Give some examples of everyday vibrating objects. Which 8y4k7u tfmq p7gq*o6b alt l48exhibit SHM, at least approxt8*ullyb f4 64 7og8ap7qqtkm imately?

Is the acceleration of a simple h :fn4r j f7kxa84d cc(s)5gleharmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile encxniqp2s pso5ul 90 *2gine is approximately simple harmonic. p 2o0nux s9csqi2l5p*

Real springs have mass. Will the true period and frequency be l9-uu9x ;xq8pr9m fy0wzcy,awarger or smaller than given by the equations for a mass oscillating on the end of aza-uwx y,9rwf cup9;0y qxm8 9n idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO)?swt zm.o wgt)jqqx/x7 i:y**3

A 5.0-kg trout is attached to the hook of a vertical spring scale, as8.k)la y9wrdnd then is released. Describe the scale reading as a function of time.8ayr9sdk).w l

If a pendulum clock is accurate a)mo :7*aj mp( :-go3 uudcmrmit sea level, will it gain or lose time when taken to high altim3jo*o mru i m):u-gdc:p am(7tude? Why?

A tire swing hanging from a branch reaches nearly to the ground (* jkoec16x9(gl:nqve kw 3o)hFig. 11–48). How could you estimate the heigh3:1( * 9kc6ng)qheojvewxlkot of the branch using only a stopwatch?

Why can you make water slosh back and forth in kbmyew16 ,mf-a pan only if you shake the pan at a certain frequencymm f6-k1ybew, ?

Give several everyday examplx6j+6oz xrl ,xa8t qyx94uf5wjpgl*7es of resonance.

Is a rattle in a car ever a resonance phenomenon? Expla70;b unb3o qtkin.

Is the frequency of a simple periodic wave equal to the frequency o*coe5d+2: mqwiyd x4if its source? Why or why w4eixo5d+d2cm: q* y inot?

Explain the difference between the speed o.sa0ohbmo (xtl/.t3t;e (v 1z+x genpf a transverse wave traveling down a cord and the speed of a tiny piece of the covot 3 x/sl.h .tbo;(xtp 0z+1geanme( rd.

Why do the strings used for the lowest-fr, n 6p-iz/h0inrx /psrequency notes on a piano normally have wire x-i n/zpir0/,rp 6hsn wrapped around them?

What kind of waves dolz)eosb pn; z-lr)fee;0il.se; 1mk( you think will travel down a horizontal metal rod if you strike its end (a) vertically fron )esz1me epr )zkif(lb.l;el0so;; -m above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature,u;lbj7oqq7 r.k 88fh* n e-tlt but the bulk moqe l 8-l7r*j qhb.uo;nt7t8kfdulus B is nearly independent 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 amplitud)m4zeiu; *5vy v1rx ebe as they travel awvxve )mrb*y5uz;i14 eay from the source.

Two linear waves have the same 6t n;(8i jkdb*i4fu pvamplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmjb8ni(vdft i64 *p;kuits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord asl zg 3. 2,4yqkxf.hxjs in Fig. 11–33, the frequency does not chan sq.xl.zfy3gj kh x,24ge (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any tv-arf) :(de vplaces you could touch it with a knife blade withvd f rt:ave)(-out disturbing the motion?

When a standing wave exists on a string, the vibrations of inci affrp q .eweb +rvl6a2 1jr5r2eg66zxfge53)dent and reflected waves cancel at the nodes. Does this mean that energy ej6rq6wa5 lrr561 gvgbp3r .2ffxa+e2ez)fewas destroyed? Explain.

If we knew that energy was bei.oq26uu3 bfs tng transmitted from one place to another, how might we determine whe2 3tfu u.6boqsther the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the tod-kli9y2sr 0- xxfjb,tal distance it travel-s9 - xfdi,y2xrkb0ljs in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangswxumz 5e qb(3; from it but is 85 cm long when a weight of 180 N hang qx e3zw;u(mb5s from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drig/ gth-x h9h4dver gets into the driver’s seat. If the car g4gx/ th9gd- hhoes 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) What hiccxk8/ e wnj,;3 wn9,aut)mis the spring stiffness const ;c,3ueak), 89 twixh nnjwm/cant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 c/a180wtb itar-w4bu kg is hung from it. What is its frequency if only 0.38 kg hangriaut aw-w10 cbt/84 bs from it?    Hz

