Give some examples of everyday vibrating objects. Which exhibit SHM,jogy2 y3d/y;*+kyljb 1(nwxs at least approximatelb(3w;/j*kgnsy + y y1xd2yo ljy?

Is the acceleration of a simplsojb-qh ls7;h rg(*c 8e harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is appr98)jruww ,uq8dj(d ib oximately simple harmonic.ujd 8r d(uwq8,iw9b)j

Real springs have mass. Will the true period and freqet4o3is n(zmkhpzw2 )y t( 10muency be larger or smaller than give24(1z )tmyiot0s( n p wkehm3zn by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a3g1 bc*6nh cyu simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the*xswqoa5+ /v+.x a3ph zlnd u kxfs/44 hook of a vertical spring scale, and then is relps/z 3ha/v+n5 4l+.w k*4oxxxusfdaqeased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain azepc aiqhvj3, j2c2ij15 e-/ or lose time when taken to high altitude? Why? j1i,q2j hc/e a-ae5i2cj3vz p

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48)a 5e vr)l;l zrft m(qy+-foi9;. How could you estimate the height- aq;)9m5+lz;fy(li t rorvef of the branch using only a stopwatch?

Why can you make water slosh back and forth i3pny( , pbhhx60)*-xb yhnl dtvm9yh, n a pan only if you shake the pan at(9h)phmh ,b 0xn *hb,6yvdly3t yx n-p a certain frequency?

Give several everyday examples oftb;5ccokzse/: m;gn9a (fu v/ym bm ,0 resonance.

Is a rattle in a car evpfe 8 0apg*x.ter a resonance phenomenon? Explain.

Is the frequency of a simple periodic wazkj p71wtu;u/3m9mm2p 3 gsupve equal to the frequency of its source? Why or why pu3g3 mp;t 1u2/ mpwzjkmus79not?

Explain the difference betwe hh0;5-rnp rqren the speed of a transverse wave traveling down a cord and the speed of a tiny piece of the 5r rhr-hqp0n;cord.

Why do the strings used for the lowest-frequency notes on a piano normally have 1gmmw88zn s4zwinzm8s mw4g81z re wrapped around them?

What kind of waves do you think will travel down a horizon 4,6owj cmkr+qtal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its l4wm6c+j o,rqkength?

Since the density of air decreases with an increase in temperath:bl4 02 prdj (o mz:wrxej8:aure, but the bulk modulus B is nearly independent j:rm l( z:28oxrb4ead0jp:whof temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as thz1+dtklr ft(hw3*) nfey travel away fro kftnf1) +3tdhwlr(*zm the source.

Two linear waves have the same amplitude and speed, and otherwise are identic9j,y6 drxqs* d ybc cr0hn*q78al, except one has half the wavelength of the other. Which transmits more energy? By what facton0rqch,b**7sdq cjd 9ry xy86r?

When a sinusoidal wap mm yz60xk trv*+olm28li;w* ih9ez,ve crosses the boundary between two sections of cord as in Fig. 11–33, the freq mprv*e+92zo0, ki xl;y6l*t8 mziwhmuency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segmentslmc1(z3hw *e s4v8 azj, are there any places you could touch it with a knifevces 3w*m l(zh8zaj4 1 blade without disturbing the motion?

When a standing wave exists on a string, the vibrations/fd;cs/yz ;u6 w)pa8, zpzwao of incident and reflected waves canc ;fzdc;w wa/z)p 6yo/z, paus8el at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energnx tp(hc,vjy(owv8v7xac ckbyy 0)33.) x o9u y was being transmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodies)jc 7 a p 9y3yvxv()(y), ccwk0o.8vxnbuotxh 3 or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is vrpr v 8j*xn,(the total distance it travels in onen,8r x*vj vr(p period?    m

  An elastic cord is 65 cm long when a weight of 71nc77 xczni5 hv1 *ami5 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elasti1i*xvmi5ac17z 7nc hn c cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when i4 0ynfe4)yfvhts 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibratfe4v)0n 4yfyh ions?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish han6k8(kas,nu41og0cwho xf l o :3ucm) ags from it. (a) What is the spring stiffnegwoh: s 3()0n u1a4f8ka6 ,mkocuxlcoss 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 when a mass of 0.60 kg isj4 + r1pefvw8a h1hv.e hung from it. What is its frequency if only 0.38 kg hangs from it? evwh 1fvrea1+hp j.84   Hz

