Give some examples of sqk*a2qi9 s d3everyday vibrating objects. Which exhibit SHM, at least approximat kqa*9q2dis3sely?

Is the acceleration of a-yucuo; b69*cd9.a csubwjw* simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is appronsubz3*u7 .wcximately simple harmoni3us*7z .b wcnuc.

Real springs have mass. Will the true period and frequency be larger or ci,rh*.2/ou xe+dakpt6i:m e4- zg yr smaller than given by the equations for a mass oscillating on the end of an idealized massless sap,red6 +e-:.cz4mt 2xgoiiy*rhu/ k pring? Explain.

How could you double the maximum spe/ikx u qrejb*n+lt 9w-jhoa+8x et(94ed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to p4ec se,ga6w 7the hook of a vertical spring scale, and then is released. Dpa,e6c7 gw4e sescribe the scale reading as a function of time.

If a pendulum clock is accurate at sea lf ,btdgxona8 x48j+ a0evel, will it gain or lose time when taket8,+a jo n4bfga08xxdn to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig6q,h:5vpj ew36rvt r h. 11–48). How could you estimate the height of the branch using only a stopwatvvth6w5hqpe6 jr:,3 rch?

Why can you make water g)x g m *b3simj:4n9mislosh back and forth in a pan only if you shake the pan atx)gm*4 3j g 9smnb:imi a certain frequency?

Give several everyday examples of resk+zt ,9,c43u2d 7sq:kr7sl plm pu2nh* peqg xonance.

Is a rattle in a car ever a resonance phenomenon?z v.rj5q 7ems+ Explain.

Is the frequency of axf;w78pm eii. simple periodic wave equal to the frequency of its source? Why or why nopwe7m8i.ix; f t?

Explain the difference between the sotqjizlz;5 2uh sff2oj4 f; +9peed of a transverse wave traveling down a cord and the speed of a tiny piece of4;uzz;2j qt5iolsjhf f2+o 9f the cord.

Why do the strings used for the lowest-frequency notes on r 8xhp5u9: dhma piano normally have wire wrapped arouxm9pu:rh8dh 5 nd them?

What kind of waves do you thiyir/s u,l h8y2nk will travel down a horizontal metal rod if you strike its end (a) vertih8y2 /yiuls r,cally from above and (b) horizontally parallel to its length?

Since the density of air decreases with an xxzf8zv 4ne5 7.0nzlvincrease in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with tel0fzzx 8 . n7ne54vvxzmperature?

Give two reasons why circular water waves decrease in amplh 8+ +* ti/cvuzmyso.yitude as they travel away from the soyoi.myu+zs +/8chvt* urce.

Two linear waves have the same amplituq8;0nssa bm 7yde and speed, and otherwise are identical, except one has nq 8m yab;0s7shalf the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sect* dfk xjxq,c 7kw /*skur+4wr3ions of cord as in Fig. 11–33, the frequency does not change (although the wavr q3kuf /7 +x *k4,*kdswcjwrxelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could .md,.x y9mxhe touch it with a knife blade without .x,mxh9d y. emdisturbing the motion?

When a standing wave exists on a string, the vibration(-xz luosb4v- s of incident and reflected waves cancel at the nodes. Does this mean that energy vo -x-u( sbz4lwas destroyed? Explain.

If we knew that energy was being transmitted from one 7 zuq5fj r(, 4)cgwgoiplace to another, how might we determine whether trgu,(4wci o qg jf7z5)he energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with am9 ior5 *su2 wdkqov+b,plitude 0.18 m, what is the total distance it travels in o2 qo*kdosbuwr9i5 +,vne period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangz qmka9m,2 2wusrr3 q2s from it but is 85 cm long when a weight of 180 N hangs from it. 2m39qm2,sz ra 2wkruqWhat is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compryi q ; i;d7+wdh6gg(dxess 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a wi7 ; x;id dg+q6dy(ghbump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm 7fy xkqei(o)e0w n6; kwhen a 2.7-kg fish hangs from it. (a) What is the spring st;en xkk( wfqy0e6)i7oiffness 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 fr*6es r-s jabd8equency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from 68j sdrb* es-ait?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at timewxb 5 tou*ar(j i-7p*kmm5. xas t = u5t*b*m k w rajpo7(5-.x axmi0,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 0l+ mz k01jy-w4wyklx),nv xy v*r ef83.25 g is caught in a spider’s web. The web vibrates predominately with ywkmk10 xv*vye+ 3l)wxfyj, 4 -zln r8a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. Whe8*y-6kr2m nc u +l7rtput abb-n an additional 680-g t2a6pb -lmy nuu -rtkb7*r+c8mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per s/ent)-e;duii bcj .z*lryj3 i1jr 6p jwlk+27econd with an amplitude of 0.13 m. Determjne-2t3p *k;iiijllu/1r7db6. ez c j j +wry)ine
(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 maximumyuip,u1 +z97krd .yxm val pr.uk,z7 91duyixym+ue?$\approx$    A

