of a freely hanging spring. The mass then falls 33 cm before it ston2bk z0ery6xky,.z,q ps and 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), comprhw7 8yxxy2v*lessing the spring 5.0 m. (a) What2 y78l*yhwx xv 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 ju1ybo1gp b a1v/st 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). ba vgby/11p 1oEstimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograph*lye. pygj ;jgt *t5,h record have a waveletjthjl;. *y g pg,y*e5ngth of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrate*p npr y:m3kh)s according to the equation x=0.650cos7.40t where x is in meters and t in seconds. Determine :pnmp3k h*y) r
(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 oscillxoh+( fmc9mrn8 dlb4;ates with frequency f. What is its frequency if it accelerates at 0.50g (a) dmlm cn9b(ho4rf;+x 8 upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man 5.cl7b 3sguapa l7h/ .wpta9jstands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates fortp7.jaa/c37gha l 9l5pu sw.b 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 il/iz /as-j wr-nstrument are tuned to play at 392 Hz (G) and 440 Hz (A)-ri wa /-s/ljz.
(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* ctpb;x hof.f4 (n9pjdqn-v7 stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the spe.cpfjn b q9ox pv4-*hfd;n t7(eds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the ti bvnt2 ml9),j*zos,a pp of each prong moves 1.8 mm to either side of center. Calculate b,mo)z2 vjta pl9n,s*
(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 fsl1( e y5-9w(1oamnzk jrps(nrequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) w -jpsr ez nn1s loy(a5k1m9w((ill not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can sl0:w-1v x ynz vjc4vf:wide 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 free.-0y :14f vjvxv: zwwcn

  A “seconds” pendulum has a period of exactly 2.000 s — each onew wi93 2inrv+q(ks)y x-nk srvwpl3,/ -way swing takes 1.000 sy isik2vwxvr q )+/ -,prkswnn339(wl.
(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 j/g)kmpdeb 0 pc+9m -qor can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical osc/ me90c)q+-gmpp kj bdillations 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 o5.p yyoi b 7:0qpu qshc,g(l:ff mass 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms lat7lqy(b.ci:5 gs :fh0q pop,y uer a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring3l9sjd rs v;+ns0;wdu with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitudels 3;0+d9svjud w rsn; 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 steel crane cable is 22gy9v nbwu)yd n1 e9u.9jlp/1 c m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. du9w.)vljb eyyg 9/u1 1nn9p cWhat 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 ( / t095/hf17u tatrr4jbjsynm which also gives the dimensions of the block). You pb/a 1snrj/m9u0f5j4t rht yt 7ush 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 (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz