Give some examples of everyday vibrating objects. Which exhibit SHM, atvuax ,:p8m +f k9zmd0tbk*hhy:9:d x b least approximat0 bdx9 8*ytu:hkka,fhb+m 9:dmxpz v:ely?

Is the acceleration of a siyo, ihd -lz0q9mple harmonic oscillator ever zero? If so, where?

Explain why the motion of a pi3zk 9r 8ld5 m*v:gmmfzston in an automobile engine is approximately simpz5*:3grf m9km8z vmldle harmonic.

Real springs have mass. Will the true period4if77n j uq:3b +labo-5twutk and frequency be larger or smaller than given by -jtl + kwi5 ua4b bno7q3u:tf7the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO)e1tg y0 af/t1m?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and t-0 cdwcjnyy w24+lyz, r t2-hlhen is released. Describe the scale reading as a function-l+cy24h w-0ltc jn2 ,yzwrdy of time.

If a pendulum clock is accurate at sea level, will it gain0i):e3srdpi m or lose time when taken to high altitud3: rmds ipe0)ie? Why?

A tire swing hanging from a branch reaches nearly to thmn/g *wl z4lh8e ground (Fig. 11–48). How coul8m hlz/4ng*w ld you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake thel k 8b l8si4v3xubd8zosty21)j (4omz pan at a 8t4bl4z z xmo1jiovd)ss k3ly8( ub28certain frequency?

Give several everyday exam + .p kn01vs-frs3fw/b.qkl a pmee43vples of resonance.

Is a rattle in a car ep) cxpdqx-onk g2;,*j ver a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequav+g3d-sl0 y tency of its source? Wa3y+ vgl0t -sdhy or why not?

Explain the difference between the speed of a transverse wave:tqho7 qb7 m17f1 s/yyp9fy v1j0uxkj,) axm y traveling down a cord and the speed of a tiny piece /joy9 kay7f:)7vbtm1ju,y smy1xf1q7 qhp0 xof the cord.

Why do the strings used for the lowest-frequencyljm(//xfa: e o notes on a piano normally have wire (lxe:m/j oaf/ wrapped around them?

What kind of waves do you think will+ aw4k5x)xfy*7k ak phm3y5bx travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to w xfmaa3k+y xp k*4byx)hk575its length?

Since the density of air decreases with an increaedco q64y 82wxse in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the spee28w d6o4xeq ycd of sound waves in air to vary with temperature?

Give two reasons why circular water 4n.m7re 8a24l vyojxp waves decrease in amplitude as they travel a4aj7 myr284nvlp o xe.way from the source.

Two linear waves have the same amplitude and speed, and otx)hakdr fig2, ;-oc*oush0;pg4 fzf 3herwise are identical, except one has half the wavelength of the other. Which transmits mo rigg0 c3xdpo)f-uos f2; 4k;h* f,azhre energy? By what factor?

When a sinusoidal wave crosses vf s3u2-dw5 udthe boundary between two sections of cord as in Fig. 11–33, the frequency does no32d -d5u wuvsft change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could )y n8 pkb1 965g/dtxoli f4sh4:gqo 6* owjylftouch it with a knife blade wit 15o4itn4fx: j) b8 y/qlohfs6 l*dkggo6pyw9hout disturbing the motion?

When a standing wave exists on a string, the vibrations of incbz4n5rc 5 udp2 o 8jj:3*ifw9 ixomq3zident and reflected waves cancel at the nodx5cbwi*o 4n zom2 i:9updq5f 83j jr3zes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitten+ z-h7l3i sqnd from one place to another, how might we determine whether ni-zsn ql +37hthe energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance / wway 2s -k3iqzq*kz5it travels inz -aqk3sw w2qzky/i* 5 one period?    m

