Give some examples of everyday vibrating objects. Which exhf7mkuxojnh q0/)f7q ;ibit SHM, at least approximately7q7 fu) hof0/;q jnxkm?

Is the acceleration oci,ign s kwubi9ec.+t2q:)iqs3 kkm,t7( e-of a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a pistond9b r7ghag596hh t /kc4ggskb qf4:m; in an automobile engine is approximately simple harmonic9: bbgd sq6khmgfhtgrgk4/9 a 5hc;74.

Real springs have mass. Will the true period and frequenc8c 8 g4q,fuxony be larger or smaller than given by the equations f4 ux8g,nq8cofor a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximu* fq hr:0k 2t+4c nf0/fssboyum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the xfwwr.5, (kuah12a-7 bsc0gb a5gbyq hook of a vertical spring scale, and then is released. Describe the scale reading as a function o ygxf75gwa bb1 h. uk0qw(r52cba,as-f time.

If a pendulum clock is accurate at sea leversbx3pjfw0 0xh jd)-m u 8 lz*j0y2qy5l, will it gain or lose time when taken to high altitude 8u2x5-swpjydfq0j*y z0b xm)h 3j 0rl? Why?

A tire swing hanging zydmqb3j7g7/acq8v.m j r:8*tp nua2 from a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the7d82rab g7j qvjyu ca/tqpmm:.3z *8n branch using only a stopwatch?

Why can you make water slosh back and forth i*wccbc p4+s)f2sx )z (t gqx7in a pan only if you shake the pan at a cb*wpc7(s)+i )sqf 4zc gx2 xctertain frequency?

Give several everyday example4zc-a, 5eosjy la o3o7s of resonance.

Is a rattle in a car ever a resonancyanf5v. g - i/flk+tx2;f.nw-t:vil l e phenomenon? Explain.

Is the frequency of a simple p3ab10c e:gshnx(kka:s 4,u d*m8z (yhx qmdu, eriodic wave equal to the frequency of its source? W*u,80s g3:mdx: nuq bszkhca ,eyxh(a 1md4 k(hy or why not?

Explain the difference between the spe 8v7(pu(+zu t: jx7 mvsorw.byed of a transverse wave traveling down a cord and the speed of ozrt:v8 ubj py.7+mw(u(xsv7 a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally hav5wm e 71qctfz.e wire wrapped aroqztf mc5 17ew.und them?

What kind of waves do you think will travel down a horizo 7mys:+8gh hfcvutuezmv)8*8c 8x,u pntal metal rod if you strike it h,7h vmum :u8 zxpfyt*cvcs8)eu 8+g8s end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an incyhna1i,z 69d wufgp5(c3bkhr 8*fa/n rease in temperature, but the bulk modulus B is nearly indepfw8ap ichuab nk6f1,3/rn95gyz(h d*endent of temperature, 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 n (jm+pa g:u x hs7ho3rosxo/-/: tf7btravel away from the sourc7: ajn-/rohsm b3pfxox+og/u ht7:(s e.

Two linear waves havir+)clk+xud0 q 53 npre the same amplitude and speed, and otherwise are identical, except one has half the wankldp3i +)qc0u5r r+xvelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the bk5fjs8esi yg )wb /+b2en)u0ooundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain b8sgb/i ue)y 2+5oneks w)f0 jwhy.

If a string is vibratipno:09f )ju3biug c*jng in three segments, are there any places you could touch it with a knife bladeo*g) pfij3c 9ub0u: nj without disturbing the motion?

When a standing wave exists on a string, the vibrwptlr+g1r5 c, :j(e( m xlfjs(5g(hflations of incident and reflected waves cancel at the nodes. Does this mean that en m5exhjrpflls (cwr (1 5:g+gfl( ,t(jergy was destroyed? Explain.

If we knew that energy was being transmitted from one place to af: bet0vn h hxd:9 n,dn8+o)yvnother, how might we determine whether the energy was being carried by0hn 8,+ved xh dybon9)n:tfv : particles (material bodies) or by waves?

