Give some examples of everyday vibrating ob;ra30hbwyv;wv 2a;q fcf1i n,jects. Which exhibit SHM, at least approxim3ncv0w ,h aw1ab ;rf2v;;qfyiately?

Is the acceleration of a simple harmonic oscillator ever zxgm ee 8ahc:q0 )9z)vvero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately*+3u4su q ezmz simple harmon uzzum4*s+ 3eqic.

Real springs have mass. Will the true period and frequency be larger o ,v d4/t720mt flwajj4f qde)or smaller than given by the equations for a mas4 j 7madf/jw2t0t q,fv )do4els oscillating on the end of an idealized massless spring? Explain.

How could you double ty rl,xaq)gzye 6,3+gp he maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scaljz3ot 5j7jt 4+ fs 7v6yy).isdkq w,jee, and then is released. Describe the scale reading as a function of tizyk7 j7.v 6,t)3s4djoe+q5 jfsjit ywme.

If a pendulum clock is accurate at sea level, will it gain or l,z* xddlx/)e gose time when taken to higd)ez / d,lgx*xh altitude? Why?

A tire swing hanging from a branch reaches nearly to the grqvka3 mh f2*+nound (Fig. 11–48). How could you estimate the heightq2+kna3* h vfm of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan onl f1n+/ji8 y -vxjcv*syy if you shake the pan at a certain yvyn-fisx+cjj*/ 8v 1 frequency?

Give several everyday examples of resonance.q(u3 zg9knd g:: fj;nh

Is a rattle in a car ever a resonance (r)hw k(afzu7 phenomenon? Explain.

Is the frequency of a si4;ikl; ivd9ysz-sm z/n w;) mimple periodic wave equal to the frequency of its source? Why or why noin d9m 4)mk;szii/ s-v z;l;wyt?

Explain the difference between the speed of a transverse wave traveling dkk by(y v c4k kdn47ijht7e;9-own a cord and the speed of a tiny piece ofne7kt-k4 h ykdb;j7 ciky9v4( the cord.

Why do the strings used for the lowest-frequency notes on a piano normallyn9i5 i-o+rws ,+gndmr have wirnd s+9rog+5,iwn- mir e wrapped around them?

What kind of waves do you think will ws p)hu4 -,fx 4/(ahb*o apv6jm5gfb xtravel down a horizontal metal rod if you strifabx5 svx*(awuh-6 f4m po jhbpg)/ 4,ke its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperatur3lh e0i33og xye, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to varxo3e3 gyh 3li0y with temperature?

Give two reasons why circ38n *l.wbhp c4+qn mubular water waves decrease in amplitude as they travel aw*lc. 8qbhmup n43 w+nbay from the source.

Two linear waves have the same amplitude lm 1m;ak4,.dzoquc c:and speed, and otherwise are identical, except one has half the wavelength of the other. Which;:k1ul .az oq4,dcmcm transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectionsx 2qck66ejr2 u t4utm/ of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do chane6utrx juk24tcm6 q2/ge). Explain why.

If a string is vibrating in three segments, are there any places you could tu s5 b+ nl30agkmu/9y7ydi3dg ouch it with a knifem3bkgg39ud5n7y as/yl0u + di blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflex4;g aj2o dsz*cted waves cancel at the nodes. Does this mean2oj* xdazsg; 4 that energy was destroyed? Explain.

If we knew that energygi uu9-3-sey tf2c:or was being transmitted from one place to another, how might :uyi- f3ours e2t-cg9 we determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHv+c0qy8yh0mra58 x nj6k7zp vM with amplitude 0.18 m, what is the total distance itqchx 08v6ap+myy7 nk08zrv5j travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it bqei mexck 7(3hme.efu: f.*-9 ikb9wdut is 85 cm long when a weight of 180 N hangs from it. What is the “spring” con .ek7 mc e9du:i*meeff- i(hq.9kbw3x stant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kgm3 :afb-s*o2k8 rwe cz/-lkt y driver gets into the drivcmtbzas3/:re f y-8 kow *lk2-er’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) qaurzg)ru,kp8);fep sr,qk2u4c 4h 2What is the spring stisprk;c )4u u4freq 2kaqh)8u 2r,,gpzffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz whc3npv),2:x64jlrtbq pbd lc*en a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangsjb6nb 2dp crlptl* v):4,q c3x from it?    Hz

