Give some examples of everyday vibrating objecmch1 dsek8q e)ch t)a18:sv-ots. Which exhibit SHM, at least approc1q8moska h)th 8dc)v:1- e esximately?

Is the acceleration of a sx+k(/c1nd qrspo;wpj59s m)himple harmonic oscillator ever zero? If so, where?

Explain why the motio8(qu - x)resfon of a piston in an automobile engine is approximately simpfuo s(xer)q8-le harmonic.

Real springs have mass. Will the tr.suh k3 u,dqsaj;i-c0/dni ri18mr j;ue period and frequency be larger or smaller than given by the e;id.ss ;qujkrmih/a-r0c i1,8 und3 jquations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic ow-f0e y8x5mohscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertw ,5ks5egww.qy1kwm* ical spring scale, and then is released. Describe the scq, k*mw1sk w. 5w5wgyeale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time why(kjgry)r 8 ,ga8i6: ouz5ueaen taken to high altitude? Woagu ekr(yaruj 6g)z8y,:58 ihy?

A tire swing hangingd) 7ozq3l liufj6(fi, from a branch reaches nearly to the ground (Fig. 11–48). How coulz u3o7ldijf ,6f)q(i ld you estimate the height of the branch using only a stopwatch?

Why can you make water slosh bacj 0gbol-n 3c1mgosz18k and forth in a pan only if you shake the pan at a cer 1cgj 38g 01-slmzoobntain frequency?

Give several everyday exampq5t1q+0j l 8iheoyb x*les of resonance.

Is a rattle in a car ever a resonance phenomenon? Expla:k wda9-. udjn0kvym*in.

Is the frequency of a simple periodic wave equalym/7/px wn*.zhvlh g0 to the frequency of its source? Why or whxyn/h0p */hvml 7wg z.y not?

Explain the difference between the speed of a transverse 9 1r 8ypd6rgrv :ihb6ywave traveling down a cord and the speed of a tiny piece of the cov18r: ybryrd h96g 6iprd.

Why do the strings used for the lowest-frequency notes on a piano nt/.gneen-m w0 ormally have wire wrapped a-etewmgn0 / n.round them?

What kind of waves do you think will w0y.fda+/ kextravel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to ia k /fx.ewd0y+ts length?

Since the density of air decreases with an increase in temperature, but the :t5 7 oiadnb15a9q1.ah n m ;e. fa6(cmcrpuedbulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to varm oed7ann.ad(t. cr1mc;i fa :h59quabe1p65 y with temperature?

Give two reasons why circular water waves decrease in amplitude a f77 u wxka/99dubcm;ds they travel away from the sb7afk9; 9mwu cx7ud /dource.

Two linear waves have the same amplitude and speed, anz*7uar -7 o uixc . tthn2cefd/+h k4vfqv*v8.d otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factor?zei48u vft2kqf+oadhu 7t x7 r. h*-nc/c*v. v

When a sinusoidal wave crosses the boe.7f, qpuh d9zj6)w99k7sm e0bwltmoundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why. mef.w z huo7 9,9eqb06p9 kjmsldw7)t

If a string is vibratingywp7ap;)48 rizm d9u m in three segments, are there any places you could touch it ;w4y8p7u )zdmrm9p iawith a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrapb3r66k x bn;q458 ;nwyrmlcj tions of incident and reflected waves cancel at the nodes. Does this mean that energy b4r3n5;p;6j ykb8lq c m6xwnrwas destroyed? Explain.

If we knew that energy was being trxim5tanv1publxk)ts*+ ) : p/ansmitted from one place to another, how might we determine whether the energy was being carried by particles (material ukx+*) s:i tlab1nx) tp /v5mpbodies) or by waves?

  If a particle undergoes SHM with ae/gg c(hx;z(xj nx-. cmplitude 0.18 m, what is the total distance it travels in one p c/.zjgxx(cxe n(-g; heriod?    m