Construct a Table indicating the position x opi 9fhe 4lw )n1i*a(5qiux4dsf the mass in Fig. 11–2 at times t qi x5*e9wfa1)( ldnp s44iuih= 0,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. Thlx:1+8n5 g 8p, xlserfh ot,dme web vibrates predominately8t,lg,n mx1 5soxr e+fdlh p8: with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. W 4.z(3sso njh--ivzxj hen an additional 680 n4 (zzi-- x3hjosjv.s-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the ebugt gm9ul:i0 xu m/,7nd of a spring vibrates 3.0 times per second with an amplitude of 0.13lu mb9u i0/gu 7xg,tm: 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 maximuze z67 dc6nn/vjk,(ozv/u3ywm valyezz u66v7/ n,cnw(jd3 oz /kvue?$\approx$    A

A mass attached to the end of a spring is stretched a *oaa+yye )9tp pg52c xdistance $x_0$ 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 stretch0tt0t(qq:z ml9gy nw aoj6,4t w1v8qaes a vertical 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) equilibrium positgt4qtmao(6aqj 1,ql0:8 z9t ww t ny0vion again?    s

  An object with mass 3.0 kg i4/amgegldet6 5ce/ 0is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.lceg/ agi6 ed4et/50m 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 0.200wl 7rfz hw9o9 ,j/4c+z nfhjb8 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun+ hfrhfzw /j7l8n cjw9 b4,z9o?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one 8iv we0,zk/f 4+xrzdfend of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the sprin+8vi0wkf4fz/ z r xde,g by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to ay ,;dz9dy kgids- v //;;ryuzlp6n0ethe equation x = 0.45cos6.4t where x is in meters and t is in s9/d ;yy; l0vd ;yz6k pdiurz/ n-,geaseconds. 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 oyh:(h 8q)ivrf9g 1c t ip37qqpf a SHO half KE and half PE?ii t ph9)713cv8fgq (r qh:ypq ±    A

  If one vibration has 7.0 times the energy of a second, but the mgfg,d*nqk wwk :2p./ir frequencies and massesk/gnd mk ,p:.w f2wq*g are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillate v4p1j4 6b;yy2ctn-cya7d2hq(c dnkd s from a vertically hanging light spring once every 0.65 s. j2 nh q;yp2(btdc-y cdv746ckd 1y4an
(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 vertxq-p/3:cz pyv ical springs, each with spring stiffness constant k (Fig. 11/c pv:-3 ypxqz–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sxmw6p *vq9 n1q3gms8rin6.5t where x is in meters and t is in seconds.mn9wp1vrx3 6*q 8q gsm 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 ( s7vz 19qazkd(qht) kSHM, labeled 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 envolp 5wjfv h49qq 34g l8r4l99tyz-bgd of a horizontal spring (k = 124 N/m) is struck by a hammer, l44 l8 hf5vt9y9v4ogg9 q lrb 3w-jzqpwhich gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrat:jf/y n1+(+h qq3yit2uh2 jnfplb;*e0e i ey hes with an amplitude of 28.0 cm w01 (*jhtelnfh2h;j q:2/by+i inye3 ef+q u pyhen 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 sprin2e9l 4wvhj1l luuqs(8gs, 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-kl j-(f 1zkmp/l)+sbyf2go u1v g block attached to a fixed horizontal spring whose spring stiffness constant lvlpy+mgfs/) - 2u bkf(o 1j1zis $ 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 bridge. After reachinglhtr g9*5z 6f.2ilzqb his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s.5ir.zlgqzf*b92 l6h t 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 vibroq. awfxnsi2f4/x7 1t ations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if l4,kbldbb*9tjnu0 fau vmf e,r22/ n;it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 s.bjfunanlt*fb k4mru le,9/,; d2v 02b)    m