  If a particle undergoes SHM wi rn;w rikg1 e69+ebb*ath amplitude 0.18 m, what is the total distance it i9r r 1bn;e+*e bkaw6gtravels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs froouu34s wc i;r;m it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” cuc i3u4rwo;; sonstant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68di +5d env-yj1-kg driver gets into the driver’s seat. If the carj-di1+vy nde5 goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm wk hanq a3.2w2tk/js (ahen a 2.7-kg fish hangs from it. (a) What is the springh ak2.n3sa2qak/t (jw stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a fresjmf lf50x6g9;o. hoequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only ohm60j;9f5l sgeofx .0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at timesx f9 slwl,;h8ntp55ii t = 0fix5;9w,i l l 5psthn8,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’s web. The we3w2mjaca)ry cr0 3 f4eb vibrates predominately with a freq 23jacw em3cf04r)a yruency 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. When an aucn llm.f7:yl70cha 9 dditional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of079. lc7:uc nmf ahyll m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second wit,+8twsppb p( +h +vthqh an amplistvtp8hp(,q+ hw+ b p+tude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the ma+0k7:7 z5qqp pwexgvjximum value?pwg 750k7v+zxe :qj pq$\approx$    A

A mass attached to the end of a spring is szle2tj2qdbv.df4mw f8p*j s0 t1 (k7rtretched 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 ved;8f pqe+ov)anep p+- rtical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equil 8+np- ep+aop) ef;dvqibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spriao+7m5pv2 zf 2zram1 wng stiffness constant z1a 25pa mw2m7+vfzr ok = 280 N/m and is executing simple 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 r8yxo+bw ,8g :y+rp horx7 0ldto compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the bwldp87b+roxg +, 8:yoh0rxy r all leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of a ,vroi2.r*bibe6 di z0 spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 edbvbri60.,z * o 2rii$m/s^2$ 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 v. i7 ,t9nh,dcx3uzsqx = 0.45cos6.4t where x is in meters and t is in 79 ,uqxd3z.stvic nh,seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE an- xtuhmc4 m954opdrbj+g90n . *nfj6 dj-ajxfd half PE? ± 4 .-4jxjprncof9j96g jux+adf-hmn*d 5tmb0    A

  If one vibration has 7.0 times the energy of a second, but their frequencies anhb2m fj3a 6.c4.ofv6kv vbt8 nd masses are the same, what is the ratio of their amplitud 4om 632v .6fnbhbcav.k8vjtfes?   

  A 2.00-kg pumpkin oscillatesut*ea15(u,uf dk0kk k l8+a ow from a vertically hanging light spring once every 0.65 s. auaudwtk5ekk01k f(ol, 8+ *u
(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 suyx.jn ca hk:9kc:q/,ipported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11– j x/k cyh:.,:aknic9q49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the eq efmp67pke: if1ogj4*2mta g5uation x = 0.38sin6.5t where x is in meters a*2f afpt kg1o4 i7e5m:6gejpmnd t 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 030 g/zy+n(ie cui( hpuzjd6c A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest oa r3wnglo1 8u;n the end of a horizontal spring (k = 124 N/m) is struck by a hammer;w3l1uor8 gn a, 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 4sdxqc(5,lmhpd c(9teir a 8knck)b - 64xvj/spring stiffness constant 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) )(dst(cc4b ivxc /5k8rn6hmdkpq xl a9 4e -,jwith 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 spcz6,x 2x3nq ew*.op pfrings, 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 block attached to w s/eqqyf uyb94yl0: .+ p12a;czpebda fixed horizontal spring whose spring stiffness constant isap 2w:zed yesb0lb c14.fy9uq;+y pq/ $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridj :q sjwx/ 6ezwh6c+ou-(ve 6mge. 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 constant and the unstretjhoewmz6 q/(w u:6sv+ jx6e -cched 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 .0p81ufy j aucy4/rvxs. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to makeznvv*81;ju)6obr e ah exactly one swing per second? (That is, one complete vibration takes a)1j vbe 8*hrzu nv;6oexactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What iel rfzc(2 zv:)s its period on Mars, where the acceleration of gravity is about 0.37 that on Earz(vr cz2 )fel:th?    s

  What is the period of a simple pendulum 80:wh0glewizik 7w w6 a1cf-6d/ cm long
(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 bob8f( ;zi1o 7x,bx ciazi has a mass of 365 gx8i1i(zo 7a,czf;b xirams, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of*p t ;e-gax4iet 3ivg2 0.9930 m. If the clock loses half a minute per day, how shoulp2g;4 3*a ege i-ttixvd you adjust the length of the pendulum? shortened by    mm.