Construct a Table indic4p*df at i6cn25 +afjsating the position x of the mass in Fig. 11–2 at times t = 0,t =c*apad4ni6 2fj+fs 5 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 web vibratesdpv88.fgeo t5ao ./s s predominately with a frequency of 4.0 Hfd o ssae88.o5tgv /p.z.
(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 cls.z8puyi 6*Hz. When an additional 680-g mass is added to m, the fr*c8ylps6zi . uequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates sp 5j5u6-ks pa3.0 times per second with an amplitude of 0.13 m. Determine kau5s 5-pp6sj
(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 t.3dn det1 uln3he speed of a SHO half the maximum value3e31dn.ln dt u?$\approx$    A

A mass attached to the end ofwqcy.e /p;cj. a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is strebwv:0bjc9) bw tched an ajbw9w0v)b bc :dditional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is att qg a)pigzjgg)/; ,,+qtt7v agached to a spring with spring stiffness constant k)t az7t,g g/,q;ijg +aqpvg g) = 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 to compress the spring of a w e7k-s6r cc8bz+o imvya).l)toy popgun 0.200 m to “load” a 0.180-kg ball. With what s c6wvk-ezmi7+ ). ob8rsa)c lypeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionlrx p:cp:7cb rj4: z8tless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J oxb74 crp:ztj c::r l8pf 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 accb-ig2m2fi4,p1z0:jkzuku x i ording to the equation x = 0.45cos6.4t where x is in meteru x zz-2gmikfj ,p1u4:kbi02is and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibriumd:0 pbtn5 8nyrd c* )m4bgrfb2 is the energy of a SHO half KE and half PE? bfb rrc0n) 2*ptb5yg mn:4dd 8±    A

  If one vibration has 7.0 times the enypjm6b r-:hf5 ergy of a second, but their frequencies and masses are the same, what is the ratio of their amplitudebmh:y-p6f j5r s?   

  A 2.00-kg pumpkin oscillatenqb -131rxs*vq5vw ft s from a vertically hanging light spring once every 0.65 s.x1 qw- *v5qtbnv 1r3fs
(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 verdx1l(y p 991us)9frr(fty 7 lz,tfkzp tical springs, each z9fdp()zr yltfp1k,71( lts9 xuy9frwith spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according towt oxudj 4z5(6 the equation x = 0.38sin6.5t where x is in meoz54jt( w6 xudters and 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, ltr13 -1r/n 4dzq4p jurx) wkqlabeled 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 on the end of a horizontal spring (k = 124 Nt: )sa.7drk8 *od*czf kzm5yw/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/kcz5mw: r *y7.*8z)fdsdo a kts Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with an a8 l;rfw37rtwo cgvf35oo,cd:l k ,e(implitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through i, rwfc,583ew3r;ll gc7 kdoot vo(f: 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 springs, with za8cv/bqez )x z8 q3 as5--ztwci.ge6spring 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 attac7ju lo62.flnw vi 1zj1hed to a fixed horizontal spring whose spring stiffne wjju. lf76i2vzno 1l1ss 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+wm 1fo*k j)c5f7rtzp 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 1wj)o+7k p5ffzt*cr mbelow the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibdwn tn5kw ah+-;4bmr7 rations 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 one ; en1kt uccf047t0qwizcm1 n4 swing per second? (T 0fw7qu mc1nez1k t4ic ;tc4n0hat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period s- h,o vhm5uhvqo, ,t*u 1)uazof 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 thatha, - 1qo) zsm,vo,h uvh*tuu5 on Earth?    s

  What is the period of a simple pend.xh 4k1tikrw;3)we nhpb+a1 qulum 80 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 bomvs37m; uh/5lv:uba ib has a mass of 365 gramsim vb37sa lvh:m;uu/5, 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 /3gtt0ckti(p 99:skwaz timpzv*(h) of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened by (/ ztcigatw(:) 0ht9m ktpvpk9* s3z i   mm.

