Give some examples of everyday vibrofwvwb.jnxldaf9h5g 1u f9* ( k:z*p .ating objects. Which exhibit SHM, at least approximatf* 9.wlu.5p h1*jvnxo:k w (fdzgbfa9 ely?

Is the acceleration of a simple harmonic n3m+.;u(fupsj51mlk-enqe d7elnsd . nn77 moscillator ever zero? If so, where?

Explain why the motion of a piston in an automobyt jrl 6hn-kd wv9ua7y5x/:5 wile engine is approximately simple hand:9-ru5k6a7h5 v/wxjyly t w rmonic.

Real springs have mass. Will the true period and frequency be ck);jql 7sy 4)jpm0xpeaq14elarger or smaller than given by the equatq j )pymea qxkj4)s p14;e7l0cions for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator9v utrev+ p)b6+r9 cjn (SHO)?

A 5.0-kg trout is attached to the hook of a wz xfkyhdj+v ms4w -y9f) : w,e7+mhv5vertical spring scale, and then is released. Describe the7wh+v,d9)fkf z4 jy y m-mww+e :hvs5x scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose timel serzx y )c *dn;y44r*eytg+* when taken tonx4 c grye *dl )**er+tzsy4;y high altitude? Why?

A tire swing hanging from a branch reaches nearly to the grru 5zr/ ,-i;.caa z f:ihwq7wtound (Fig. 11–48). How couldzf/wt,7.:z ;a-c wri q5 rahui you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and fort6(qt37n euegb h in a pan only if you shake the pan at abq( 736teg nue certain frequency?

Give several everyday examples of resonanw f-v e/+gqe8.bcv+b fce.

Is a rattle in a car ever adw7ybc- 1. awh resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its source,5co 6 am rcp2pr 7k;wzw2d(gy? Why or w,zrwr gpcy2;2akcd5 m7wp (6ohy not?

Explain the difference between the speed of a trr8r5gp :e:dcransverse wave traveling down a cord r cr8: erd5g:pand the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notebx/y/ccb2 la m3;q 2cxs on a piano normally have wir3c/bycqcx/2 m2 xbl;ae wrapped around them?

What kind of waves do you think will tr( ycq+8 nqgt-hnr3t5 kavel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallrnqn5t-k3q(8 ghc+ tyel to its length?

Since the density of air decreases with an increase in temperature, but h)a rtbt/rz02the bulk modulus B is nearly independent of temperature, how would you expect the speed)r0rbh2at/zt of sound waves in air to vary with temperature?

Give two reasons why circular watjp/rpor *3todj7egip+-mf )-s x8 lrma0 *yn4 er waves decrease in amplitude as they travel away from the source.rx-fr*+ eoyiam3)7mgn 4plpr-8pd *ojj/0st

Two linear waves have the same amplitude and speed, and otherwise arcz s+g0a3i d ;5zpen.he identical, except one has half the wavelength of the other. Whiche; zh0+d. za5s3p ncgi transmits more energy? By what factor?

When a sinusoidal wave crosses the ul(amyi*me c )u5 7eslz3e,b7 boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain 3lmuyl, e7c )u5m(as*eb7ie zwhy.

If a string is vibran2emi./m2hdt 0x 2vh tting in three segments, are there any places you could touch it with a knife blav/22n t2m0i ehxt. mdhde without disturbing the motion?

