Give some examples of everyday vibk2:ma/o fl(71 bqntfc4ph s1trating objects. Which exhibit SHM, at least appro4 l1 (21fk fqbmsta/tc:hno7p ximately?

Is the acceleration of a simple he;k6i.31c0 ths sybzlarmonic oscillator ever zero? If so, where?

Explain why the motion of a pistjr9+ hvx/uacd* .ky; y:a;kdb2hqrd ; on in an automobile engine is approximately simple ha;: +kdh.r cv;xh9d rb;/ud y*ajyqk 2armonic.

Real springs have mas3sd jk /-yu9cos. Will the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an ideali3u-s d/yok9cjzed massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator ba ye;.mo.tb ((SHO)?

A 5.0-kg trout is attached to the hook of a vertical sp)o k2a3dyw)z2nq(gj4kpl dy2 ring scale, and then is red j) nglk(o4)3azwpk2d2q 2yyleased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when tak pf33vhymb (fhj2* t-jen to highh-hb2m3*3(tfjf vp yj altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48).o)/uip pw .li. How could you estimate the height of the brau. .pw/oipli)nch using only a stopwatch?

Why can you make water slosh back and 81xfw c*2kmgxx8 wpa+ forth in a pan only if you shake the pan atawm * 8c1wf x8x2pg+kx a certain frequency?

Give several everyday examples of resonan8i(4-p,kopcv e ajy2l ce.

Is a rattle in a car ever a resonance phenome fd2ndrgqow/;/q/z3s non? Explain.

Is the frequency of a simple periodic wave equal to the frequency ofm93u (hx:-cwna 9tl r:hbxb 1r its source? Why oh9x:h(un rt9w ma:xb cl 1-b3rr why not?

Explain the difference bep9:wwu j:kpg(w1 ;o38heskqdtween the speed of a transverse wave traveling down a cord and pk1k3 dp8s(ow q9;:w uhjw: gethe speed of a tiny piece of the cord.

Why do the strings used for 9(t49tqijyg wthe lowest-frequency notes on a piano normally have wire wrapjy9t g w(q49itped around them?

What kind of waves do you think willk37j0( tl.n:aelbuki travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally p. 0lekbu37( kjna tli:arallel to its length?

Since the density of air decreases with an ina kni /o0c6xc-crease in temperature, but the bulk modulus B is nearly independent of temperature-ia xnc/o0c k6, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travedkfc-1u zk /tcj; m4-ul awf c ktjc4/zu1;--kmu day from the source.

Two linear waves have the same amplitude and speed, and oth*s ff1frlgl +,f o,cfr;x y+o)erwise are identical, except one has half the wavele ,y o+*)r+c;loxfff rslf, g1fngth of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between l.x 7)0yjo ydltwo sections of cord as in Fig. 11–33, the frequency does not change (although x .y)od lly0j7the wavelength and velocity do change). Explain why.

If a string is vibrating iw:rql 7k9x3c+gjp g0wn three segments, are there any places you could touch it with a knife blade without disturk0l gw9: qcrgpxj+w 37bing the motion?

When a standing wave exists on a string, the vibrations of incident and reflectex-ekfl0:i kx k;8s )h2gjzsc. 1ec v3ed waves cancel at the nodes. Does this mean that ener;s .ghc02-1s 3) cvl8ie :kfexzk kejxgy was destroyed? Explain.

