Give some examples of everyday vibrating objects. Which exhibit SHM, at least w xag;l-/. ttdgkhtnd*qj1 6/cxy1 r:app-th ;/gdyg*t.n6a lk1xjd/xc q 1t:rwroximately?

Is the acceleration of a simple harmonic oscillator eve5, -d 1i3 zl:hrlwvnzy mt2yn5r zero? If so, where?

Explain why the motion of a piston in an automobile engine is approk e08xrxl;ry 1 j-l/zxximately simple harmyj l x-x;8lzk re0/1rxonic.

Real springs have mass. Will the trueq8)auj j52 r3swk1)ra 8 tmt4og+x ttg period and frequency be larger or smaller than given by thjam2s g8t 1xko)8rt+45j tt 3qgrau) we equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple nbkhr ab;t5fh):l pb:86 /malharmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scjh*ll9-/hnu1k oodx+y38 -oo nf hr8rale, and then is released. Describe the-lo-8o3/ yhf rdnklr *o9h ouhx8+1 nj scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when.e)vb. +c2 4 mx qrbghha )uqpzv3cq3q4bba .6 taken vg.e3.p qq )qxbbam3 6bchu.a4 cvrh4)2qzb +to high altitude? Why?

A tire swing hanging fria-+s7jjzym6 z rp8u:om a branch reaches nearly to the ground (Fig. 11–48). How could you estimate :-jyiz7jpz8uamr6+ s the height of the branch using only a stopwatch?

Why can you make water slosh backyyj9n 7l::u nfx(jh2s and forth in a pan only if you shake the pan at a certain frequencf:n:j 9sh jn27xy(yluy?

Give several everyday examples ofs3mpuc 3 :a.hr resonance.

Is a rattle in a car ever a resonance vs zg17yxo)1k)m/v , 2dnfmqlphenomenon? Explain.

Is the frequency of a simple periodic2e)zjc y1uz(w wave equal to the frequency of its source? Wh (2)1uwecyzj zy or why not?

Explain the difference between the speed of a transverse wave tw, ne.nrdrldy;8ss 8;raveling down a cord and the sp ;ndlr,;8ns yw 8.sredeed of a tiny piece of the cord.

Why do the strings used for the lowest-frelsb n)dhf ,41uquency notes on a piano normally have wire wrappe41l)n,subh fdd around them?

What kind of waves do you think will travel dow7qea5f, /jww yn a horizontal metal rod if you strike its end (a) vertically from above and (b) horizont,qef/yjw w5a 7ally parallel to its length?

Since the density of air decreases with an increase in temperature, but the- eqfg+rmb-1j r (:rsftgo,b6 bulk modulus B is nearly independent of temperature, how would you expec + ,6-gsqbrf-1bot (jrg f:rmet the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decreaseyqo:djx e9,et:n(q 8o in amplitude as they travel away from the source. qq8:ood ,9n:ejyte x(

Two linear waves have the same amp.na/cs bf+ pm :9khe5rlitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which rn.m:hc kb9fs p5a/e+transmits more energy? By what factor?

When a sinusoidal wave crosses the bound++ n7;.pwdyeug:oe s gary between two sections of cord as in Fig. 11–33, t:ug+7osgdeye .+;w pnhe frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, a k/tfr0(p cxjfm;1,u( tp1oq qre there any places you could touch it with a knife blade without disturbing t1p tkrt0( /m(j ,ouqqf;c xf1phe motion?

When a standing wave exists on a string, the vibrations of incident an x;9 l199tvq2g fiucnsd reflected waves cancel at the nodes. Does this mean that energy was g19v 9;fcx sntq9i2ul destroyed? Explain.