  A pendulum has a pery; dp6jbd3iqw-a+d ;f5jr bx)iod of 0.80 s on Earth. What is its period on Mars, where the acceleration6d)+d;;j 5f pa-3wdiybr xbqj of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum xtte/oar.8w1 rva f+ 480 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum oo6f7b c+u s-eis 0.760 m, the pendulum bob has a mass of 365 grams, and it o sbeou+-c7f6is 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’nhbih 4bqr/g2-6p4wss pendulum has a length of 0.9930 m. If the clock loses half a minute per dayib4 6-bsqhp h r4ng/w2, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for8l8tau 7 8foo3curk;y 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 Hz. At it is releas,72g r f3(+kcjvkdb(w /m-g v4ykfv aped from rest starting at an an k2b(p/jkdv 4fg7fvw,y3kmcg ra v(- +gle 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 of his ancho tk.o 5dfqcc 2g(ihc)a q3dc.6red boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are dfhgcd) .6tcc qk3qioc2. (5athe waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343vdnv. 0ky v,b8p9vc(k m/s How far apart are the wave crests (comprep,b80kvyck (dvv9. vn ssions)?    m

  (a) AM radio signals hakty1v64r -+dlgm/y uive frequencies between 550 kHz and 1600 kHz (kilohertz) and trave+y/4 l myrkgi1-uvtd 6l 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 longitudiz s s;/lr9tap7nal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as th1q 99vrjo;g myhgav*rg d6 *lwm k9g9)e other. In which rod will tm*9vr9hl wv k*9)9joa;qmr y1 ggd6g ghe speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 k*s4jkwub i,2e(so7l xg is stretched between two supports 28 m apart. If the tensil7,(e4wbx *2kouijs s on in the cord is 150 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 hill by a steel cable of ll 2*g.mqm; idsvqc 0*out1a 4)vjg4ipength 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 pul olvtu0m1q**.gq44sij;c2 )vgipm dase 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 s ,qtraj ;6*(x3 enhc,5qd:ppgtz3gk k.(rw qsurface of the sea. He hears the echo of tr* qkt6p.p:wnr qgt,axk jq ,z3ec;5g d3h(s(he wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this diffexz5 e24 q*rjswrence helps in locating the earthquake “epicenter” (where the disturbance took place). swe4q52j*x rz
(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 sinusoidal trans0vumab.1j 75s lo mf0z hhs4bc,jed+ +verse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so tdsl0 01c,bj+jh74a +b ezv.5f oushmmhat objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities p1kkocibdw-,a b ;k32, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detect1 b3k kb,;wkpoc2-ai ded at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Eakxhao 46;e/z+1cs0 rr h lxoew9eiw1* v3eg m9rth is measured to be xw;3lies zecw/*v9+1 h0ra1 m9he o 6o4kxerg$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portion *e ,wf4x;szr n*1grrf 9fm-id of the Earth, but one fgrd1, 4-n** szr;f fmir9xew is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a str y:uqt/mfp /o7etched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplqou/t/ m f:py7itudes of the two waves?   

  A bug on the surface of a pond is observed to x1dz )ya0 h5htmove up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a waved50xz hthy)a1 passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch the v;xx3a s zv:8przn pcg)v:*-9 sed2alshape of the string at the moment they directly overlap. (b) Sketch the shape of the string a f8dv:-vgzzae 9 xasl nx2;r)3v:p *sc pew 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, what a 0/ n)sj+-iqbwi cv*bp0 / 3*gomxzjcbre the frequencies of the first fci-x*) ijz cg3 wvnbjq spb/ om*0+0/bour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrateb v*czf9ohdq0*61q mqs at 294 Hz when unfingered. At what frequency will it vibrdh9q bo*0mzq vf*61q cate if it is fingered one-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 in four loops at a frequency of 280 Hz. Name at l 9eln7:f/7(lp lwzaeqeast three other frequencies n:w/ll 79e f(7pqazleat 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 frequ- ps,hrjvb 4uu9f7 m: 6u)tqovency of standing waves is 475 Hz, how f7vhvpsotuu:4qru )m-j9bf,6 ar apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 28 q1tk:fh: gq,k0 Hz and 350 Hz, what is the frequency of the :q : ,htfgqk1kfundamental?    Hz