When a standing wave exists on a string, the vibra ( t;*xyzzswa1tions of incident and reflected waves cancel at the nodes. Does thitx (yasz;* zw1s mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another4;4vz ;ck njpn, how might we d;;c nzp vjk44netermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with ampli/71 jgig ph; fk+z;pfgtude 0.18 m, what is the total distance it travels in one pe fk ;7/+g; pzfhj1ipggriod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is8p/ .nct q 0)w 7dgnqn*kot)dj7s.s us 85 cm lon)cgk.ntu8*7dnqo d) .jw7/0spn tqss g when 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 its 68-kg driver gets p3c)ip g :x b,/pmdg8zinto the driver’s seat. If the car goes over a bump, what wim/gb)cd,ppg :xz38p ill be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fishkqy(./fm:u3 vgxib9 dclw6+7n.ozj m hangs from it. (a) What is the spring stiffness.9 mj6:dv zqk.xf/w+imn b 7(guoy3cl 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 pnv1x/wz8duoy r6 ;0v with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.3r/y v08op1 du;6nxw vz8 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times fg4v )c+ *rbti,xh5f vt = 0,t r*vb fc )f 5x,4+thgiv= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 whz:-g h 5r0hjmeb vibrates predominately with a frequency of 4.0 H-5hj0hm : hgzrz.
(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. When an ad*v* s(l4mnb(t:j8 mu -ywkltuditional 680-g mass is ulj*l m*wts8 yn:bku(4(-tvm added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at thebuh r)y2u5rzb:(s 9lc end of a spring vibrates 3.0 times per second with an amplitude of 0.b(b 592:rczlsruh) y u13 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 f1l k6 fr6m*fe:3aq-f;f/gowa k+fyn nrom equilibrium is the speed of a SHO half the maximum valy3f6/n :+k ql *1;offwen6fm -rkfaa gue?$\approx$    A

A mass attached to the end of a spring is sk nuhzn+c6 0i v+ep6(ntretched 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 ;g/1msf kiwb2v:0wiv is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?1b/gk w: fv0ismiv ;w2    s

  An object with mass 3.0 kg9g,z6/0 twkj aw)n fze is attached 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 its9anekwt )z f6gzw 0,j/ 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 80c hr)4fer 8huzl qd020.0 N to compress the spring of a toy popgun 0.200 m to “load” a 00urf) 08 lhr4dzhe2 qc.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfavnravav2 47lx m 278q+kv otmyhk- /x2ce 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 mavarlo- /+ x4a7v xh2mykkm2782nv tqvss 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 = 0.45i.5znjg;qpl.d 3 m(hr cos6.4t where x is in meters and t is in seconds. Determine j i;zn mr(gh.l.dp q53
(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 PE2 ww9*xzu:p6tkscc 1m? ± 2x1wszc*: 9kupc 6mwt   A

  If one vibration has 7.0 times the energypwt4d7u h7 wz) of a second, but their frequencies and masses are the same, what is the ratio of 7 puz7w4hw) dttheir amplitudes?   

  A 2.00-kg pumpkin oscillates fromkmf3g8qq1o ipss3 (dsy ,ib znu0-:4da-yn;b a vertically hanging light spring once every 0.654dns3;: kqn,iqpys-isd (3uf 8ygb zao1-bm0 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 verticaljck.8) ng*( j lxj ob(m41ksax springs, each with spr xn4(jo j)*js.8bkx1ck almg(ing stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38s,8i6h 5rw20xn -ux bvgx*nahu5u t-w uin6.5t where x is in meters- 5, x8nxuhxghv0iun2t au-6bur ww5* and t is 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, labzv +y;adks,9djg3kjwp qb 5(+eled 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 re*oo- *wa gxg21s s*upl9loo8y st on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives t8 1a2oy*o*lg* go-swxopl u 9she 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 st zoriul-aj,uo ;k2/; ziffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The masok2o;;ja iuru/zl z-,s 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 )a.9q0gm srb qconstants $k_1$ 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 attao,dnu(pxpp:iw0q8ddu:r3oj nd u2u9 8.t + hq ched to a fixed horizontal spring whose spring stiffness conu0upq8. iurp:p donw (q: 8+3,ouddhn29 tdj xstant 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 reaching 7gw:ya7iuv2s 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 the27 :sia vugy7w 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 ej kor* ).w9,pd.seut oxactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactlfbbbqinrz/.pg 0872ly 9: t wty one swing per second? (That is, one yw8bl2 ibq pnr79t.0 /zgf: tbcomplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period oniv cn wk7y,g7al. 3y(r Mars, where the acceleration of ,g y3c(.avykw7 7nirlgravity is about 0.37 that on Earth?    s