If we knew that energy was being transmi-dgtt t6 qpq, 04ch6gttted from one place to another, how might we detgq66-, 0g ttqdph tct4ermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is nrrriw*ybfx0 ,o qaj 8++x *r,the total distance it travels a+jx0+b, , riq rynrrw8f*x*oin one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hahmn w/lfb5-otbp 9 *bwu:-c0hc ga/(nngs from it but is 85 cm long when a weight of 180 N hangs from it. Wh h-9n: copch *w(t/n b0buam -lbf5/wgat is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg ca n+cwhe7 ,3s b7tlxo*vr compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what w l3 bvo7c,n t7wex*sh+ill be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when *ar;+mv(g yixn(d h :aa 2.7-kg fish hangs from it. (a) What is the sy*dn+(i; xmragv( :ha pring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0 4phx0 b5f+xkn ue0tk0.60 kg is hung nu 0kp +fxb450eth 0xkfrom it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the positkw3,jrv9 ,q h0p*dlr/6:edsac x ( trmion x of the mass in Fig. 11–2 at times t kewtdj s qrr:x(60 c,/ ra,l9mdv3h p*= 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 02va08negt9:e(p,mu yjra - vv.25 g is caught in a spider’s web. The web vibrates predominately w- tmajrv02 p,y9(8vv:geu enaith 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 sp 0gdlq3l6xgnt*h/ j; 8zm8fbpring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the vfjqzn 0glp 8h/8 m;bg 36xtld*alue of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 timewu4rx b2 )z: -ist2gbus per second with an amplitude of 0.13 m. Determzxb:b u)s2rwug t4-2iine
(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 displacementrn+vga k t4o1pw c25egoqt0t*m0 ce2- from equilibrium is the speed of a SHO half the maximum valutpg ce421a 2 tqonmw 0gv rc5t*k+-e0oe?$\approx$    A

A mass attached to the end of a spring is stretched a distance bv ,sn.4 lav(euch.jk/ur2 )j$x_0$ 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 vert8u-zya;-d mpmye l *p3ical 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 mal- d*mypy;up3- e8z position again?    s

  An object with mass 3.0 kg is attached to a ik-i(*j;dn jv spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. Whenj-*i kn (vdij; the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to co;+pin 5b49s7c, v rjp y7l5gah)lzje rmpress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave thepnl75+ 5l9ea7pz c,y 4g)rji;hrbvsj gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end ofx)f0, njiv2 cf a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the )i,fn2vf0xjc spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.-/xtfy7 b2r.n egol.g4t where x is in meters and tl o.7.enfbygtg/r-2 x is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement lil-0s/ aahpi+gxdc96 7 qoory- -ju+ from equilibrium is the energy of a SHO half KE and half PE? ±i a sl7 c 9-0y+qr-u/gah+li ox6-opjd    A

  If one vibration has 7.0 tim-qbz.me +c /w)slhlmk: j(,oges the energy of a second, but their frequencies and masses are the same, what is the ratio of their amplitudes?mz( kg+shl)mwe-q l,.b/o jc:   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once evc )w (w9s+edjrery 0.65 r(swc)d+ ejw9 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 supportu 6)wch/ qc9:jfs gl0qed by two identical parallel vertical springs, each with spring stifsqg)9lq/ : c6 hcj0fuwfness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sodhs95g vavvse:0)6 w98eex2z5ox ns in6.5t where x is in meters and t is in seconds. Deteres0gnv svdw2zev :95axoh58)9 xe 6somine
(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 l 2d68 n5iw b6 hwq.pae6t:swvA and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k =6xho 3:gt.jgaat .v* o 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Det3axj6 o tgv.hat:.*ogermine
(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 vibrateshhk(;fw*e ) clly,s /u with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the/he hku(slwf)l,cy; * 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 spk: an-y-/doaprings, 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 fap yis 8s e6(6ej4)wrcixed horizontal spring whose s)y (re48jes p s6iwc6apring 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. Aft22v h .zh5 (hcp)gcaiter reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 sp 2ch 5hica( vgh)2zt.. 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 exactl,eylk+a cg(u8y 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is aepowa+zhk*8juc r/e9i1:5 vto make exactly one swing per second? (That is, one complete vibration takes exactly pi*ha v8co+u/era kez195jw :2.0 s.)    m

  A pendulum has a period of 0.80 s on3x*p)icf ngz/ Earth. What is its period on Mars, where the acceleration of gcfxpi z3*/gn )ravity is about 0.37 that on Earth?    s

  What is the period of a simple pen3)4 t+mct7aqb7gngkrdulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum zn02zypyq u91 q-jo/:/smw p p-yo lj,bob has a mass of 365 grams, and it is reyz po w,/myqqjpl uos 92p-yn1 :0zj/-leased at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0l;k,l7us.mag ) eq*cx*k(r zj.9930 m. If the clock loses half a minute per day, how should you adrclk (l)e z*a* s;jgm,q k7ux.just the length of the pendulum? shortened by    mm.