A mass attached to the end of a spr 9)tulxb gxo mqk:5p9a (b.gn2ing is stretched 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 vec0nx grdih6 b7b(s- y gn,),xdrtical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, xigbn0,6n- y,dsxb c)d(r7hg how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached tjkc 7v9mu+oqq+m hwrog4f 1 1/h :)evho a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the objectv9r +cmuomf1og 7)whjh:qq/+ vk41eh 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 popgi9/dcso-7 7bj pd::we g4zajz un 0.200 m to “load” a 0.180-kg ball. With what spe:wds/e:7c7 zjja odpiz9g4- b ed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, qs k4e ;,y vxwq:m3ihhvg 3)m9frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of ;vey4 9gw3 ,:qskvhmixmhq )315 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates irxvv g9jpp 7.f5gb05wqte8 *according to the equation x = 0.45cos6.4t where x is in meterpx0jv7i*v5q.gbpr5efg w8t 9s and t 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 from equilibrium is the energy of a SHO half K 7 :l75mz )yhvo9zakqlE and half PE? ±ky m9)7q :5vzzho7 lla    A

  If one vibration has 7.0 times the energgq8(ic c hga1oar (,lv4w *btzumm 9;)y of a second, but their frequencies and masses are the s)mtg8u4;mgqcv,w1 lbi( o9 *z(ch araame, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangin:ra;fl ys9rsb+mo/fe*h +qy vq5.(xopbc;l (g light spring once every 0.65 smeofbpsr(:9vlr+;x/.fyb5q(ohs a+;* ycl q .
(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 p i2z 1cqydq4;vertical springs, each with spring stiffness constant k (Fi1cd iq4q;2 yzpg. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is iv:c pr.4o0 sb2vh aw-hn meters and t isboapsvw-r v h 2.4h0c: in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, whattj)zay. 1i qv 6xm:6yg 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 o a *t81 )xnie,ov3o/ridfno:b n the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Deio3ni8,n/1 oxabr ev*:tfd) otermine
(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 constanhsrc9k bdoqqn9:.9 g+ t 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at 9h bnc+9qk rg9s.d:oq
(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 constant quod1-ipd)v)vpgvx0 s) fyr( : rfo-8s $k_1$ 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 attachedev, ,j:porem0 to a fixed horizontal spring whose spring stiffn0orp,meej:, vess 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 br x8/ lfgiff x*kumf. l x/i)w/*zrkq,4idge. 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 rest 25.0 m below the level of t x/mlixfri*/u k lx*wf./f)z f8kg ,q4he 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 exactlwh6 /2hj (rcvxy 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one -()kyszdpo yr 9 jgd rs3/g9l3swing per second? (That is, one c3rs /sdoy 9zjkgpg lydr3 -9)(omplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on M8ib*bx*, j pa/jrcu)m ars, where the acceleration of gravity is aboutuxjj*8bcm )b , *pai/r 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cq bc g9d8nqel0h0i p5r3.3wyim long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum imccnjw s.k,9td+ c:l mkm9-a9ap 00dn s 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at m ,sm.pkd0ncjam 0 ckt9c9+9dnw :la-an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock losp50,k-dnzts1(xekw dkl c;,zes half a minute per day, how should you pds5-w knxc k1zl(, e;dt,kz0adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximuzc.wi l b- )jxesf:0:zm 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 ig:*nc1qm*;4bdbvfo uss70wx u c-7 g mt is released from rest starubvxc1 4f g7sq *dgcmsm0b:7; uw *o-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 pa+u9gum o,(-yp 6: jndoi *xpaxss the bow of his anchored boat every 3.0 s. He jx-u* m6dgni auo9px:+( yp,o measures 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 of 262 Hz and travelsa;.gmc4rt ()/ b3k qhpr m3hot with a speed of 343 m/s How far apart are the wave cresbpmr)3hm q 4( co akh.;tt/gr3ts (compressions)?    m

