Give some examples of everyd;19/ r,vt tc rytt8od+vwz;bmay vibrating objects. Which exhibit SHM, at least approxi9 8zvb v/+,wtc trmt1r;yd;tomately?

Is the acceleration oflmfbmfw kn nbo1fe ,w 2.(0fr0;ug7p3 a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston 30/ncqr 0r b4v*mfy;n eugba2in an automobile engine is approximately simpu24 0ancbb/0rnvqyr*fe 3m; gle harmonic.

Real springs have mass. Will mdh nl l qnx238psc070the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless0n7ldcsqhm0x 23pn l8 spring? Explain.

How could you double the maximum speed of a simple h0w zez)a .)0cj)vuqd2ot) zwiarmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, andbxzitrmx+. 0 s(y+)qe then is ryi).q +stm+er xz0x(beleased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea leveljfvj*+7qsv a:1ylodg3t 5fk 9, will it gain or lose time when taken to high altitude3foqk:f5s j1avy v +97jgld *t? Why?

A tire swing hanging from a branch reacp 4g-hfku0l nd:3e( :nni2q.prh* zdrhes nearly to the ground (Fig. 11–48). How could you estimate the height of the branch us 2gz4udnlk0 hfpp -: (r q.hnen:di*r3ing only a stopwatch?

Why can you make water slosay4 .hkgs//vyhxj(nuc lz ka8u4- 36sh back and forth in a pan only if you shake the pan at a certain freqj( 6uaxa4shnklk gszuv. yh//- yc843uency?

Give several everyday el1;p rf7j 5zyaxamples of resonance.

Is a rattle in a car ever a resonana6)wzu q5pycxom, r7 .n6 wwm1ce phenomenon? Explain.

Is the frequency of a simple periodic wlm;ha kx z/:y9ave equal to the frequency of its source? Why or whzhk 9/amy xl:;y not?

Explain the difference between the speed of a ;nyia qavz4xc, q-7f /transverse wave traveling down a cord and the speed of a tiny piece of7vxqfyi az; ca/4nq,- the cord.

Why do the strings used for the lowest-frequccdff(e241s7f c:fmf1nn vi9 ency notes on a piano normally have wire wnvnf:7 cs (ff92im 141fcfdecrapped around them?

What kind of waves do you think will travel down a hom-bwf :kfda:. rizontal metal rod if you strike its end (bmf:adwk - .f:a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase is7vi,6py /pmzs*d/e7.zc ,5zmbx tsjn temperature, but the bulk modulus B is nearly independent of teey,p*tm7s,v 6cz p5z mi7/dsjzb/s. xmperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular watefv 9le q/iq(h+oj;*c vr waves decrease in amplitude as they travel away +j/9v*clifheq ;(v qo from the source.

Two linear waves have the same 14(v3iya snjim rst63 amplitude and speed, and otherwise are identical, except one has half the wavelength of the othes1r v4 as6 (yn3i3tjimr. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary brim*c6-lz , y5wccbq 4etween two sections of cord as in Fig. 11–33, the frequency does not change (although the6imcy *,wbccl5 rqz4 - wavelength and velocity do change). Explain why.

If a string is vibratavj(pw0w, i,1av9rzh ing in three segments, are there any places you could touch it wita(9zjpw,v0v h ,wa ir1h a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflecx:qxcol86*;g 4+ pbig c *iwdyted waves cancel at tho6dilx:*w cg 8cpbx+i *qyg4; e nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mr9xnb hp*6qruwo0 bh.)h +9evtt0 n+dight we determine whether the energy was being carried by particles (math o+r9p )0.nbbvde6 9 uhxtn*0twq r+herial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total dbw.l :7lf00p+08iw7umw u vvvuf6bgt istance it travbpw 0ufg07v mul.0lvb:6 +v8uit7wwfels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cmm *2omgpo6wy(f /gfz 3 long when a weight of 180 N hangs from it. What is the “spring” constant k of tm* fzomw3(2/ygp6ofg his elastic cord?    N/m