Construct a Table indicating the position x of the mas d3:*rvs;v kmfs in Fig. 11–2 at times t d*fr kvms;:3 v= 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 spi4acy4 o7 9zhz.a2ewixder’s web. The web vibrates predominatelo zyw. 4i2he9 a4xza7cy 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 vibratn.jw gokqmu( .7vm,2 9kj9 ibees with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, .( iqvub,7om. 9 kj 2mn9ekwgjthe frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of ktcri97gz(w* a spring vibrates 3.0 times per second with an amplitwzr(9i ct*7 kgude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equi+-7nrc h1 mgrulibrium is the speed of a SHO half the maximum valuu r17rhcmg-n+e?$\approx$    A

A mass attached to the end of a spring is stretched a distanq 9evb( ta ,//ejf1)gbj mqgi2ce $x_0$ 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 0.31p,vhazr5k9o*7u j3xf(pxl x .r7bp 7a5 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reachz53 ju. (fbr7ppr *9ahvxaxlox7kp, 7 the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spri,rsw+v+c1 df q,vbh o(7pa+jang 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.jhd+qs(wrav ,, 1+b+c 7po vaf55 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 comp r1txc1yoy*m q: wi19rress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With whaor11cwm9i r:xy1*ty q t speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end ofzbi4c1cd5kv 3,n* z(w6up wof 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 6*1n4wc (oizzp, 5fucwb3dk vwith 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 apveprw3.x.*;0g kv(xops5 p 0lx7rtv ccording to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determinpvr x3 s. p0gxrxwp*kve( p.;05vt7loe
(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 ene7jxs+5ttf pyjs4qdxtk8w)2r mxk9r;im , 9f; rgy of a SHO half KE and half PE? ±9 ytx+ t 8kmsdrj2 9k,4 ftx5jw;;risx)fpm7q    A

  If one vibration has 7.0 times the energy ohli duo/vnvc)+1- ey+vnz:pi o 4z;:pdex-4 xf a second, but their frequencies and masses are the same, what is the ratio of their amplitudes? ) ylvzhxe 4c;po+ zpxnv:ndu- d/v:-o4i1i+e  

  A 2.00-kg pumpkin oscillufa86eg2q s0rates from a vertically hanging light spring once every 0.65 sg8afre0q us 26.
(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 vertical springs,f f2f0) ,iikqv each with spring stiffness constant k (Fig. 11–49). What will be the frequency fkf, vf2qii0)of vibration?

  A 300-g mass vibrates a :skst2rbo4/;ps96m e 1imm jxccording to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determisrtm m exo1mkipj ;/6s s2b94:ne
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what is *;ahkxsig 11b
(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 x d9nwo5t5fvrwl1e2 z5.+ ifm = 124 N/m) is struck by a hammer, which giiow w+r9fz5 df1e2mxt5n .5lvves 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 cons 4;p6,hix cy4tk5z(b vtb+ ejatant 305 N/m vibrates with an amplitude of 28.0 cm when 0.26(btpv6h ey ti4c+x 54;azk,bj0 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 , u9ipr(4oyv*+aqrkif m7f. xtwo springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontaqv+4bbs94j6zm ofl (wl spring whojbbw z46f9l4 (v o+smqse spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reachi4q1sbf zjn5odwnuw,m77f r+ -c;0z fy ng his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bung7szy jww51rb;cd-4qf znumof0 + ,n7fee 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. What is.cdpu89nh hr- its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to ma8srqz kp. 13qnb1rvm :ke exactly one swing per second? (That is, one comple:1rszk3n 1b8r vmq. qpte vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, whsr:majsrd l6y (1fin aw5*:9zere the acceleration of gravity is about 0.37 that on Eart rjsazr sy:i6(lm9da:nwf 5*1h?    s