  An elastic cord is 65 cm long whenr q,2xwiivfc9 m7)n sz)q2lyu :ozm26 a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from i9yz) vnxm 6 o:,s qzlm) q2if2i7crw2ut. 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 into thh*y( )xogf 46omybft2xr ei0 5w)n0yg e driver’s seat. If the car goes over a bump, what will be the frequency of )5*mgx wofr0ynt6) ygb04yhxf2i (oe vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from itx p) smib8s: q82qmpv5r yi8:j. (a) What is)582jsmvpi bp srq m:8:yqi 8x 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 m,vd0fowe *e33.0 Hz when a mass of 0.60 kg is huvwd *o3 m0ee,fng from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fykikwcb. .rp -j9-8*+cyzjypig. 11–2 at times t = 0,zrbp. 8. 9jccyip +yy-w *kjk-t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web5hku zs/dw.ff p-e :7ef7 4cwf. The web vibrates predominately with a frequency of 4.0 /f5 . sek7-w7cpfzud: ffw4heHz.
(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. Wh,9 dso88x.x royl db(fen an adfdsby,9d8oox r8l (.xditional 680-g mass 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 vibqt2d6au :-6fov k aw,mrates 3.0 times per second with an amplitude of 0.1d 6,v6at ak:wu-of mq23 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 equilibrium is the speed e z l;o7v)o)wcof a SHO half the maximum value?7 ov)cloew;z )$\approx$    A

A mass attached to the end of a spring is stretched a distan mq qq:6vy6,)qo p3gxnce $x_0$ 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 0.3f4-k 3wqe,2 r qz3fuwmbup3z615 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again? -3uf4wb 3w zkp ,eqrmz2ufq36    s

  An object with mass 3.0 kg is attached to a spring with 3njiy +j9;80y sa y,3cd iwofhspring stiffness constant 9nojy03;iw+y cyj iad38f, hsk = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m to “logp,8h03o* xcqjdj1ybpbl ; i/ad” a 0.180*j x01hc bdop 8/y; pj,3ligqb-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfm bxwf-f- )sn56cg2 smace 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 experiencesc ms2)bnfg- w5m- 6sxf 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 accordingfmrobzwmp+5t + 3+r6k to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determine+ob p5tf 3rmw++k m6zr
(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 q5 gykaif sp3 m0mgr(840:dch a SHO half KE and half PE? ± 0h (3ki:rdmgs0 4f8aygc mqp5   A

  If one vibration has 7.0 times the energy of a second, but their frequencieg zm,.) n ;yo lyu0o v3.bpusu8v,7bats and masses are the sameo3ubboa)ny ugvuy ;s8 zp0t.v.m ,7l,, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically haa0p q;c/ nztws4o,7ac e4y4q1ay b2--znd p mjnging light spring once every 0.65 s 2-/qt4sy oed1qca0y;na aw-7ppjb4 nc4mzz , .
(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 par+2f)a;bqmo 7xy2 n qvyallel vertical springs, each with spring stiffness constant k (Fn7 v2m;fa)2yo+yxb q qig. 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 in mer8 kcjh,;r(4dp vvwwvx* u7m- zfwx01dk6n.uters and t is in seconds. Dete d0-cv1mxzw k n wr4w.*,;uj (r7vdxkfpuvh68rmine
(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, egcybpd:ej2n l +61/zlabeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the / idqsj *,gut6g r(jc:end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an is j* 6tqd, rgc/:(gjuinitial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness clrfdy16.idx 5 onstant 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 .id y rldx165f
(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 stio/(e b qd5q1v7p --v7fu oc5mvxm4oyuffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block att-oi9, zga op7gd w74)uv-nchxached to a fixed horizontal spring whose s d,hz g9-)uxpn w7a4i- ogov7cpring 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. x0q5me:* z sw: ivlcvofr-a:c7v7z0fAfter reaching his lowest point, he oscillates up and down,:vfclm zx05 vf0:q:-zcw vseo7r7i a* 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. 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 vibratiori vg. *1ihur9ns in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simplejwak: myv7h;hx ial9,+i3 dq) pendulum be if it is to make exactly one swing per second? (ayi lxw,;i :3 mdavh)jqk9h +7That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of +6y xzq t9ly: ;hejfecjn89/u0.80 s on Earth. What is its period on Mars, where the acceleratio yh q89z+u:t f9 yj;jxc6e/lnen of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lgd2pho , zfc64ong
(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 ou5:rqui;3th )xaw.8q5o4wp; 5 *ckydv r a dlkf 365 g4;5dvo8ah5: ;wi yucrra*. wlkdx3tqup5 qk)rams, 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 8i,joz1, lyq dlength of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shoyld8oq ,,iz j1rtened by    mm.