Derive a formula for the maximum speed r/n o pqo )rk(p*jrmat(iprm2r08x8 ,0y2qo r $v_{max}$ 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 2.528,bnz ogj. hk Hz. At it is released from rest starting at an angle of 15 gzn 8okh.2,jb $^{\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 wac5o 94g 9qxs(2j jwmbcve crests 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 t5m9c w(s b j42qogcxj9he waves traveling?    m/s

  A sound wave in air has a freq1yc2kd;cnu ,l h.rt-zhxfg4 ) uency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (nz)gh1d.rul;h cx 2f t ,4c-kycompressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (k5uyg uu.hj9jhu1 tuu (xyu-26e2+zo gilohertz) and travel with a speed o jg( +jxz9- 1hue6utuuyuyh g.u25u2of $ 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 longitudin./ 5ig e )ozajibyjv-i.focz (2vv7z,al waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same:xevn. s 3lo15,dpb fv elastic modulus, but one is twice as dense as the otsx d1ve,.n: ofvbp35lher. In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretchew vao:6r/*ou,j dv+u/gzn0ri voi9:nd between two supports 28 m apart. If the tension in the cord is 15/g6uv v0oi v9 drjon: :/az,+ronuw*i0 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected ) 7 9zq08dhcxo)xt hr*9zyifp to the top of a hill 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 wav8))yt zd09c x pfi7hq* orh9zxe 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 ,+(19(jxl q /rw.4rnzl ku vcb ozv-vbof the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. Holb z(,r v crl4 +uzbk1onqv. xw9/(v-jw deep is the ocean at this point?    m

  P and S waves from an earthquake t2: 8ci:kopt z*:ulstxmo +tq 1ravel at different speeds, and this difference helps in locating the earttx:k1o qpt + 2ti*8u czol:m:shquake “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 cq7:rw/ rct 8ysx6mo+ dan be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earcmox qsrw /d78yt:+r6thquakes, 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)iu5 rt9 ( sqxf3:vs5gx the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the sourcs 5grtsvx3fi(5x: qu 9e?(a)    (b)   

  The intensity of an earthquake wave passing through thgh dtr 2otyqf(h2ai wl(7.6 mcli e*9a97x v6ge Earth is measured to be .wmct r7qh 7lfg(6(vid9x62teha9il 2ya *og$ 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 throug7x -y b-apy8k;er 9kyoh the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the7bey k ;rokxy -9ypa8- two waves?   

  Two waves traveling along a stretched string have the same frequency, bury)qr hptd +o0qf,;oc j)e:y9t one transports three times the power of the other. What is the ratio of the amplitudes of :yoto ,ef c) rdp9 jr+;)0qqhythe two waves?   

  A bug on the surface of a pond is observed to move up and downhrse h 0*bw*5kgnv77/0rhdoo a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor r7 ehg/o5vbr0* w*s7ohn0k dhdoes the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward k59 z-,gi5fzy,w1snr 0b2negb : jfvveach other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shapebyjs w1rv5 ,fg:9 ,nf 2ek5z-ivbnz0g 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 its fundamental frequency,rdx8 (1gj7izp what are the frequencies of the first four ha8g7dx i(1jrpz rmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingerkk, amwcj q)w- j38ss;ed. At what frequency will it vibrate if it is fingered on,q;a cw3s-8kws kj)mje-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates inb, n5eisk0,a x(5t puvce +f-g four loops at a frequency of 280 Hz. Name at least three othebas g vt(e0ei5x-,c p,5+fnukr frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequencyr2budb ivq4u)7k 7e(x of standing waves is 475 Hz,ub) (uqi kxb772edrv4 how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 or95.ey(po7- i )vuxko/hnx bHz and 350 Hz, what is the fr79oo ipk br/y vo-uhxex5)(n.equency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 /yb7kxewcfbm8p(* f/.vlnth;km+5 q g. The distance from the bridge to the support post is L = 62cm and the string is under a t+fkbwl;(ych xf* v mpbm8k7qten/./5ension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar strin +50 jr lsuz.t3ef-8z(we ornxg is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tenzo+w zus-3t. rx0jr 58 elne(fsion 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 suppo t8r i2tmmd2yewsa396 sed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?r9ya e3smm8t dt22 w6i decreased by    %

  One end of a horizontal string is attached t,dmp1a/ooij8q9c+nws wh/s hm)n y28o a small-amplitude mechanical 60-Hz vibratormws/1qo ,pnaw2n8yoji c+)dhh9 / s 8m. 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 )str a9 atdr(+may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, r(+r)ds t a9tahow 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 justodgwk52 pz/ ng:0dc 4k 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 Hz. What is the speed of the water waveng0cp k42kg5do: wdz/?    m/s