  What is the period of a simple penduwwgm2d1dvsv b/f6yo75b+ sq5lum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass( 3n9lcz-+9xg v*yaf wls nl;s of 365 grax- gnn l* av(sysl3;c+lwfz99ms, and 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 cloa cy,v3404n idifd8;uwib *zm ck loses half a minute per day, how3n48m 0vi,d w b4zyiidu; *cfa should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum sv.nhflse2fsn /)u p syz,32s:k 8e1ty peed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is releask6:ixm +3leq3o)g wamed from rest starting at mi3k) l :+m wogx6e3qaan 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 u wi wsst89j+w,uc 4m1pass the bow of his anchored boat every 3.0 s. He measures the distance between t9iw8w ts+cwsj,u4m1u wo crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frcf0 4( /cresusequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave cre f(4/esrcu0s csts (compressions)?    m

  (a) AM radio signals6ovvv2f ,s rmx bs3c/6 have frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a spe/6v xsfv ,or32bv 6cmsed 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 oofmjgi fa2y9r p66ug 7 n.t58wf longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have thej+ir r 0hgqn2*:jn*dk same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longijni* 2:+* kdrnj gqhr0tudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg jdys8p jrym:c0 jy,+r8 (eb0 uis stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long 0prryj j,u:0ysb+8me(d cyj8will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected tji)bk8vr +.sq,r ;koa o the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps r vjabq8r )si;ok,k+.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 juckfs( 5ou ro5ip :+l*ost below the surface of the sea. He hears the echo of the wave reflected fro5+oi*lp ksrou(f c: 5om the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds,nf(u.k1:osu*fmqc+ng ;l ;bf and this difference helps in locating the earthquake “epicenter”kg ;los1+ *.bfcq;uf (nmunf: (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-producedh*aa8zp-y9 ba surface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquazb9hap* - aay8kes, 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, ge wbnuz/d-k9a0)trpau9p ;- 6f8wbt and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the so8d t 9aaufrpgk9/)w6wn b-ut bezp0- ;urce?(a)    (b)   

  The intensity of an )r w-md 2ydvt 4gj0bo*earthquake wave passing through the Earth is measured to be -ygod*m2jw 0 bd4v)tr$ 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 t*rz2tx 3lk fap0wn*f; ravel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the rxl 2kp30wff*t;a*nzamplitudes of the two waves?   

  Two waves traveling along a stretched string have the 8:rce;evky4t/*s+ pea :om yssame frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the twvpk/o ya: m8eer+:4*es;tycs o waves?   

  A bug on the surface of a pond is observed to move up an r ;ksqlwriw+5ma-*92v j*leyd down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passe*+l-;vw q5 sa9me2y kw rrilj*s. 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 toward each other. (a) Sketchr *;sl6h72dzha.nb ze the shape of the string at the moment they directly overlap. (b) Sketch t*7 2 6nrl;dezh a.bhszhe 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 frequency, what arkejawsv3j507gj 1sxdkr (s i+is7,1 je the frequencies of the first four harmokwgrjk0sa ( isv11sij5x + 773ejs,jdnics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency wv t+65khis 2,rwzhj j(ill it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the strvih,hsjtr256k(+ jz w ing vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 281 cxpu fg;ye2xn9o.z+8gxe0 e0 Hz. Name at least three other freneepx 1uo90ceyg8fzx; +2.x g quencies 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 frequency 2ow5(il (ih twf6p4h2w b sdrf fi)39vof standing waves is 475 Hz, how v 2ofwd543frb(2i i w p9hhwst6 ifl()far apart are two adjacent nodes?   m

  If two successive overtones of a vibratinaenc ;(jodqpz95bax1+9v wdfe.*x *xg string are 280 Hz and 350 Hz, what is the freqbx a.j*z+;v po9cx 1e5nfxwq9e a(d*duency of the fundamental?    Hz

  A guitar string is 90 cm loh2mgz/bnh; y+ng and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamenn h;+b 2mh/zygtal and first two overtones?    Hz

  A particular guitar string i imdz19+( qbgos supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shoulqdm+ ozi(g19 bd the tension in the string 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 vmlb2m*:dzipk:9 ya*ul qj,;e ibrate 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 fre :ap ujdm**qylb:9km zl,ie 2;quency? decreased by    %

  One end of a horizontal string is attached to akmo/ j kc. teqm4g 6by,*/znddy,1 st/ small-amplitude mechanical 60-Hz vibrator. 1mk4 e z.,,qkddnby ty6cjo /s*/m/gt The string’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 movq d;k.4 k,yol lq 8jo8d*0keqying 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 be * klj,0doqo;kke88ydq4.yl qtween 10 cm and 1.5 m?   