  (a) AM radio signals have frequencies ba4b 5e //sridqetween 550 kHz and 1600 kHz (kilohertz) and t/ a bs5r4eqi/dravel 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 longitudinf(c3+rcd: l dtal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice a,u:wnz6i2ilq;o g a7 ns dense as the other. In which rozw ;ql u6noi,i7g2:nad will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between tw4j cs -bs0*nkykov jy(k .9/dio supports 28 m apart. If the tension in the cord is 150 N4jjb9k-dc i(k/so .ynyv *0sk, 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 pu1v8f.d5 bmccable 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 duvm 1bf8.cp 5took 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 shi:t86sujnvw hds s7:9f9h 2j zjaa09 rhp just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. Hhasnh 9sva2jz tjhr89ws juf6: 9d0 :7ow deep is the ocean at this point?    m

  P and S waves from an earthquake tra2bd - vsc0f9xnna .qy0vel at different speeds, and this difference helps in locatin0dx0s 9avfcb2y .nq n-g 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 surfaceoz wzs8/mblrd:2i ,: sh.b( on fk(8.vc5laow 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 i oz (l l,:a 8:(csob.omdr5wsh /k.zb8vwf2nis 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 intensitieog s : s8jttc;uu5u7*bs, and (b) the amplitudes, of an earthquake P wave passing through the Earthg tbuc 7u*:us;8o5tj s and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Eartfbhp1b8(nwb7kuvx p l00:mr/h is measured to be 0wblrp x(vhmu7kbb80: n /1 fp$ 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 frequenr (rbey*1e2qy oi s4ls 6q-ue.k/q1a fcy travel through the same portion of the Earth, but one is carrying t qq-bss yify4 lq/ (6reekeu11.oa*2r wice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequ+ 4ljws2f8 7becra (pvency, but one transports three times the pow84f c7sbla( rve2jw+per of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is , upc*)2spasbdb9m ;3vp/fhrobserved to move up and down a total vertical distance of 6.0 * u )9acsbdrphms p,/;v3 2pfbcm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. qcjs a-x)w:/ir 814o y: xfjkl11–52 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 m il qfjo8k)cys/a:xrj x4-:w1 oments 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,(npa/u)yab m-8 k eeh its fundamental frequency, what are the frequencies of the first four harmonicu/eaeapnh8m, b-(k) y s?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what fra(u7b7 ilb9s yj7orj uw3k//x equency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a sta7ol (wbx739 iarkyu/j/7 sujbnding wave.)    Hz