  The springs of a 1500-kg car compress 5.4qbvcsj 8:bjn 5 /d7en0 mm when its 68-kg driver gets into thenb7c veq/ds:jn j84 5b driver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretchesc;uxz wt-x1;/0p0 gm sztw-js 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stifj0pzsx0 gc-m/x;ws w t1;-ztufness 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 frequenci,m71;h9 a/d (vgeq;qyc6 bmym8eh zay of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if onhhz,deyvq8yeac6m7 19b ;m/(;iq a mgly 0.38 kg hangs from it?    Hz

Construct a Table ind(9vfbg:;8uq7ybr ii gicating the position x of the mass in Fig. 11–2 at times t = 0,t b(9bg ; igq i8yu:rfv7= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 wet )y kd8ovr0d8b. The web vibrates predominately wity t0vr8do kd)8h 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 frequ0 sc(d l3sy4hu3nzm2qency of 0.88 Hz. When an additional 680-g mass is added to m, the fre2q3m4snzc0y3su d(h l quency 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 +z(l +3rsxmaksecond with an amplitude of 0.13 m. Dr3k+lasxm +(zetermine
(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 equilib7x4 qfk,hvqp7z7yd -hoj pg( b/,5gserium is the speed of a SHO half the maximum val bzh gj(y47pe/,-hqxs of,d7vkq5gp 7ue?$\approx$    A

A mass attached to the end of a spring is stretched a f/z lc 5+b:snldistance $x_0$ 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 s:srkt)shwdtg 4d 7+3apring is stretched an additional 0.130 m and released, 37t+hst)4gwrda d k:s how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attacfifnczr e8/3)v (p8 tcvqi+)d5g;hx k hed to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m c fpg+h5cn(/ 3k)t efvzqi8r) xd8; vifrom 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 toy popgun 0.20q 6sm 29fggz uvjq9v/,.+t aen0 m to “load” a 0.180-kg 6ngvqsu9zg vaf9+e,2 qm tj/.ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to onelu c zr-19q- sjbodgq(f);qp0 end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 159ofqb p sdlq-rg)0 (1uqz ;jc- $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates a;ta1*oxs,kxbj* l u0o ccording to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. o0 albk** sx xtouj1,;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.oew-ml9j -hvjx9d78o syyg4 equilibrium is the energy of a SHO half KE and half PE?x ogvyjj8- 4s-7.lwm o9dhe9y ±    A

  If one vibration has 7.0 times the energy of a second, but their* 9mfbaijp.j(n yx: e1 frequencies and masses are the same, what is tae fynp*i( .j:j19 xmbhe ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light snwh fw wn1g x7vj,9u;*pring once every 0.61g;fun wjn7*xw, hvw 95 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallet olgu p(y+1s4l vertical springs, each with spring stiffnes s1yot (u+4glps constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t wh ml8a6jcq)7 oy+9-djdpuoui - ere x is in meters and t is in seconds. Determine ujlpid8y )o7 96m oaujq-+ d-c
(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 ht +9jm/wxx qf,ta5+w upp *eok;x4g6B. 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 i, tm2.g1gfqk rest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of qg g1m2,f kit.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 stifys7n:m;ad5 /j jjhe4k 6mym i.fness constant 305 N/m vibrates with an amplitude of 2mdj;sa/n6ym .emyhi:jk 57j4 8.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness consta8fe r zdg/va82nm8 h;znts $k_1$ 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 bloce j2nxx631d4+zxglo uqg ,b1hk attached to a fixed horizontal spring whose spring stiffd +u gz6q1j1bo x4h,3e nx2lxgness 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.q8:;lzaigv *ggtb*eg 6go up 1c4 ck0 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low p06g qbuc1;g:z. li* egpt8gkgc* va4ooint 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 unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. W:dc(lhv *nds: 1c2e/ub. bv jahat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to44p i/ 3kj6ut 9fksakd make exactly one swing per second? (That is, one complete vibration takes exactly4 p39 akukfdtjs6k4 i/ 2.0 s.)    m

  A pendulum has a perig6bfut tqkpky 4,0+:nod of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that tpn0g4kqf tk, y6b u:+on Earth?    s