Derive a formula for xxk:s01 z5t ) ljpbfj6u /6t:3sjjc jqsi1wl, the 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 frequency of 2.5 x*w /qq0x edvw3f61t3 j1jhpy Hz. At it is released from resxe/3tw1ypqj3 *q f1vx0 dw6hjt starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow ofq,n+48mdb,d dsgfr,f his anchored boat every 3.0 ,4nd+s , b,q8mfrdgf ds. He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air h hdoou+h:xs ,*as a frequency of 262 Hz and travels with a speed of 343 m/s How far a h,*dohsx o:+upart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 k;/u p /q2ks ;f2y0vnaj zo,:rffa3 szmHz and 1600 kHz (kilohertz) and :;u,s 0vqn z23pzkf //raas ffjyo2;mtravel 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 z1z3 h/pb. u cyt/eu4gue6ot, in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same 1hi7tq -coa+a-xji g5)2 tg wxwqtz;rz505owelastic modulus, but one is twice as dense as the other. In whicj- txi-qo +izq12hxgg5w0ztra7w;5 5wao )t c h rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretch2ubq,o6vj.y p;c -z qced between two supports 28 m apart. If the tension in the cord is c6p j;uqy 2bv.oz-,q c150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hikr b)bg /iz2d *.v5vkull by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took2vvz* bu./ k5)db igrk 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 kg, 9,p hiic- s*ljz3wthe sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deepi ,p3,9-l wsg h*iczkj is the ocean at this point?    m

  P and S waves from an earthquake travel at dir*9zgl(r/rsb 8gh3 mqfferent speeds, and this difference helps in locating the earthquake “ep3 r*g qlr9bz(s/m hg8ricenter” (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 sinu92 u(upw v5laqsoidal transverse wave. Assuming a frequency of 0.52p vul wq(9a5u0 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 intensife.a wn0tv;f :ties, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two pw:t va;.0ffenoints 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing t jaig e9+ -zgfs: 4u:o.tbb;xon0re- xhrough the Earth is measured to be ;zrx 4geoej : s:b.0bon-9 uft+-agx i$ 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 po m5o70o-zy.gfhjj+2hmunm/2k 1q ldo rtion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wavesk70mj+1h n d fom./m25yzg-hl2jo qou?   

  Two waves traveling along a stretched string have the same frequency, b d:m 3pahdc;wrzjn/1jf up5m53+ ol 5jut one transports three times the power of the other. What is the ratio ofjzf 1 :dmrlpphm5d +cj3 5wj/noa3;u5 the amplitudes of the two waves?   

  A bug on the surface of g 0qaa d7*-go7so k)o)8v/vti xufb:q,;vq nka pond is observed to move up and down a total vertical distance of 6.0 cm, -:iv) q,ox *v t dgb/av7ak7n ;k8gqfo)s uq0ofrom the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11v8m ,,1f 5jdom2kukdv–52 are moving toward each other. (a) Sketch the s f2j,u8m1 mkdkvd, v5ohape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as tw,,1izszi 6ld7xcf / its fundamental frequency, what are the frequencies of the first f7x zci,wt,is/f z1l6dour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz whe 5okb/0.rk+x r r(,ug0(ljfze1uokmv n unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as rgu kzk+(v0k.o/je frxlro(m0b1, u5a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name hsqowt)s4da6s ni5t,u c*7 u,at least three other frequencies at which,duoc s4 *uti qan )76w5ss,th 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 frequency of standing waf2mnilbh)ewi b37ry4.zke 93ves is 475 Hz, how farw f4 iy2mkeh733li)b ezn.9br apart are two adjacent nodes?   m

  If two successive overtones of a vibratingvr vc/+o8*nci6sud 0r string are 280 Hz and 350 Hz, what is the frequency of the fundamental? vr*rc8+nu/oi c0 6sd v   Hz