  A particular string resonates ibbhspoh nb78uc2afu/t 1w7/ )n four loops at a frequency of 280 Hz. Name at least three other tcsu8h72 /bbwnp1buoh )7f/ a 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 92m/s If the fre.+a)fz*/ qv qba: 7*oxv spbkrquency of standing waves is 475 Hz, how far apart are tw)sf:vq bozaa7.rqb*kvxp* / + o adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz anyj8d3ae*+ znacnnq*9 . 5hykud 350 Hz, what is the fr9cqh*.j+3nuy5aynd n z*kea8 equency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of9r) cqh0 *n c siyy7nj/*x0kcv 3.6 g. The distance from the bridge to the support post is L = 62cm and the string i0r/ jyhynivs*c n)7c*9k 0xqcs 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 measurbo28 2bbbf7g v2obe2eed to vibrate at 205 Hz. By what percent should the tension in the string be changed to corrv2 8befogbe22o2bb 7bect 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 measured 53ohv 1d 2z*6avca b tkv;fon;to vibrate at 205 Hz. By what percent shouldvcnhaa3 k;21 5v*; ofbt d6voz the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is atjn qx8jx93*vuo)e2nnmk6 zk -tached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unitnnx9nzjq8k j-v3o62uk x)* em 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 adju2h y-7fydkrn2 sted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L berkf n7-d2 y2hytween 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency,oee y75qj)26ocgf j3 g the water alternately rises and falls at each end, remaining relatively calm at the center. Supposj7 3q cgy6efeo 2jo5g)e 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 trave q9xr p 57b9-e dfy(rm3age)xiling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the -efqgi a7m3 dbx)r(9y95x repboundary 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 “shmq/a f r0dl4u8mchm;b)tr ,wi)fjd87 elf” where the velocity changes from 2.8 m/s to 2.1 mwrmd8 a8cbj;m ), fl0 /4idhrufq7t)m/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 o)smd5etv 1aaxl rn:t;xen* sbz b30r0,e;+gtf cold, dense air. If the sound wave hits the cold air interface at b,lxxsemv)n:*r t+aa beg5 ;t 0s0 zedr;13ntan 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 between t q2+lep)i ov.;yjxdutch6k8*wo types of rock at a6 v.xo;d 8j p +2yc*lui)kthqe 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 hqu,l;zmcsrf*)70 es . According to the user’s manual, the dish has to be pointed in the dire *lhfssr,)z0;umec7 q ction 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 3:s6 xbaa. piz3n ,krd:kqtsx*o8 )gavelocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted toikpotkb3g )sa*rd:8q3.xan, a: z 6x s the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bump --ngs;ytz 0kgkv -h)xer has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, withtn shgk-ky; 0 z--xg)v mass 1500 kg, collides with 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 a6yh wt5jun k t-)2mzn8 window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a si5kzn-6tmh2 8yjnu)t w mple 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 e.9st.) l4bnzmh b/aza7uk3 t end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the7t.)b9uk/at 3em zlz4a.hn bs oscillation?    Hz

  A 950-kg car strikes a huge springwkhkv/:cd;s f 5,e2n v at a speed of 22 m/s (Fig. 11–54), compressing :vc5,s kk2dvhwnf e/ ;the spring 5.0 m. (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) at just the right d /(0to;jtyck23oibz .,mzrx pace of about 1 y 3td xjzc(/,rto.2 zbik0o m;step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonogriyxeppi2. 7 2yaph record have a wa .e yx2pi7i2pyvelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the euppx x)b73t ee ,.*0cbi dxdr2quation x=0.650cos7.40t where x is in meters xd 7b te0xic*u.p pr, d)2eb3xand t in 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 withmu fgzj; 8x(h y.su0 03tdys3n frequency f. What is its frequency if it accelerates at 0.50g (a) upward;(jsxmd3 .uygnyzf 0u8s0t3h,    f
(b) downward?    f

  A 220-kg wooden raft floats on.mr st uk.ho lpgs+/ dp/6/8vd a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while.phvgmt.6/kdd +srou 8.spl//
(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 asu(+b -ml2h:(su mbg tuned to play at 392 Hz (G) and 440 Hz (A). hbls(+agu(ms-: bmu2
(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 thl-(-: 6ehp7igo yk ytge stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavio(il7pk6hye:yg tg - -er section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of d 24lyo6bfp sv f5x+g*each prong moves 1.8 mm to ef 65yls2 gxvpfdob+ *4ither 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 harmoniosjpiz*fu0;,4a , vc rc motion of frequency 1.5 cycles per second. What is the maximum amplituou 4;*acf0jzs,,v i prde with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slide 4v swlij/ b6 br5,w, gv/2y-0uyasgrt without6wug2sv5 4v//ryjgylb-rb ,sti ,0 w a 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 other free.

  A “seconds” pendulum has a period of exactly 9o7), nrqbn sd2.000 s — each one-way swing takes 19,qb 7d s)onnr.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direcjistxym dq6o nhn6ej6 /e.9b6;g3cv1tion or can swing as a pendulum of small amplitudc66j6o nyn 9/qe3vt;x1 ejbid g hm6.se, 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 stas0lko ikduz6i93lix9g9xx:z b/(: x retched 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 0ig ik:ux lxk/9ox6b(li xz9 zas93:d the two pulses first meet?    m

A block of mass M is suspended from a cznl sfp9w*5fno9nf/ 5eiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is 9 p/*5w nflnn59zos ffthe 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 v*+,j m jth4+ d8qhftfn)yw-zthe junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–14)n-fvh y+hq+wz mt8,jtf d*j.]    s

  A block of jello rests on a plate as shown in Fig. 11–58r*:kwv8a mdl cn5wq:- (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and ba-v::ww r *dklqmn8c5egins 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