Give some examples of everyday vibrating obje ctjptf(.6r7 c 3 00dyu(aouaocts. Which exhibit SHM, at least approa 07o(aoy(rctjdu 60c. tpf 3uximately?

Is the acceleration of aho6e0dg 6a/m7rr:bo p simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is axz3rosyx2 xu 4 a*b1a.pproximately simple harsuzoyx4b* x3a xr2a1. monic.

Real springs have mass. Will the true period 2acod d61 lm s:dmmw-p3eza*/and frequency be larger or smaller than given b2ez/p3wda:l* cd1sad 6mmo-m y the 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 oscillathya e4sx;.di-x-zoi (1y nud 1or (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scalp)tl rp ci-+w6e, and then is released. Describ ip crltw6-)p+e the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gaan+*7g51hyf wv0cjep *ss 6zdin or lose time when taken tdh+ wesf51spjzn*vac7*6g y0o high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48uv x )b1cqjri)r9/g7n ). How could you estimate)g rb1jr uqi)n7c vx9/ the height of the branch using only a stopwatch?

Why can you make water slosh z7z1 4-lnzhj eback and forth in a pan only if you shake the pan azz-ehn1j 7 l4zt a certain frequency?

Give several everyday examples of resonance.:ucy*7dzcayq gz 04w 6

Is a rattle in a car ever a resonance phenom/e6 ,buz-.qzz q nv8lzenon? Explain.

Is the frequency of a simple periodic yld7 bbwyzj ;f,;q*ejwo(n g8 i6 6pg5wave equal to the frequency of its source? Why or jlb6bd 6; ngqp(,ww og8j 7 5fyy;*zeiwhy not?

Explain the difference between the speed of a transverse wave traveling do9bfhaa::woy - c. hc;own a cord and the speed of a tiny pi9h ac:bc;:w.o f-o hayece of the cord.

Why do the strings used for the lowest-y qe(t,un um7k06t cw/ w tcy2. daro)(zp3*jbfrequency notes on a piano normally have wire wrapped around them?co2(bd.037qyuc/jz) t p*wyk em n , t6wurt(a

What kind of waves do you think will travel down a horizontal mmnu7t1 7dt)ny1:geda96tm pq etal rod if you strike its end (a) vertica mundty :qe9177ndt mg 61at)plly from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the 32(+ z+9kmpznntnw1m o* 2 yp0rio eidbulk modulus B is nearly independent of tempera o+mirpeny1*i2(wo3p nz 2 0kz9 +nmdtture, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water wad0d dm eajm j:x/jz/t j2(/5xsves decrease in amplitude as they travel away from the sou j//:sejdj50xtd x /j2mdz(amrce.

Two linear waves have the same amplitude and speed, and otherwise are ident-w/ r*3gg; r nkv lx2-nwoec*tical, except rc* kv-*- oggewl;w nnr/tx 32one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave cros b.zr6*1mur atjl4yh:. gek8j ses the boundary between two sections of cord as in Fig. 11–33, the u:y8b te rk*ja16rzm4lh.g.jfrequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibragg lt3i4g s/otptpsj *h2k524ting in three segments, are there any places you could touch it wigs hgp p2j2t3iso 5k/ ltt*44gth a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident an/ 8lbn 2z/rbgw3 r )qu0mr:oan26nv shd reflected waves cancel at the nodw6nrh:b8v2qn0am gn/ )/bo2zls ur r 3es. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, aph vntf tl;g+ 4.60ih9ios0 whow might we determine whether the energy was being carried by particles (msh.tng9l ;aih0 itfw+6 ov 4p0aterial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.jx5jlw7 l+;g g18 m, what is the total distance it travels; j+g5jlw7gl x in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs frg-h. dqy8tw 6i tq(zh)om it but is 85 cm long when a weight of 180 N hangs from(wqdt-.8iqh6 g ytz)h it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car coccbe ct vlt:8beer s:,. j5+z/mpress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, whatlz sb/e:,jrecct t:8+ve .cb5 will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg f jy0/ct,q 5l)rtdvhz0 ish hangs from it. (a) What is the spring stiff,v/tj) t5cy0qh ld rz0ness 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 vibrate:5d myhwvco6f /9-c lss with a frequency of 3.0 Hz when a mass of 0.60 kg is hungwsm l-vohc5/69 c:dfy 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 Fig9myfe4 rd) j(b. 11–2 at times t = 0,f9bjd(e y4)rmt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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. T ff1zy vgz kr:4opd b,/(lz( apnw7y/2he web vibrates predominatel/w 1g 7zvdny:k p4f2/rpz(oz,a ylfb(y with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When ao)kz- 5fly,x2qs5y 4 h4yotvw n additional 680-g mass is added to m, the frequency is 0.60 Hz. What ks,4) 2 f5o v-hyw xzt54lqyoyis the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an a - *6g tq:s*juugc*plkmplitude of 0.g*qsgj6u * c:p *uktl-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 f, g/rv3to lbig8ju. kl8 ky4a;rom equilibrium is the speed of a SHO half the maximum valk3jolk ug.brt ag/ 8v,i l48y;ue?$\approx$    A