  What is the period of a simple pendm (gx(pu15 6wx:o vjogulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pemcj371 vv 4jngh,vu )e(pifm*ndulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at 4 ,*hfpji)3gvm 7(ucmevn1vj 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 lv-e vtbfvmo3u+pk;2 9oses half a minute per day,k;vtevb up9v +-23omf how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for t cfw74i/g-vs /- vhzqdu83, nq*fanqd he 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 Hz. At itj 3qar(v1.a2gvv8 nhi is released from restv8va h2inr 31(gqa.jv 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 crest-dia 7 b2el wywq)i6i*s pass the bow of his anchored boat every 3.0 s. He measures the disi2ie*d-6by liw7 )awq tance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with u xw.k9;uq;xf8kp: zwa speed of 343 m/s How far apart are the wave crests (compress;;8ukkwpu zfq9xw.x :ions)?    m

  (a) AM radio signals *4-xr7fk/irey( .u mucyxn*f;x (a4r :bmr oshave frequencies between 550 kHz and 1600 kHz (kilohertz) ayf: n(;obce-*s*.fm i7ryxxux4/ r amk( 4r urnd travel 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 longitudinae :/pggtxhdgo; (h;y6j f)jha 7ly45fl waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice asnm cm c2a8w/qn+d4- yafqf 2)k dense as the other. In which rod will t8)m2ky adf -q+q 42nmc acnw/fhe speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched cf7z.c7k3v yppcic 2+ between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support .f7 32zcpipc c7v+ cykto the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 62( -f/bqevn 8ai0 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 obsieaf8 n b-/qv(erved 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 su 4elpu7 sa 59)u3lyrvqrface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How u )ea9lyq3s 4lr5vpu7deep is the ocean at this point?    m

  P and S waves from an earthquake tr37l c)q om0v61dfruf ts .pqf2avel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took place)uqt ro6)f.plf1s q3m cf 7d0v2.
(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 si*cr/5b6ndwir z mcs7,nusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Sesd/cmr *i5nwr76 ,bzc t the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the hbk( )k7k fgnz;de*ly bz .qk14wixc--2*tfv amplitudes, of an earthquake P wave passing through the 4 be-zq fyidk bvxlnf; w.zkkkg2)1h7c*t-(*Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing througq l:gs :bnlv(/g fs.p;h the Earth is measured to be (gnlv.:f /qb : ;sgspl$ 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 throuk0-(xkobjzn.r 0j(oa gh the same portion of the Earth, 0x.-0ajkoo(jnbr k( zbut one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along yb g nl* ;xzn-obh,pg-ey a0r337z-oda stretched string have the same frequency, but one transports three times the power of the other. What is thy x*g-zn,blope3 -30yg o -7bhza;drne ratio of the amplitudes of the two waves?   

  A bug on the surface ofrw (.af,r3 c/bkzkh1u a pond is observed to move up and down 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 facto. 3zk,f wraurhc1k(/b r does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward eac:se( zeuca 2) ;h0dnfwh other. (a) Sketch the shape ad f)(uc2;e:hws0nzeof 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 its fundamental frequency, -1rr+m*av4y ;5vtshwonx g bnneewe/- * c/1mwhat are the frenrmrtyem;1e5a-+ vhe/v*n-xowg c 1n* 4b sw/quencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it vi/kuw4it1ab d8 brate if it is fingered one-third of the way down from the end? (That is, only two-thirds of thdk/tuab4 w8i 1e string vibrates as a standing wave.)    Hz

  A particular string resonates in fouvfow/7d8 k b+x 4c/ ggeg88vznr loops at a frequency of 280 Hz. Name at least three other frequencies at whiczw c/8 v8gbgv 8g4koxe7/dn+fh it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a strwbj3zb+* w7c kn;v 4roing is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjawkb ;jv*3 +7w4zcb nrocent nodes?   m

  If two successive overtones of a vibrating str0 4dgm8biv/vj ing are 280 Hz and 350 Hz, what is the fre/vd b8vmg40i jquency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the 0n ag+ltn 2; e7hf0ybfbridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamenta0;2+n bygnff07tlhe al and first two overtones?    Hz