If we knew that energy was being tr5w ita6m9iao 3bd1c1hansmitted from one place to another, how might we de iaad 36mo1iwbt95 h1ctermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with8tk3b *zo ev 7c*vtt.h amplitude 0.18 m, what is the total distance it travekveh o.*zt v87tb*ct3 ls in one period?    m

  An elastic cord is 65 cm long when a weight of,2h5d.ggt x pw8s lmd5v9 ;xmk 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” cons.px8ld59m2gg 5 ;hxvsmk d,twtant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driv bh.hosk1qvx.1(cltz2 ie d59 er gets into the driver’s seat. If the car goes over a bump, whah1hx.cko9s1 v .eli5bq2 zdt( t will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7nz 6 *,jiy camzz co(030juq+e-kg fish hangs from it. (a) What 0 0(mcoz6z q y*einzju+,jca3is the spring 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 0.6f): 8xl rme+1q kqtxs)0 kg is hung from it. What is its frequency if only 0.38k)etxl:) 1 qrxfm8+sq kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times t k w6p e4 rko;f(xb((f fty5ec,= 0,t eko(bcf6pfxfr(4e;5 yt k,(w= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vf, oi9hu8*udnc-;a k8 j1v ispibrates predominately wii8ui8-dkcp9v ;*,sjnh1 fuo ath a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency o,eup z t*z9x;ff 0.88 Hz. When an additional 680-g mass is added to m, th,;ez 9zt*u xpfe 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 second with)/l yl-k lm(pc an amplit-pmcy l)lkl/ (ude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibmjrg h6.b37kf5k +1+vqns,zmyl q5ai rium is the speed of a SHO half the maximum value? q17mhayf+q3 n,vizk5lr s m+5kbg.6 j$\approx$    A

A mass attached to the end of a spry,a c39ejn1uw b-d r- +).ccudm vc*jding 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 vertical spring 0.315 m. *bao*t amqoah;;1c j 9If the spring is stretched an additional 0.130; m* hbo9qj a1*o;atac m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attach2 bmae ft,kaoj(gn7 +8ed to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibr ajo7(bg8, nak mte+2fium 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 p*fb .4jx c,8ovwjsa1xopgun 0.200 m to “load” a 0.180-kg ball.v 8 xfocbxwj s4.*1ja, With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, fricti ictz. ).1fq3s btbhr,onless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of iz1.3,ct b)rqsf .bht 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 t 3f4 fvuv.w9c xc/m3ywa-u*l wo the equation x = 0.45cos6.4t where x is in meters and t is in seconds. *u w -/wulf3acmxfyc.3v4w9v 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 fr)lv ihl (-c,ojom equilibrium is the energy of a SHO half KE and half PE?(,ov chj)li-l ±    A

  If one vibration has 7.0j0es35 *nqhbq* 7oag8yu l+ kf times the energy of a second, but their frequencies and masses are the same, what is tq87anyfeslj* bu5+gqo h3k* 0he ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprqnl(pp ekk (n zz5/h,7ing once every 0.65 sen 7,h/((z nzpql5kp k.
(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 supmrn,yf s5-q*p-vnc1 rxe/u,f ported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49) -/y15vxm-,r pnsue,cff *qrn. What will be the frequency of vibration?

  A 300-g mass vibratezn3t:q v8wr t2s according to the equation x = 0.38sin6.5t where x is in meters and t is in secondntr 2wt8zv 3:qs. 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, what istv 7 go( /zejj85yvw;k
(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 th gz4,w+z b+yseaz(yb/e end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass awzy,zas e4 /++zb y(gbn 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 sti 3h ;w4ot7a rckiqniy+l4y,h4ffness constant 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=47ol4 haqrc+,wtiy h;y k43ni0) 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 consuesx0vv (u+x; tants $k_1$ 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-fw/s ot8z3n.a 0r hkh*kg block attached to a fixed horizontal spring whose s rt3hof/w8z ha0.*nkspring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching7 gfysiywp n+6s:f2t*t lz c)w+w nu:* his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Caul7wt62 fpw+y+: nts s*gc y*w: zfi)nlculate 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 ex rv4,i rw:wg( 7p7fnmqactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if kho:d37nnb nyo 31bx 9it is to make exactly one swing per second? (That is, one complete vibrationn1 bxhydo o7b3nk9:n 3 takes exactly 2.0 s.)    m

  A pendulum has a period offt k55 q2mywptxrv-)l0k)hc 0 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Earth?)-c0v rw5tl)p qm5 ky khtf20x    s

  What is the period on1i tk2:+gfv sd 3l c0;bf.dusf a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendul3)ragakl(q2 m um is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle o3agqrl) 2kam( f 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 clo*w7f ubg8uv31n az-, ekvp/hwck’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length7 b3fu ,/ghn1vuav8wpw* ez-k of the pendulum? shortened by    mm.