  What is the period of a simple pendulum 80 cm lqp99 dtz z(g)oong
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple 80)hvfsxvn omz 2 r1ti7vd//zpendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12.0 vo/z/8stfvv)7xiz0 ndrh 1 m2 $^{\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 szrbk h;h- (.2;fsbwiloses half a minute per day, hob 2h.(bkfi;h-; z sswrw should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for *kt)eat0 v )qjxvz ) )9npw c.phy37nvthe 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 is9 n j/dwd77 3z4qvfsh kh;ij/q released from rest stardk fhq4h9zwj/7 ivsdj3;7q/ nting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored bou1 nn:di0us1 bat every 3.0 s. He measuu1dusb01:n nires the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency ovm55cim5 9ufzf 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressions)? z59i5mm c5vfu    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohet*cau;w5j7nw rtz) and travel5u* jnww;c7at with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves x hiqkl)ngm23 4 *dq-gin
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic ;u)kf.zpuj/ kmodulus, but one is twice as dense as the other. In which rod z ku;k/puj) .fwill the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the ten+e+) 94pbml ilm.lqrision in the cord is 150 N, how long will it take a pulse to li9b4ll)r +e pi.+mmq travel from one support to the other?    s

  A ski gondola is connectuute59mf)g b.ex:*g ned 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 we *mu5u:ge ngfx.)bt9ave 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 t+m 2 +s o)ioq1ki6mlvof his ship just below the surface of the sea. He hears the echo of the wave reflectedlqomm 1o+ tvik2s+i )6 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 t fnlgsb2ilon-i56i ) :his difference helps in loca niibgf-n 5)6 oli:2slting the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can tim15-j(q2i:3enr cfbkmb/dda d6a*be approximated by a sinusoidal 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: Sea5*e b3j1/- nd2it6ickfd( mqdb mar:t the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an eaz r 5c)lmz:0kjsze9fvzg41vs2 4z1x g rthquake P wave passing through thez4gz f:g9ls 2 j1r)c v0mk1xzze v54zs Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an uwd xvh:tm1h jq 7m431earthquake wave passing through the Earth is measured to be u1tw 4hd73h : xjm1vqm$ 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 s,q5(b tgobs .t d--ek*6t mznkame frequency travel through the same portion of the Earth, but one is carrying twice the energy. Whtq dsttn b,*bomkk.(-zg-65e at is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but onv3imxja+e2 *i e transports three times the power of the other. What i*vm2xie+ia 3j s the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to*t btff 9/.sbl move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If thb s*tf f9/bl.te ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 a(htp0ba;9xidic c3w q;d6 4y clw,6ce re moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b; yeqwci3d dxc6t, 6;pia9hc lwc0b4 () 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 Hz2r, 4.x:zovbr fpbj r0 as its fundamental frequency, what are the frequencies of the fzp b:bj4rr v02.orf, xirst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz 1jwh8cys+) wmwhen unfingered. At what frequency will it vibrate ifh8jy 1m cw+s)w 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 ; za:.bziboid3sl66 t at a frequency of 280 Hz. Name at least diai lz.s b:;6ob3tz6 three other 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 92 ,6pe w +6bszu23zre1 5gbmkfkm/s If the frequency of standing waves is 475 Hz, how far apart are5fp ge u+k 1zz6,sbmw3kr6e2b two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 35u z .obev5+p-i0 Hz, what is the frequ5v.oeup+b-i zency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 7-ams4k irxzl-f- d c7g. The distance from the bridge to the support i k7mdcfs4-l-za-r 7x post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 zk0xa0( psqh -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?So the three f0qahx(-ps0z k requencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to phmax uylw 5-,x+gn. 2vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what pemg w-, xlh5nua+yp x.2rcent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached t,abq9j7g 5htxo a small-amplitude mechanical 60-Hz vibrator. The string’s thgq9 5bxj,a 7mass 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 tk;;7,ppbs5j ( jyxsmavj 14b whe string may be adjusted by moving the pulley. If thk;pysb5jw1sp7;4jvma, x b( je hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at vo p-16foqwlsl1/v8 u* y2cddjust the right frequency, the water alternately rises and falls at vy-d2/c f6l os l1pq1du wov8*each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.o3o ;f2 e+engy0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident anglofo;egn3+ey 2e 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 underd b nd4 7/ *ko.zd;qt ylxd.md:aiz,g6water “shelf” where the velocity changes from 2.8 m/s to 2.1 m47gilb.*.:ztzd;o/an, yd ddqmkdx6/s If 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 layer of cold, dense airx r4,vjazd4yltt :+6sio8:a r. If the so4tr+ y48: :ai ld,azjov6xsr tund wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary be*hzm 4oo y.ol z,wns7m,tf5c*tween two types of rock at a 3 tn4wo m.yszh* *,7colmf5o,z8 $^{\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. Accor;q*s7 (4sqdj dwjkf2fding to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of about 2 7kj2 dswqfs( ;4*fd qj$^{\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 9yc(n:d kvv 2tkm/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 dnct vy(9v2:k 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 y ye/4.9brjfc constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall a9 b y4eyrjfc/.t 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, whic 1w7t+,bg tdkkdz3 mxno472fdh stretches the net 1.1 m. Assume that the net bkdzd17t, tog+7 wm4d nx2kb3 fehaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring.k)m:bf0h;(cox rv0 y sj3nw9 n4 toa6n The mass then falls 33 cm before it stops and begins c0n3x(n: yb)asn0fo;tv4mhk ojw96 rto rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig*u n204u hosql. 11–54), compressing the spring 5.0 m. 0s24 lqh unou*(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 coffee (diameter 8 cm) ata. b odaasiz- o8a:s*0 just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the sd a0a* s8.aoo:ba z-sipeed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center (u0kia92qxc ye ebv)-i 2l5ch of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitt2ckuv0e x2q eii9ly-b) ca5 (hed?    Hz