Derive a formula for the maximum spe6s u01 )zjnnlfed $v_{max}$ 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 frequency45q-5;ujyle1op wp4a(hi e do of 2.5 Hz. At it is released from re 5pa(yo4q ui-4 ;jld5phew1eo st starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every 3. 4 ,jnwz99wh tcwdh,5u0 s. He measures the distance between two crests to be 6.5 m. h ,5ct4wu9 njzwwhd9,How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and tz2g; r1oibu w79swj5 4ofz.uv6fh 7ji ravels with a speed of 343 m/s How far apart are the wave crests (compressioo7rj wiob6zwvu74s ;ih5f1g z29 jf.uns)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kH gdp k+bx2 ke,1f rsyr8c;x(g7z (kilohertz) a,g7kf pseyxg8d (+rc1kx2rb; nd travel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in ah0o1x:/.s6 frdtofm
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as t+hi5qk do uf:l koac,.ys*-+d he other. In which rod will the speed of longitudina l :casdoik.k u5yf +ho*+-d,ql waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 2 5b vgw m2a-e6k; e(ojgz-pc0o8 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the ot- o5gew 2gv6 mp0j akebz;(c-oher?    s

  A ski gondola is connected to the top of a hilxo91f w,rm l9sl 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 into the terminal and sends a wave pulse along the cable. It if9s 1mlr9 o,xws 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 ofz;lfz sj (+hf6 his ship just below the surface of the sea. He hears the echo of the wave reflected lsf f+( z;zhj6from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an (4 kyx*ye em(a+i aqd*mmlnn3 rwm(2; w0rsy,earthquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (w+lwa*;nn syq y( earmdm0kwr*4xe3( mi 2ym (,here 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 surfaceekb5qe3:ze x+ 9byw ;oi9z2 jw wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave c obzey+ w2qk3 jw 9ebxi95;e:zontact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudey k4 p) .ax:i9vs2zsbos, of an earthquake P wave passing through the Earth and de:zsvx ab9 oi)42. ykpstected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passinbwa7qvlo . -(6 qniop4g through the Earth is measured to be ovo pq47(6aqnilw .b-$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the * o4q2 5oy3 nxlbsypa;tf*-k dsame portion of the Earth, but one is carrying twice the energy. What is the ratio of the s;f o yxpn*do* lka2b5-ytq4 3amplitudes of the two waves?   

  Two waves traveling along a /7t1nes y*x+uzzteyl1 ib /7z:pxb;istretched string have the same frequency, but one transports three times the power of the other. What is the ratio ub;ztyx: elz+7nzbiip1e1ytx7 * /s/of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total vertical 78zu4q lz vlw b/ox59edistance of 6.0 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 /9oz 45qubz v7 llew8xchange?   

The two pulses shown in Fig. 11–52 are moving towi0s cb0gdth9b4 il;oys7z/ )kard each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of thyiti0k)d9zl ob0/hs4s; 7 bcg e 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 Hmombm 3 6 gyj(nl9:(ckz as its fundamental frequency, what are the frequencies of the first four harmonic:m3j k oy9l6(bmgmnc(s?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frdj aa(ei-(45 o5vyfmc equency will it vibrate if it is fingered one-thiyc mjf iodv( -54(ae5ard of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a fre.js/ee n.vo0; -mrxg dquency of 280 Hz. Name at least three other frequencies at which itx .;nd0sroj/vegm .e- will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string55j+ chz)1k ux;gv dee is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent nodes?j;) g+xv 5zhecu5 dek1   m

  If two successive overtones of a vibrating stri3ss87xd,0 n jwb8.f pzp/2 - oqmn1 -eswfdrlkng are 280 Hz and 350 Hz, what is the frequency of the f-w8lzfjss 7/ep 21 rmo0qsk3 wd8-,nb .nxpd fundamental?    Hz

  A guitar string is 90 cm long a-9-s:0afqs. 2j pydcx 2jlqtr nd 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 funda-j at0ss2y-fqd9:xc r.2l qjpmental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is meagzqdmic j 4lkc9) ;t9:sured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the fr ti:4zqd;cg) m9j 9cklequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Ho /c oybj kuz 2g7s01n8hw9ze0c5lzg9z, but it is measured to vibrate at lzw9n1b92 5ke oh7g08jo/g0czu s zcy205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60-i japo8eqv:h u9/y)n980gj hnHz vibrator. The string’s massaj) jnueo8hh:q09i8 yg9 np/v per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the puloa826h4gh a.ysvfnt e9 b6o i.;fi+giley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m? io yiagfa 2sge+n96v4;f 6t..ohi8bh   