Derive a formula for the maximum speed g 8(wee7l /hkm$v_{max}$ 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 ic3 xg uzcrkuaj4p :;19t is released from rest startg3z:p 4cu 1;kxr9a jucing 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 hpkg 2t,s-98kf94dqa k .clvf his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fastth9c8q fldgf ksp-92 ,.v k4ak are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and gjt/ ylb:q0)5 ;mfeqh travels with a speed of 343 m/s How far apart are the wave c q;:ye5jl)h ft/qmb0 grests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz an;6p1;jq+dcacdorcm 4 )saxx 4 d 1600 kHz (kilohertz) and travel with a speed xd pas;xc1+odc ) q6a44cj m;rof $ 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 st*roaf f i u3yqa.;8:
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus,cn85b w1or1kd but one is twice as dense as the other. In which rod will the speed of longitudinal waves b1 drnwk8c51 obe greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports6zcm uhw/a2 si/1h8v j 28 m apart. If the tension in the cord is 150 N,hu8zh2ascw mv1j// i6 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 ca4prvj9 oo(ta: c1nhj 3ble of length 620 m and diameter 1.5 cm. As the gondola comes to j n:ha1o3pr 4(9jctovthe 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 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 surxb jr6- r-jg 9l;)cm4 ux4hvrsface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at 6jlv;m-rr 4g4-rxjs uh )9bcx this point?    m

  P and S waves from an earthquake travel at differe6c;s -,1g0hyptqrp iant speeds, and this difference helps in locating the earthquake “epicenterspq6 ;g1,r i0tapcy-h” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave c8 yd +xu7(agavan be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (t8du(y7g a+xva ypical 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 intensities, and (b) the s 4ilj(x)4vsq;fe ct 8amplitudes, of an earthquake P wave passing through the Earth ais 4(sx4);tlcevfq 8jnd detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through tvxfqe3hl bfsfe6,+ ;9he Earth is measured to be hq +, s;6f bflx3vef9e$ 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 travelr w ztvx71ea6x x.,ti71d*eg b through the same portion of the Earth, but one is carrying twice the energy. What is the ratio ofze6.dbxgae tx*7vi,rw x11 t7 the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but one tuqiptlo.k7/px3/bk hx .1x/pranspoptx7x1k/u.h qilpk/o3 xp/b .rts three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed t2ul ze gmpv,-+-.hl cno move up and down a total vertical distance of 6pv,llenm 2z-u +h cg-..0 cm, 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. 11–52 are moving towartx6oy 6ii; 6:n:qxgwud 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 pulsio t ;:xwx:6uq6nyg i6es pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency,n0y r8cp, vbu(-i2oq b what are the frequencies of the first fo-oun v2r8piqy , (b0bcur harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates zfnguju0z5q fh)l );7a x.ud2 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 strin.f flha)n2 )uzzgdx uj 7q05;ug vibrates as a standing wave.)    Hz

  A particular string resonates in four louxh9 6 (r pwkohxz3-6fq)9yq lii,c i3ops at a frequency of 280 Hz. Name at least three other frequenci66o3qip 9) yr, u-(lhcxw qi9hk3xfizes 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 freque*qb bq)u.v:e lncy of standing waves is 475 Hz, how far apartb*q .q evu):bl are two adjacent nodes?   m

  If two successive overtones of a vibrating8d(w x y)bele u0sly59 string are 280 Hz and 350 Hz, what is the frewl0 eu9)(d5xyls e by8quency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the brb)dbjbc-h/v) r :u a9xidge to the support post is L = 62cm and the string is under a tension of 520 N. Whj:u x- /c9ahb)brbvd )at are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to y;1aakk40* eebd*i*ypk9gq k vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the strin4;kq*y*aeap g0k 1k*y9 dkbie g 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 itu.mh gdk-nkh *p;r 1a+ is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? dr.h+ mh au-gkpk1n*;decreased by    %

  One end of a horizontal strin sc7 p/79vz3 melp *vzoe-i:kmg is attached to a small-amplitude mechanical 60-Hz vibrator. The strc7ml: *oz7 pv-sv zm3 e/i9keping’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 t( qbnupj12(itx gp+.btu- (vmoving 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 b-(t+i. 1t jpgvubbu2 (t(npxqetween 10 cm and 1.5 m?   