Derive a formula for the maxits5v4jqy 6th f tp8-g1mum 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 fr: *hdvk8 3obshequency of 2.5 Hz. At it is released from rest startinh voh38dsk *b:g 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 anchohny9;)0nuw fx:ndpf+red boat every 3.0 s. He measures the distance between two crests to nhfwu ;xnyf: +p)90 dnbe 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 a speed of tqbc2hge3h6u*et9m5 k jy(i5 343 m/s How far apart are the wave crests (compressi9quk h36y2be mehtj5( 5 *tgicons)?    m

  (a) AM radio signals have freque zv:j1 4z1mzcpncies between 550 kHz and 1600 kHz (kilohertz) and trav 114:zcjzp vmzel 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 ih4ci8ukz ** guu6y p biry29-e0xyfa/n
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elvp u6g ,yci9v*qk +bo4astic modulus, but one is twice as dense as the other. In which rod will the speed of longiu ci, q9yvbkp*go 4+6vtudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If t-t1spbpvgzh 9p a;,n*he tension in the cord is 150 ;v9naz bp*,t sg-1pph 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 length 65g0i )t x brvt4lb.nbwrb5 y+*20 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a xtbnr 5+wr)bbl ti0*gy 5bv4. wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just1c/qwj*j 3oatk y)1v q below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is thwj* qky/ avqtj31o1 c)e ocean at this point?    m

  P and S waves from an earthquake travel at diffei -snmf:m61r trent speeds, and this difference helps in locating the earthquake “epicenter”1-mmn6 f tr:is (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 su1m9;h3wb o px*ud5sprrface wave can 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: Set the acceleratim9dhpr5 s;p3 xb w1*uoon a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an eari .k. xwkpzf;;o+z t0qthquake pq;t f.kx+ ; iwzkoz0.P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measureg4(e /.v4 zx/jp f 4wgofgnt,zd to be / 4o,nwe gj/f gxvt 4pz(f4z.g$ 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:c. b7osgkre+ mlcvnsjwb5 c.5*- , te portion of the Earth, but one is carrying twice the energy. What is the ratio of theem-g+b:5 twk5ls.bocnc,.j er *v s7c amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but o dduq*6/a; wbqgwx*6 kne transports three times the power of the other. What is the ratio ofgxbw6 a6 d u*q/d;*kwq the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total*l bt2q+ 2grf:tryb5 *y9 uzrb vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cmt y92rufrg*z yblbb+5* t qr2:, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–5ia( o( 7u,ect vo.o;gj2 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pae (oouvoc,.g7 j; t(iass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibsfjrd0dir;*p,ai , w.eum r r+7p/s:trates at 440 Hz as its fundamental frequency, what are the frequej /r* m7 sre ;r,i:p .i0dr,swf+ptaduncies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrat*j:0ref9jgxwi db rxn l;5d5y55kk4d3pm y7i es at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vib* djx;bmfw dr 4ieidyk 9 0kg55l:ny r3p7x5j5rates as a standing wave.)    Hz