  When you slosh the wat9tkm r8cy:n*fsy y8 i75 2fydxer back 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 cy 8:2tkfyr x*d7yn yi8s9f5 mwave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Ear s*zz8h rskx0.6xd5mhd zv/:k th bemr8ss:/hxkzd 6x.*z0hdzv 5ktween 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 velocity changes from 2.8 60kekhpvz c5.lp/8w bm8ce6h.p k5w/lbk0 zv p/s to 2.1 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 travesly amn4d( 2.hling in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold my hd al2s(.n4air 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 strikes a boun5 nh04zodn;0m j 47fmzbeby,jdary between two types of rock at a04bofb, 7mz0j;zdhm5 nn4jye 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. According to the usec 8xd3f iyj7-lr’s manual, the dish has to be pxd -j83i 7cfylointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h trave lpnb6 qk08ix-l4l( xlls 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(pn l xlq8bxl04 6lk-i, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of,cd6* oi/z(d a u4auueuo93 gn 550 kN/m Find the maximum compression of the bumper if the zunu,e* 9adu/3o4u6do(g ci acar, with 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 a window to a fire neq njx5l -5n)kht 18 m below, which stretches the net 1.1 m. Assum5lxj)kqn h5n- e that the net behaves like a simple 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 opjx 6.4kz zj.bn the end of a freely hanging spring. The mass then falls 33 cm before it stopsj. kpj4x6bz .z and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a d.;z1h,whw p9kwm bi0huge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness co;k1w 0.zi ,mdhhww pb9nstant 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 rfxuweg:ybwjeu+ua,8gv9p t11 -p9 6h ight pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55h9w+jvuxw69t:buefp 8yg1 u -,1aepg). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10 gey7drabvo:f 3++9)seaz7i k.8 cm from the center of a 33-rpm phonograph re+ zokafe)s+3gbea rd:7i9yv7 cord have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cosek)0 ws *bpsx/7.40t where x is in s/0 )w kse*pxbmeters 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 its frequency if it c3 gc7.:1avma f .tzxhaccelgaf7c t..vcz:h 1m3xa erates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands o)8rx9 unj z)lgn the raft, it sinks 4.0 cm deeper into the water. When he steps z 9 )ulrn8x)gjoff, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 2pa.(d9ki rj8/2 1wtymjhugw Hz (G) and 440 Hz (Aj92rhm ptj a/uwk8.(2 wg i1yd).
(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 k mis+ l6 e37 jh:r,wfqmoqt(.ws;jc;the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the sp7l tmhsomf:wc;36kq re (s+qw;ij,j. eeds 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 a frequency of+ g6cksdyv: 2geoy a6nfhs(dh .q 9a., 264 Hz, and the tip of each prong moves 1.: ga ckd(e.vn6f+o9a2s yg, h.hdqsy68 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic mzfz3fp)r 2f :zotion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board 2) zf:z3frfzpduring the oscillation?

A string can have a “free” end l* 8c0j27(a.:din 0ycuw iv-obe hojeif that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11 8 7y -ec2wb0hd .a*0jcv:eoi(iloj un–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 e mnk5ibxp c)3)xactly 2.000 s — each one-way swing takes 1.0p)3xb5kminc) 00 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 direction or can sw*x,a(25dw5 sxhquhlwl3 b f6yv6 .plt ing as a pendulum of small a u6( t2hlx,.*xpq b5 ha6w3dlvyfsl5w mplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension ohr t*-myef+.9 3qh lrf2vrd2e f 255 N. A pulse is generated at one end, and 20.0 ms later a y-rrf92tvrmhe+ q e2hl. d* f3second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a *vhp;qy)t/ mrry.n ,z ceiling 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 jusqhrvn ,y r.p*mz/;)ytt stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane ca yj 5g3d;fk7zoi 6*1xgbm))s5gqcdl eble is 22 m)qb1dif6l seg yzd )xkgm3j5c *5o7;g 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 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gi xphv -ya o1x0:h*4zkw.lvdb6ves the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy toh holvz*-y :. v6bxxda014kpw 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