  A 2.00-kg mass vibrates according toxxbi(20 lpq h5 the equation x=0.650cos7.40t where x is in meters and t in x5h2b0xp(q li 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 with fr0s z)uiav r78/ wbjl(eequency f. What is its frequency if it accelerates at 0.50g (a) upwardu i8s0va/ lrje(7w )bz,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on o hwgw:dkb9qr782vi 3 the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a wh2 37k q ow:wi8hvb9drgile.
(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 inst73d lx(y3qb znrument are tuned to play at 392 Hz (G) and 440 Hz (Az3xqd3nb 7l y().
(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. sorg-22a3 xxg 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter 2g2- 3xosxgar 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 Hl.b i 2 -q(.hdoehy;xtz, and the tip of each prong moves dyhe x .qi-t lbh2;o.(1.8 mm to 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 spo4 gjv- ,8y+2fvdqv 8 bs1(svj+ru kximple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose c- j dvvsqvpg 1j2s8, (fykxr+u bv8+4oontact with the board during the oscillation?

A string can have a “free” end if th2y 7nn ajq a6nwkt+94xat 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 with one end fixed and the oj9nynqa xk 27+ t6wn4ather free.

  A “seconds” pendulum has a period of exactly 2.7;k/zo5k ju be000 s — each one-way swing takes 1.uokjz/e ;7 kb5000 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 directb9dc5b8n dv(3 /3 iy vualrmmyoh+x17r h44fnion 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 horizontalxr5 fb3 8 ymvmlda+/n1dhco 749ivy3n(rh4ub swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass u od a)-9i8ydau y16 s tj,y:a/va;gkd123 g is 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 opp9ja/vs-; :1,d y6ki ou gyaaay8)dtudosite end. Where will the two pulses first meet?    m

A block of mass M is su m/lk48uj2z4t bznyj ;spended from a ceiling by a spring 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 on to42zjj mtkunzyb84/l; p of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel c0+c x3 jv:tlqfrane 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 bouncing? [Hint: Refer to Tabl3 lxv0q+ cj:tfe 9–1.]    s

  A block of jello rests on a pl-vu2x(; p 0dd4guijcye2bw- hate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate thx-2bj0v uie-2u dyw; d(4 ghpce 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