  When you slosh the water back and forth in in;1 l q0noa3rq)d0vr,qy9 y ia 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 0.85 Hz. What is the speed of t03a0n,yiqroqri ; yvl91 n d)qhe water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Eart/l7ey) na 5f-c8een2pt9t yzoh between two ki 2 )fpn oay-79z8ty5eet /cnlends 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 uaise 9w/2 *gj5 kjb9mev fxy-7nderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave cres e97kay 2fs 5/eb *jj9xi-mgwvts make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in mv e2glo+mu kq lpq6;s lnch5,22 x;e.warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interfacq;nl6 kqmc g+5emls, uo.e2lxpvh2; 2 e at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two typ8jfvf ::ofxx ;es of rock at a 3 8;xf:ox:jffv 8 $^{\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.u0w4 m :xy*3h mie-tgh According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an xt3:*hmmehguw -y4i0 error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pff ih)/85(ttpx09hx2p jua eiacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximatea5ippxhefx fju()ht 9028ti/ly 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 b3mt) ihqu* w4oumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides * 4)3o mqithuwwith 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 netc-k)0do )i swq 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, andd0q) -) iwkocs
(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 spria/ixgt a5*0dj(/q8s 9ejaa;d pn xik -ng. The mass then falls 33 cm before it stops and begins to rise. What is the fs-j/*a/5 0i9x qge a aid(pda 8;xnkjtrequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 eb 4 7lv-jee7mm/s (Fig. 11–54), compressing the spring 5. b7-74 vmeleej0 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 jq nh1:x5k8ai1as mnc 3 *scvt*ust the right pace of about 1 step per second, the coffeeaki 5v18caxnnm1c sq*s*t: h3 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 lu( g)s6p7vkkvd jdl-;ud 9t933-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of6tu l7ksvpkld d 9 -u9d(g;vj) the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t whe86 o6l:jlazjeqy ;qj dxp,0 4ore x is in metl0;a jyxqolq6ep :,4djj 8oz6ers and 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 with frequency f. What is itj -eyt(kh(rv4p, )qq ys frequency if it acceleraqj y h) tpqyv4(rek-(,tes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft qkfw+ga;p4owl0+: z szgq 1n(floats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the watef:azsw0+kwng q op 4lq1;(g +zr. 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 ( z jg1vsmt/0z()8rhyhqw(nr at 392 Hz (G) and 440 Hz (A). tr ((sv8w(mq0gn /h)yjh1r zz
(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. 11–33. ;wfly rh k.hfj+2fjw53j au;fl(0d* gDetermine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) forf;u (l+ ljkhyr0gww.;f5j 2jfh afd *3 the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and t hhh 7p:w/pql; wwmh6)36a4 v(ztg zethe tip of each prong moves 1.8 mm to either side of center. Calculazp6mz)w(37whtgl6 pwh;/q ae:h4 tv hte
(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 freqmpw i4mxbjtp8 -598squency 1.5 cycles per second. What is the maximum amplitude with which the end of-5ws bi4m8tpjx89 qp m 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” rj vp,yqfi+/;v2, tjaend if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths ovi2vq a pyjf,jt +r,;/f the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one6o8d k:g2w/ (sudyuz6r/ g bm1cge*1la )wlxm-way swing takes 1.000 s. g g28ulk6/d1xs6uclg:)z1(m bo / w*dmy aewr
(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 cavr3oafpp.1 7 dn swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillati713od a.vfrp pons or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched undep c7kmdztw;ankgac/ou*n* p.*kh 3;5r a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generatednakh3 dp ng5o.;*k7kza pc*/tw*m;uc at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceikh .-c+k7-d1aimdw wjling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplit1jd w m.k-7+kh-wdc aiude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. :b rg*pa 7xtn 4.s.tppThe 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 pr:tp74..xtgpn a bs*. 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 (which alsiv oqfo(/3x vl48ag -vy1c h(zo gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and bo i-(o zly1(x/48vcqagvh3fvegins 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