  An elastic cord is 65 cm l pdt kf oz)*h-+ncswu-y z3*v5ong when a weight of 75 N hangs from it but is 85 cm long w5pkz s) -owtvznd*c 3u+-h *fyhen a weight of 180 N hangs 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 5b)x e -f,zafvits 68-kg driver gets into the driver’s seat. If the car goes ozba) 5vf fex,-ver a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-q zxv 4eg5q)b6s82+ugslyac+kg fish hangs from it. (a) What is the spring stylgbsvg c6+qe)+ q8xsa52u4ziffness 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 wineomljd2-0 *hd k.er*th a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequenrje*2oln dk- de*h0 m.cy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the positionv1 z7q2ke*bxjp:wd bkvpn (30c5o(i o x of the mass in Fig. 11–2 at times t v io x q1zceb:vwkpdn20b5p(k3*(jo7= 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 caught5ptd:z8dj t :e in a spider’s web. The web vibrates predominatet j5tpdd 8:z:ely 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 sprnfgr 9x)m6c cd9 (npqz82ap 8xing vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. Whadxc2 pnfzp9aq9)g 6n 8rm8xc(t is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0e 2xbi1psf- l.no:)yg times per second with an amplitude of 0.13 mnsy.b-i l12 f)xpge o:. 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 maximu/pu,bx + 0 7ticflxcfejc73l:m valu x0xut7l,cpb:+3fjeif/ cc7 le?$\approx$    A

A mass attached to the end of a spring is streu oe bbiof/ra2/2x u q-vx 6svmr+.u32tched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is h; . /wc7accokstretched an additional 0.130 m and released, how long does it take to reach ca7/c.ho;w ck the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spr6a0hsrybuv1aq 2j: (ving stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object u:6hvyq aj2sr( a0b1v is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.2 nm8ts1 te4 2qy2cuu/hfyp )be2ok/6 v00 m to “load”c22ty4q/ osp un2u)6y m/8k vf h1teeb a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfac: o9/sa **5owzqq u amdcsiy53ny+ 4yeg3;bmae is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of w3y q*o/mn 5+;c ay ou3b as*q9ze4amgysi d5:work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x2 dn /xjxui2u( is in meters and t is in seconds. Denjdi 2/xu(2x utermine
(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 of a SHO half KE and half Puig09n fx4x .,6u nc:5wxgk hiE? xi6fxhn4.xcgu0: u,gk 9in5w±    A

  If one vibration has 7.0 times the energy of a(qz -izgtjtj0+2i;x a second, but their frequencies and masses are the same, what is the ratio2t (+qtjaxjgzi- z;i 0 of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging ih8gr6z7dlf 1ee1.y llight spring once every 0gl1z r7eldf h y6ie.18.65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs,xe5gp 1tm 7ijrm4i+g4 each with spring stiffness constant k (Fig. 11–49). What will br m7 +i emg4gip5tj1x4e the frequency of vibration?

  A 300-g mass vibrates according to the eqiz28dgux 1*cog0 o g87j.v lid i3ki:zuation x = 0.38sin6.5t where x is in meters and t is in seconds. Deter2vxg k*o7 i10dj8:.gz c 3di giziou8lmine
(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 SHMos 7id*( ydhuhu *, 1,tjteg2p, 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 end of a horizontal spring hkx8c-mbi+/ 5mh35dvym3vbx .gw h0c(k = 124 N/m) is struck by a hammer, which g w mb+cv/g-hcy.3x mmb 3h80 ihk5dvx5ives 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 vibratk 6n)*i, innroes with an amplitude of 28.0 cm when 0.260 kg hang nno6)r* i,inks from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness co:fw6egc k+va 3nstants $k_1$ 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 atf f,qf3j( /rketached to a fixed horizontal spring whose spring stiffness consj3ekqf,fr /( ftant 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 bridgevefwgbkf1 0,7. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to resvfgfek0,7wb1 t 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 e(q3v* cglwfc0y.xegas /gu1,xactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to t*+82r: cab(drkop kf r)7ztr make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 spo(dat bktc27 k*fr rz rr)+:8.)    m

  A pendulum has a period of 0.80 s on Earth. What is xq,3vr . dz6qzl:l5guits period on Mars, where the accex:zquqr6gd3 5 ,z ll.vleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 umyt7 dode7, .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 bob has a mass ( rfu +3p6yy2d majgbr( y5l(qof 365 grams, and yr 2yuj(al 6gf+bry(3(dpq5m it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the cli* z;cw0tinv0 9rma/ nock loses half a minute pervnim 0 tciw90a*;/z nr day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for , 39eas+oe (rgmpaf6 jthe 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 frequjmo qkfyg6/v-r :m( i;ly .gv0ency of 2.5 Hz. At it is released from rest starti yg6r-;lmiovgkq0 vy:j (f/. mng 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 anchofaw(9 gs5b;tgred boat every 3.0 s. He measures the distance between two crestsg (st5fabgw;9 to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has j;hp9r q 1*j bdd54lnga frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (comprebjd nql;rj gp1h54 9*dssions)?    m