  A guitar string is 90 cm long and has a mass ofp5 gito1cm9j) 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tensotmg)pi91 5jc ion 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, lm .5xvsaxkv:/2( s-cig jxb.but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be csx k25 .vxl:si m(-gvxj. ac/bhanged 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 20+9oexd,urhxu, i h6 f,0 Hz, but it is measured to vibrdf,ihh 9ou+, 6exxru ,ate 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 aic4m2d/ru+yv ttached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit lengy c2d/4ir+ vumth 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 by2,jmxgv yhj8 yl336ue n xwf(4 moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave pattv gh 36l3x,f8yu42wj mey jn(xerns 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 the right frequc* :xlyt3xmmj)(t 1e tency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose *mct31te(m y)txl: jxthe frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the E x5fz m*8fnwj2arth betweezn5fx*8j2 mwf n two kinds 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 underwa3+ q0ymutzj -j1 wg:azter “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the inci z:ugaq-0y t1w mzj3+jdent 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 as/yxj8 7rc k dy6hs5u8+ a6rhd layer of cold, dense air. If the sound wave hits the cold air interface at an angle ofy/ 8+dh685rc jakrs 7dsyxhu6 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 betwnd;lgvv wti: v wu9;c-/3jrmat9 .*sceen two types of rock at a 389dtav;s;l/:tu 3cmc*v 9rg.iw n -wjv $^{\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 usemwlkb;gv - qa542a va,r’s manual, the dish hak,b2q aav5-4 lvam ;wgs to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 25s 8 ;h-2* spdsvogdhii ;rn9r50 km 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 ; *9gp -ds5 sh;rsvndhriio28 to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a(q6 ksdxa 2qt/drez,* spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conserv6qa*z /2dx(et dskr, qation of energy.]    m

  A 65-kg person jumps from a window to a fire netl0jset.hjp060 sa rj 1 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a sse 0ths0rjpa6l 1j0. jimple 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 thv tt7oz, 1 zvj4g6ar9.i2 :4xmgav immen falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation? ti1 6o94r.gv,v g:4 vzaxitzmajmm72    Hz

  A 950-kg car strikes a huge spring at a speed of 22oqkz4a6) zl dg-lf)s7 m/s (Fig. 11–54), compressing the spring 5.0 m. (6kla -g)lzz7qd4)fos 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 ctle;uop g 09wibhv0 95offee (diameter 8 cm) at just the right pace of about 1 step per 9wgtlhpu9 5 0;b ei0vosecond, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certainsfpz ;5)lt8t c groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the freq8tctsp 5zf;l)uency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650 m+3z nx-lf ld1ze+3m2dz8x cmcos7.40t where x is in meters and t in seconds. Dme x2m+z-ln1mdz3lx 3d z 8+fcetermine
(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 oscillaa((lktx;tw)(m4 rjqqg i1 j(etes with frequency f. What is its frequency if it accelerates at 0.w 4 x;(l1q)trjkjae(i ( m(qtg50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raf7gk04o1(ge y tnn96fkpu+vgot, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whil+9geyko g7t6v41pfn kg (0oune.
(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) anuxi9y 3-f-ctjr6 ao:s d 440 Hz (A) cxjyit9rs --u a6f3o:.
(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. 11–z23t w rny.f9 m3um1zr33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the1w .29umytrr fn33zmz lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and cb8hbua r; +y6-cyl(wthe tip of each prong moves 1.8 mm to either side of centub( cr-6;bl+8cw yha yer. 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 frequency 1.5 cycec:uu9mxn0urd83 szf 9z66plles per second. What is the maximum amp 9 93zuxcn6 e8um:zuplr0sdf6litude 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?

A string can have a “fru4cdry45.j 3 8cpdzs iee” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string w ujc4ircd83spd. 5y4zith one end fixed and the other free.

  A “seconds” pendulum has a perio(oyzk(e sfv;r3z/ zo*d of exactly 2.000 s — each one-way swing takes 1v3o( erzzky s *o;/(fz.000 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 vertib pi y./sm6af1cd.s4lcal 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 period of the horizontal swings, and by whapa/ci6 4fdlssb. 1y .mt 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 ismlyfpkm0pj47 ;ph 5 (whx*m c7 stretched under a tension of 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 they4 5p( xlmmhw;f77* m kjppch0 two pulses first meet?    m

A block of mass M is suspended from a ceiling by a springm5px6 ub(t1terj+ v1 u 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 will allow the penny to just stay ob +rjt6emv15(1uutp xn top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kgj sn ,; myam4wb,q73yq car at the junkyard. The steel crane cable is 22 m long an s q7 n4jmam;,q,3wybyd 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 showna7p )t x pqnm0j17bgb9 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 sprinap 70tjnq79) gb pbm1xgs 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