  A particular guitar string is supposed to v1:y9jq/ wk) i5wsllgk(cww g( ibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percenly 5wk gq9) /c1wi(skj w:l(gwt should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar stria4)mhye e2;yh v bg(obz(g:m5 ng is supposed to vibrate at 200 Hz, but it is measured to vibratezyb eg2;4ea( m(h ohyb5vm):g at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mech5 ciz5k9asfdt;pk -h v.p9a (vanical 60-Hz vibrator. The strd5z-k a9avtk. 9 i;cv(5sfphp ing’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving tp wmqnshl gmbkh +ba( 0:.3ca+n8lb. 7he pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L n(bmnh mabla. sh b+3+ .lg0:kp7w 8qcbetween 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the rightz*zm z*djxby7x+ lfz*1ofz 6- 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-wzz*-+xd7zfy6*zb zlmxf o* 1 jide 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 sj*f fu)sns 4;u e-ps+e5d(pxoin z) rq60g4ijtrikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an inci ds) oufenirf 54pji(x6 se -gz* sj)+;p4q0nudent angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from xmfn3x a4,ia ,o4v w)h2.8 m/s to 2.1 m/s If the incident wavefxn )im 4a,wo xvha,34 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 y9ee+(e7 +h;3zj2ynn hktijo it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an an;i3e y7h+2jnkyo9e ez (hnj t+gle 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 s. q:2:kx+*xgjupi8g zb6sjobtrikes a boundary between two types of rock at a 38 xp g2* :o jjuqz+gkb8:. s6ibx$^{\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 k 2 an8oz0ebmopmo*f)w 3m*h 3in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an er )hom33ozap2mmo e n*f kw80*bror of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h traveli3p,d(l;mo+gk m dri+s across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors.(iipm dk+ d;om+l3r, g 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 shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 irtr8 /fi;a mzt.;k4c kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (apprci4;m t.tk/i rf;az8r oximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whiq27 r-rpba5wxch stretches the net 1.1r7qrp25-ab wx m. Assume 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 enuz5j*qw e5:9 tn-j9r, kcthuy d of a freely hanging spring. The mass then falls 33 cm before it stops and begt,n cu*- j:rhquwt59j9e 5 zkyins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge 0f2sag/oq qx( spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness const(o0/fg2x aq qsant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the righ kdpr32b haxvifc8y*6yx ,7l8 t 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). Estimate the speed of wa 8fy2hdlai8k cp*brx,673yxvves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm)qifls;:c*2* jjwmvl 5 zos li6 +pgn( phonograph record have a wavelength of 1.70 mm. W + o6sw(l;fm i)n*z2:iqg vlc spj5j*lhat will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibratl g3.2z9m m :nuucfmd/es according to the equation x=0.650cos7.40t where x is in meters and t in secom9 2 /m.dguu nfmlz3:cnds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What kpd tx+ktj3cm i5 0u*7is its frequency if it accelekmp0dj75c t ixktu*+3 rates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lal l,h +j+sy5)of-vem wke. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water.+5mys)+w,j evh fo ll- When he steps off, 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 are tuned to play at 392 Hz (G) f,h1rna +a2j3q* fvneand 440 Hz (A).vnha r2,a+fe 1 *njfq3
(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 stoh 19nr/ f)uwmretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the 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 s m/uwhn9fo)r1 ection of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 a-dbkxi 8 u/*kcj8f-d Hz, and the tip of each prong moves 1.8 mm to -bdjk/ f8-a cki*ux8d either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of fre s..1 ,n5acpec .uhrkvv3ou+oquency 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 (F vup cv+ .rc5o,a.s on.ku3he1ig. 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 n-3tmvgq djk 98 :jgw;slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and thd9;vjmk:gtwn8gj q- 3 e other free.

  A “seconds” pendulum ha7z-zd co:1woi(rfvl( s a period of exactly 2.000 s — each one-way swing takes 1.0(wo-v7fo1ir z( :zcld00 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 o +wj-j5d5s3d qgi/ezfscillate 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 oscg+/zwjesd53 d-iqj 5 fillations 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 o/5s kn8 bys*:qod;3x)fxx gyvf mass 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pvf5 38nxys:ogyk)s */ x dx;bqulse 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 spriy g7 ut-jm 2c89mqw;ybng with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that wilwy-9tg7 ; mbmy2u c8qjl allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg cark i) 8b s86z oyz*gsybp/(nsi/ at the junkyard. The steel crane cable is 22 m long 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 bounbn/*zi s g8py/ok()z sib8 6sycing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (whnymytk62ct4drs j5-mk,3m a1 ich also gives the dimensions of the block). You push it sideways as shown, and then you let go. Tk-,yd62cs3tmnm mjkyt 14a r 5he 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