  (a) AM radio signals n :t(t/.(dv sq9ev eilhave frequencies between 550 kHz and 1600 kHz (kilohertz) and tr :lsv tne(t iqvde(9./avel 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 in+ti61i 7dsdhy 8fe q1p
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice ass2/)uwztweorh2,zy 5qi7f d9 dense as the other. In which rod will the speed of lo / zqdzsi2w,uw9 )hr725etoyfngitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between me+/ew s;em i6two supports 28 m apart. If the tension in the cord is 150 N, ho/smi;we+ 6eme w 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 cabi cknfm/73 go8le 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 wave pulse along the cable. It is observed that it took 16 s for the pulse/mik8c3 g7nf o to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of thz 1 :x2q;x1mf.lt kcm):x+x p(vsybpze sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep iyl+(xb:x2xptv1 zps .) k1 fm mzq;c:xs the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, a9huii rxw-vx 45n+;itlu 2(mund this difference helps in locating the earthquake “epicenter” (+;wiixti-r uun vum29l x(45 hwhere 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 be approximated by a;ym5eqdafd8)22(kj c0r p da j sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typickrd0ae) 5p (jcjqf ddm;y82a2al 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 acceleration a>g]    m

  What is the ratio of (a) the intenszcxgt4 twv69bt/ -myg/j ,cb/ ities, and (b) the amplitudes, of an earthquake P wave passing throu6z/xc cgmwt btj4v/g/, -ty 9bgh 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 measure5skxpi8 1:-hh*b.ktrzbmw; zd to be *k hwmb ri-: zhx;.bt 18szp5k$ 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 thegi,u.xykcj *rj2b70xddx; 5fqui o 5 2 same portion of the Earth, but onegucu7o*jb2fjir50qi . ;kdd5x ,xy2x is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but oneujkfi2 z3e-ztx ,7-; cuxv ga5 transports three times the power of the other. What is the ratio of the amplitudes of tv2t-zuzfu3a, k g;5-ci x ejx7he two waves?   

  A bug on the surface of a pond is observed 4fh6xr8 /,v,cj p. kj;mduo quto move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a ckv; 6u4d.qoj,p/j xmf u8,rhwave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Figl)d.7 fj:j wm .b,dp5 p+ acerge0 b-.1bdwztu. 11–52 are moving toward each other. (a) Sketch the shape of the sb -urw.:7 0e)5lt. m1ga pdjbd z. bf,j+pecwdtring at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental;hxd5b ; wsk e j3gc3o0tik(g5 frequency, what are the frequencies od3sti; k(xc e5hw g0k5j3bg;o f the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when 1i s uam-ng44xunfingered. 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 t-mi4sg 1x 4nuahe string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops ays578r.kvtnn rgf a- (2b9ecj cg4 qom905cg jt a frequency of 280 Hz. Name at least three other frequencies at which it will resonate yg ja5b c.r920frn-s 7(ncc4mvogj9 te8kq g5. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves7fd f hzuw-ju9odyi/t4 7g7d+ on a string is 92m/s If the frequency of standing waves is 475 Hz, how faj-7iu7h fw7dyug9+/o ftzd4 dr apart are two adjacent nodes?   m