  When you slosh the water baceboh7ka:z)*1tgbk -l ikds, - k and forth in a tub at just 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-wide tub is 0.sab -*kk7do t1:z) bh -ekil,g85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s stri8kuqj:ng th.f+ 0u iyw2t(h ss w6i,4hkes a boundary within the Earth between jh24wsuf .ktyw+:8hiutn( qgshi06 ,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 underwater “shelf” where the velocql8;z9r osxw/kgc3e3 t 5w 2yiity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a xwk2 gwo5qt/l c93ieryz8;s334$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling icix4r0v zc+ow6e r/(b3j: blk n warm air when it hits a layer of cold, dense air. If the soun(lzce/b bjr4+wv3 i 0kox6rc:d 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 striwo: k-odsa )qz h66xs/kes a boundary between two types of rock at a 38-: s6dwozhao x)k6/sq $^{\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 * m 0*;stg8sqosgtde .user’s manual, the dish has to be pointed in the direction of the satellite sggt sme**. o0tsqd;8, 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/3h)h4d f/vmz2n x 6fimh 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 to the shore to see stranded fishefv 6m /n4zhi3hxfdm)2s and boats.)    min

  An energy-absorbing car d;2kw7( *wrb ss-d9irzt2yeeza)f0r bumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at0wr9fzwrkzd dy2 s2res;*e-7ab t i () 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 mswhh.dr3, 7 aqd0i*d18 m below, which stretches the net 1.1 m. Assume that the net behaves like a s.,s rh37dia0qdhwmd *imple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging sgs/, (-yu8 wrs. fjsizpring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscil.s- z8s/ r,jygifwu(slation?    Hz

  A 950-kg car strikes a huge springb*eez*,c 66h t y y8xuw5d,jfb at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the*b,e8 6* uwbyexc dt6zj,yf h5 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 (dizr9atz ;yu r zmqpo);//t.9t iameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually iyai zopz9tt. u);r;mrtqz// 9t 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 phonograph kbz 9jkmo ;i 0wzvg/zg k507+jrecord have a wavelength of 1.70 mm. What will be the frequency of the sound emitted5z+;go0wv bkzjjkz 9/70imkg ?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is in ywezso/k bw6(u9 dx(1meters and t in seconds. Detu (dw(xkb6wosye1/ z9ermine
(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 acrhta0 29jg b.a wdg4j6xww0 w6celerates at 0.50g (a)wta9wbwga.2 6 h6 x0gjj40rd w upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lakew7os-wic i+ :r6.dizg 1tc q5u. When a 75-kg man stands on the raft, it sinksuswwg6r:ctiizci. 51+7dq -o 4.0 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 tuacy*5akh s9m,ned to play at 392 Hz (G) and 440 Hz (A)5a*msc hay k,9.
(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. , dwwd+2(qdj.n 0chrzqby5w 511–33. Determine a formulncw5r+q,b0(dywqh ddj.w 2z5 a (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 vibrates at klj qy8amh:tv( d/qui;p10;l a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side hq:ul;qk tv8 i0mjya; 1pl(d/ 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 harmoni; r d.ua:ak5aqw ;,ya2 0 zhrwfyts20wc motion of frequency 1.5 cycles per second. What is the maximum amplitude w a;r,hra52yafwy2 ukaq0 ;dw.wz s:0tith 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 atapeatudp6 b6ytrt xv3(- 5* 4vtached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of tht*r6b34 (5pv6taxptv-d uye a e 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 — eadkq/8 sw8fav6ch one-way swing takes 1.00k8 8wdfs aqv/60 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 directi o8kycd(pr d+myb ycfi/+-1e+on or can swing as a pendulum of small amplitude, but not both at/id+y-1kyc(e cpmor8y+b+ df 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 stretc jlw j++im thy23qk89xhed under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a secondk3 q++yhi9xm8jj2w tl pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ce0 m d4r9pak :asoueh-1iling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stmrka:sp auh9- 0 o4e1day on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is c+6u b;vauz y 5/,gywe22 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? /cau6y; 5vuey gw+ bz,[Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in( v a-fvo+g3coc*lr (v Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and th (lovo*g3cvvfcr- +(aen you let go. The jello springs 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