  An earthquake P wave t0.xyk5xa b+l-oy2yk i k;de3eraveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. l3 y o205k+xy-.eydbae xki;kIf 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 underpggglg0o1rk m ,8 y5kp-)al,rk5 /ez zwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s )e gk,g r kr0ok-5gm llzga 1yz5,8p/pIf the 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 it hits a la6uknz(, 8lj4 grd f3cdyer of cold, dense air. If the sound wave hits the cold air in,fg4(zdc 3kju86 rndlterface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two typex*ijhs :wqiy 9w(k0+u(q*qg ( en zx963xgkeks of rock at a 38 zuhk wg*ygj 6(qxkx (:93e nxi9*w q0qs i(ek+$^{\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 user’s manual, k,e6xcdz e9h8the dish has to be pointed in the direction ofecd ke,6z 9x8h 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 kmyl24syzkf0*+vrl 7 pw and 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 knowledge and warning, people have died during tsunamis, some of them attracted toy p kr7+v sf*l04yzw2l the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring s r7gtyl2h10 al9 fbtn6tiffness constant of 550 kN/m Find the maximum com76ly ftlh19 g0btn2r apression 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.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretcaj o384 ,me7s 0ljj /:regyt 6xxwf8mwhes the net 1.1 m. Assume tha 3amw,w sfog/8mxl:7t 6ej e4xjyr0 8jt 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 sprinua4e+6gd( dgpx y.)t xg. The mass then falls 33 cm before it stops and begins to risuxgt . xdd+4e6 gypa()e. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a sju6fw( +gixc9peed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffnes9w gc6j(fui+x s 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 than;oqt q4 mp8 8a71+v u1jxhpie 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). Estimate84pq v utp;xha1i7j n+a1oqm8 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 p6i4 sf ova8,tkovv2h nop vn4.//n pz5honograph recok 8aovnpz oovth4vv n62ipf5/ /4,sn.rd have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accordingv81kj x +ffaq8(azp) o to the equation x=0.650cos7.40t where x is in me)kva 8azo f(j fp+xq81ters and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates wi4 ,ay6x(8; xyiqm;fnv jgj ro/th frequency f. What is its frequency if it accelerates at 0.50g (a) upwy;(x;6avxjqi,4 y/gmrf 8jo nard,    f
(b) downward?    f

  A 220-kg wooden raft floatcum f)j5t.o p wd /dbkv9+7x1gs on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrate md7d)ukwb+9jv.c51opx /tgf s 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 plac -4do pgtojd 9z;j8q(o. kl3ay at 392 Hz (G) and 440 Hz (A). z jd(4oo;.3 9pacjdqot8kl g-
(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. 1zvuh3-wb1x 4 lq/c4yq 1–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength grea3-hxw4b/qy 4q1lv cz uter in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip pr;v )65aw;qje hnu6uof each prong moves 1.8 mm to either side of center. Calcu; 6u;ep) 5uhjqv w6anrlate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 c*pt1hgw bu 2b1(il (xeycles per second. What is the maximum amplitude with which thbltuixe 1 bh1 p(*(wg2e 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?

A string can have a “free” end if that end is attached to a ring that can vm defr))y j+g/0d if7slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such 0v)i 7ff /ddeyg+ rm)ja string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing taketga i,j-/-bzy s 1.0y,t-/j-zi bag00 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 directilw uf t v2fyq99mx0*(we6y*fpon or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by whuyw(*2 yxf0e qmfpvl 996wf*t at 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 ofbvz :)vfocb iah+mr06w4nz8 6 ete0o, 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two+b 8to rvc6 h0b,) :owzze6in4emv0a f pulses first meet?    m

A block of mass M is suspended from a ceiling by pstw 2 rzf)wg63 0,ttja spring with spring stiffness constant k. A penny of m js,r g pt20ztw3)wt6fass 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 car at the junkyard. The steel crane cable is 22sa7/-g-xhfc6udc q1x m longx1a/ -6gsqc-hfu7 dcx and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11td1xe4st- 56 6,jlm,w ngsxr d–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 sprx6 njg, ld14s,r6tswe5-dxtming, 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