  If two successive overtones of a vibrj fy.3j(v)fqln. 6 dnxating string are 280 Hz and 350 Hz, what is the frequev.ny 6ff3jj.dl x)qn (ncy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. T i0alx*,*u ylxp(1d0 okp6ow ehe distance from the bridge to the support p oo*0 l1kd x0yu6p*ie,laxpw(ost 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 supposetrn,idmni 7;e 5vs+8fd to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the threer ;s,7inm8v+ efdnit5 frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to v5b76+ mjw9+ i box,vgkdm cr;ngu,d0eibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string bbc rd6i+gon,v wdg 9 m;xubj0e m5k,7+e changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached tocoi 9tfq uk63 -jer 7g)(;faih a small-amplitude mechanical 60-Hz vibrator. The s6o (r qth)g 7ceki9ff; aiju3-tring’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. I2tlf,btxh8v m.c zm8+39oqnef the hanging mass m is fixed at zcm9n2 3f,x8tqv+ob8.lht em 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 just the right frequency, te.a+ ka,lf0 /3wbv0iwosu hebj8 0f 3qhe water alternately rises and falls at each end, remaining relatively v k00bw3a.aqu8wi+f/3e sl 0fejbo,hcalm 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 hv r, o:o9t.gv2 ipco(z1 1jbstraveling at k.0 km/s strikes a boundary within the Earth betos ,pr2jgoo hc9vvtb.z(1 :1iween 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 unde:13l0.(hed px9hp uzeh mn:ftrwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the ince.1thhpdep0(: f uzx ml3h: n9ident 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 air. Ii 8 f2bfmj.pdi.*o:wj q0r)go f tij2opo*rm bid)f wq..8 fgj:0he sound 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 strizz3 o.:rt.f:gtk /ewfkes a boundary between two types of rock at a k:.t3.:zwofrfg e t/z38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s manual, t5.ha)usikg0wdd huvy)34 )gl he dish hd4 kuhg5hi )wd 03lgvy )a).usas 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 250 km and velocity 750 km/h traoeqrhjs 3 6a(*vels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decreasejsae6(3r hq *o 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 the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m Fin;;g:xky 6upo l;zd-cqr vph17 d the maximum compression of the bumper if the car, with mass 1500 kg, collides wi:-7;g qph;dx z1 lc;orvyup6k th a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whichzvg9q6 zv-a x(gza40y stretches the net 1.1 m. Assume that the net behaves like a simple z q0vy -a94x6gz gza(vspring, 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+z s6 s unb);2vh+ik ,yqzdi*l. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the osci+l zikhbq6vud,s)2sy ;+*z inllation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–546q+ka) tl+ xag vm53qk), compressing the spring 5.0 m. (a) What m+qkv)lx6ta5 3 ga+kqis 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) at j7jop+c u+t2 c amfsn9f:,yaf6ust 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.2yufco67 ++9 jmsaffcn a,p:t 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm fromvqk0i5: u)x jllfa0c;-dg bw 9 the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emittedg ufj )5w;q:9 l-vxi0alkbcd0?    Hz

  A 2.00-kg mass vibrates accorq a2y tg) yqk4l3s3 im/lyh)s:ding to the equation x=0.650cos7.40t where x is in meters and t in seconds. Dete s3yk)l)my ql/2 :tgi3asyq h4rmine
(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 frequency if it a sigl5 pdu 01p20kdtr*ccelerates d1k iu 0*lpspr 205dgtat 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Whxvi9e 5n qsc3;en a 75-kg man stands on the raft, it sinks 4.5n ex ic9vq3s;0 cm deeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 3 es1l.)xfv;nd92 Hz (G) and 440 Hz (A)f );ndvxel.s1.
(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 Figzcz+ r en1m9) (l 5dgnjta;qq+. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelgdj1 amecl)59;r(+ zq qn+zntengths 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 the tip s hcjqf01lu.9y,8blk of each prong moves 1.8 mm to either side obf0lh. 1 qjyuc l9,sk8f 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 frequ7. o e6z ypdxb5b4+ m:2pfxysmency 1.5 cycles per second. What is the maximum amplitude with which thxb fb5yo6xd4z smm:p2py.7+e e end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end /x 7p.+l sdvq.mgjq9d if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determinvmqq+ jx7p../gsd9dl e the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly d 0:t (-5 gmtvbqq/zxk2.000 s — each one-way swing takes 1.000 s.v(/ gd btqkq05: zmtx-
(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 direction or can swts ,1 v7odiw3ming 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 what amount? [Hint: d 7vwitos,m 13Let $l_0$ 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 1)7sqoag62 4 vuv5s zjt23 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 opposite end. Where will the two pulses first j 7a ts)o24szv u65vgqmeet?    m

A block of mass M is suspended frs dpk,(ro/84uihm5 u(poob cppjp) + )om a ceiling by a spring with spring stiffness constant k. ji(o h)+)u8p4 pcum(5 p bppso,rkod/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 top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car iqwd4yq)k: fd. qm-8yn7.e meat the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze 7mn)4y.d yk. -qfi dw8eqm:qe starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (whic;xzc5b)g::ro g4kbs ucv dy 0xx.s 8a0h also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello sprino5;:yxd 8v0sba4 urs)bk 0xz cg.xg:cgs 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