  A particular string resonates in fourw ,-v;t v;wjtp loops at a frequency of 280 Hz. Name at least three other frequencies at wjtw ,-wp ;;vtvhich it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a str2o gb zmq)1:v9ozrp :f(mg0duing is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjg(pm :mu2o9 )zbfov0zdg: r1 qacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz .ka l;b7, t)rk ;rvt5xbnep6fand 350 Hz, what is tr 7ka;5xtb,bt;.vn lpf)ek r6 he frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fj o+wzd5-; yhbrom the bridge tozowh +;dj5yb - the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is f :ch995/wruid k eu/ bhm,rz.measured to vibrate at 205 Hz. By what percent should the tension in the stri .zurc:duhf9irw/5k/,bh e 9mng be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is skrn ,l:9afy z)h b.p,measured to vibrate at 205 Hz. By what percent shoulh)plnf,b zrk,s. 9ay :d 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 m x*yuo5uuobg5hw )t);echanical 60-Hz vibrator. The strin h5 *yg)uxo; 5twuu)bog’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 the pulley :dc.d /xsvae/. If the hanging mass m is fixed at 0.080 kg, how many differencve .:d sdax//t 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 j 6n(u*k jqdk dn)57zmxx56mkqust the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-66 d5k7qkj5x qzm(xn d)mu*kn 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)0 esr jsu7 8gmuux5/iarth between two 0u8 i s)ersjgu7/ mu5xkinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from 2.8- *wxfsc: hb5s m/s to 2.1 m/s * c:-hf5swsbxIf 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 hitfy)5uzm54k( 0de0di fn,ce- 1qj 2ohbtfi ;gbs a layer of cold, dense air. If the sound wave hits the cold air interfad eb;f( z h50i5jfq2yedb0c gf)k4m nu,1i -toce 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 earthquap1,o5yke+6 nx,jljy kke wave strikes a boundary between two types of rock at a51kjxnp,, o 6kly+yj e 38 $^{\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. A-)ob4b)zxc pttgns 7 m p/ts:)ccording to the user’s manual, the dish has to be pointed ib/mg-txcp 7ps4ts ))zb : ot)nn 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 250 km and velocity 750 km/h travels across the Pacificwho0l ;4bw5d7hj yz,2o7jwe4 d5l vfc 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 to t2ll4hbw ddj0,f 7w zwhj7c 5o5e;yo4v he shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m F cbah:6tbe cnx-; 1(sts1gen 7ind 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 ebxa;h -bs( ecsn:g7tc61t 1n5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whiimrl* 4pr5b5xk 0zb9fch stretches the net 1.1 m. Assume that the net behaves like a k*i 95lzb0x m 5br4rfpsimple 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 i k lu/wkli-g23bj-:va freely hanging spring. The mass then falls 33 cm:kulwi/gv3-jk2bi-l before it stops and begins to 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. 2 xi7sbu6o;dn11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of2si7bu xod6n; 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 righ80q;j9q yv urht pace of about 1 step per second, thj vuy8q;r0q9h e 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 certain groove 10.8 cm from the center of5+l*owo v8 fam a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the freq a5*mofvw l+o8uency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7w,g-(r bre6xj.40t where x is in meters and t in seconds. Determing-e6w(b xjr ,re
(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 is its frequencypgpj9drzvp 1/h(fiupl, ixsb45; 7- d if it accelerates at 0.50g 5r/4h dif lp v, uidxppzg; -jb9sp7(1(a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake81e gc3l 0nj xhp)t5ny xb;us7. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, t8;scbun 5 geh 7ntl03 jy)1pxxhe 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 instrumeta04;tvcbf41 rnat66o fb q0 ,wa7 l-l:lq pount are tuned to play at 392 Hz (G) and 440 Hz (A)lfl0-l 4c 6 af:;aa0u w6torttv7pbbonq4q 1,.
(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. 116kjz(6ublm ,.1hena ot q2qy )–33. Determine a formula (zjq 16l ey 2b,n.uo(6matqk h)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 section of cord or the lighter?

  A tuning fork vibratesjq,s)dyam x6) at a frequency of 264 Hz, and the tip of each prong movesax )6yj)qs,md 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 simple harmonic motion of frequency q(4 mjh5hy ki(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.( h jq(mhi4yk5 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if thatbo:.x 4uc u1ww end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of wb .:1 uwoxuc4the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing teo.n l,b 7zg(qiq: pvy, mms;-akes 1.000 nzp.lybqs o,m7mivq( g-;e:, 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 0.o+k2ey 3rt3 eqfmd,8oodp rcan oscillate in the vertical direction or can swing as a pendulumfd3oe2o.t k+3q m,8r yero0p d 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 what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched u eb-m+z*7cd9hs cne4ynder a tension of 255 N. A pulse *e94dm+hszyc7nb e- c is generated at one end, and 20.0 ms later a second pulse 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 spring .v 1 upxv wx9ly x5pw*8h9vwy:with spring stiffness constant k. A penny of mass m is placed on top of .xw5vxp h8 l:wwypu 1 vx*y99vthe block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The stmj7nmuv))9b 9m hgrb:-3ofhaeel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze star j ovmb3b-:f unhg))9rmm7 a9hts 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 shkyzqh . .((wn53jryy;a/jfvedfq+ v 0own in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequaj;d5z(ej .3khny v(.f/qv+ y qyf0wrency 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