  A guitar string is 90 cm long do5snw: cxo8q n.uvr4l9;qs)and has a mass of 3.6 g. The distance from the bridge to the suppov 4. cnro: 9n;u8ql5odsxw)sq rt 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 string is supposed to vibrate at 200 Hz, bu cve.h 8zm83 b(o.xznit it is measured to vibrate at 205 Hz. By what percent should the tension in thm.vzb cn3. o8xze(i 8he string be changed to correct 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, but it is measuredbo+spku* m4a/ to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the freque4 s au*/mo+bpkncy? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60-78ldo/ gg.pwh Hz vibrator. The string’s mass per unit len/hd78 .gogp lwgth 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 pulley.d,qlgzy w7e/3 d3n7di If the hanging mass m is fixed at 0. neq37gd/3z iyd,w7dl 080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just csma e0 f-9y91nt*sjhthe right frequency, the water alternm 9 9jayh-fsctnse *01ately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave t6z yrw2(omt kjrstx (hn1/49,ss hcg2raveling at k.0 km/s strikes a boundary within the Earth between two kind(1kt,szst26 j(s/2 nrch4xg y9r hw mos 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 “shelf” where the velocit91cn* t rqeqv)qld ,ncu ,kr7/y changes from 2.8 m/s to 2.1 m/s If the incident wave crests make rn,v,7 l q cqc*1udeqn/kr)9ta 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, den8hi nvr4u --l.xt2qk kse air. If the sound wave hits thln4-kq h k8.2-rtivuxe cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake kv0qpr6 su7:o8p/gzj wave strikes a boundary between two types of rock at a 38 pjvru:kqgz 87 0/ 6ops$^{\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 in0wot4n +o-i 0p ivb4 at:wm jtuq:-cy6 diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error oi6 w tw4:0bv4t -qpn j+a0t-uooicmy:f 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 au+m*o)z g8f x6tgb ( 3m3z8xplhxmfy,nd velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledgg83om yf )z8+xbhxftp*um(gl6xz 3m ,e 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 stib9 ir-y9y xas--ipgzv t hvy 91kkl. j165si3iffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, col-i 9yki9 k x-1jl b.gvpt56aiv s sy3hir-91zylides with a wall 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 fi mb)ka6 7k r2g0ujs lql yagh5..,-ppyre net 18 m below, which stretches the net 1.1 m. Assua .m)0 h7ukqpy skylga gbpj- l5r6,2.me 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 freely hanging spring. The mass thj pr.f ibu+w/;46 k0 aodzqs:ken falls 33 cm before it stops and begins to rp zri0 ;jw f.b:+ usak/6qok4dise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a f2y-rd*bv tr6huge spring at a speed of 22 m/s (Fig. 11–54), compressing the sprint6 *-d2yrrf bvg 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffe12 q5; 8ou-hx;fjepf d nppld*lw7:tv e (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over th-v 7 ejpp;xuto p;w2nh*f ddl1l5fq: 8e top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from3*.x k4lx ocqf the center of a 33-rpm phonograph record have a wavelength ofx.q4x*ko c3lf 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibratejh v4t1 p)j+yws according to the equation x=0.650cos7.40t where x is in meters and t injhy1tj vw +)p4 seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillat.m+wbgb;u,o1y c6ir pes with frequency f. What is its frequency if it accelerates at 0.50g (a) upward, r, . gb1+ 6ipu;cymbow   f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it t-ef+84bvq tgqbj9 7 lsinks 4.0 cm deeper into the water. When he steps off, v j+9-8lb7qt f4tqgbe the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument areucwxv qw +8*kmrz-h8f a 62zt- tuned to play at 392 Hz (G) and 440 Hz (zmwf t-286+ aw*kv q -zuc8rhxA).
(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 tw n,av1k*f74ow .d2r jpjwlj+ckccx j711h8 xgo-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 lig71pckrjcax2 ndw8 j xvgh7ojwflc *1,j+.1k4hter 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 Hdjq*9hbl cz+ -; orv s:zwp7wuqpn 55*z, and the tip of each prong moves 1.8 mm to either side of centewq; *rz95hl5qp-ons w:7u+bcv* j pzd r. 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 f.kp7igj m(9sc 9wh,l motion of frequency 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) will not lose contact with the board during the oscillation(fik ,9.p s7jw9lmcg h?

A string can have a “free” end if that end is attached to a rinw1asnwkx+ 6h ims x(9/g 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 9 mx(/wn+6hwk x is1saand the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swingcl4 pvv; )id*9f8x2pq gsh -dhstyk(; takes 1.0g-cyk*qspx; (4dvtlh v9;8sf) 2h p id00 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 ca2oca2tn x essj2 ,d10pn oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the perio012tanp csd jox2,es2d 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 st twvt9 /8 pzqpd50zyv wmpt, giqtuu :*3(fo),retched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is gener* 8qtv0 uw)z,td zpi:/o,uy5p3tpq wf vg9m(tated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspenuwe7i/8lcjl8 we( i4jka 6 cj,ded from a ceiling by a spring with spring stiffness constant k. A penny of mass m iwu(ca8lee j7w48, ij/ k jc6lis 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 car at the ju 8,(scuyfczc7im/3da h -q4shc ip)/wnkyard. The steel crane cable is 22 m long and has a diameter of 6.z3 ,y( hcp cia8/fq4/isws)c ucm7d-h4 mm. A breeze starts 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 on ij5/ ra 8ulgcfhro c y604o*v2a 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 vibration, given that the shear modulus (Section 9–5) of jello is 5c c2 68oygfj4 ari*o hl0ru/5v20 $N/m^2$ and its density is 1300 $kg/m^3$    Hz