A mass attached to the end of a spring isrwp jkw4,s1j 3 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. If the spring ie dzn(3 ;kt g(rr:,xmes stretched an additional 0.130 m and released, how long does it tregrn e; m(x,(z:k3 tdake to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kezs s7* tnn6u2g is attached to a spring with spring stiffness constant k = 280 N/m and is executi unz e*6n27tssng 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 popguntq xg2so*j5*-bqi z,b3utrf : 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun?:otxj gq b*,b2tz s 53iu*rqf-    m/s

  A mass sitting on a horizontal, frictionless surface is atta*kdj+(iu 7q( qx;duljched to one end of a spring; the other end is fixed to a wai(jqdk7 d*ljq+uux( ;ll. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 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 f*vzg nj)vd,f. 1a 8azr(dlmbs ,/gg(equation x = 0.45cos6.4t where x is in meter j1am/g8zf.), ,gb(r(vvdnadl * szfgs and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the ene0n tr)kpz-ew,t1iv mn:f rqujh) ,- 1hrgy of a SHO half KE and half PE? ±n, 0m:f-1nhvt1-kweu) qthzp,r )jir    A

  If one vibration has 7.0 times the energy of a second,ri)l3 yrtjw 53tp6rl bk: c3/j but their frequencies and masses are the s5:iklr)l jw/r3jttr y3p3b6came, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin osci oc08bz qhflq9 ;)4edyllates from a vertically hanging light spring once every 0.65 s. bcfy8e l0)qdz ;4qoh9
(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 eh+l;al8f :f pby two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of+a;flep8: fh l vibration?

  A 300-g mass vibrates ac ggqqf ,q(39lydu0w:i/c2unucy9)rk cording to the equation x = 0.38sin6.5t where x is in meters and t is in (uiclnq kc)qgdyr29 gyq390 u:uf/, wseconds. 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, k0 i wq8me.d l+rc3qzt -:)nfcwhat is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 1v jnl wrvc(oij9 /i0 ke8+5j t.9glnn.i 5tcj,24 N/m) is struck by a n/ j5jteg vro.wkvi t.c(9 i8l,+jn5n9 lj0ichammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring wit5fus la 9e17cl:fp)vbh spring stiffness 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=0) wiv baflc15: )79luspfe th 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 stiffnesfgf5 :/tg kzk*s 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 ab/j5f*,yikrt; 1pym-;v efwattached to a fixed horizontal spring whose spri ;kwy*m bt favj e-,p1r;/iy5fng 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 kgf+(* r)d-ot/ 0foxnj+ nferc 86wyskn jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in *+rfn)ed-xf6c s yft(8 r+ono w0 kj/n38.0 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 vibratio qs4uo9vve 9.gns in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be i,/qho dw d*ztjobc*;np, ;qk 9f it is to make exactly one swing per second? (That is, one complete vibration takes ex;ow ktn*p hbzd,/qq ,jo9c*;dactly 2.0 s.)    m

  A pendulum has a period of 0.80 s oy w,uff. +.t9wot-rp bn Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Eabow. prf. y ,+utftw-9rth?    s

  What is the period of a simple pen m*/ru nfzm(z45)w eyu op9h6adulum 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 may.wb yax moe8f1r*8r 3ss of 365 grams, and itrbyxmfray *18o .83ew 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 clock)8v x9t5;ae27wkws1wv -xve6a gnxfm loses half a minute p eagmxv7xt f951e6xwvwnk2-v ; aws8)er day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speet1ydi 6 ijhc.2d $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillatedazsi9jgmi8vb;b 7o4 iz+ 9u /m) gwpo- ku-i4s at a frequency of 2.5 Hz. At it is released from rest starting at an anglgz)o9gw bim ob-msz-ip47vk u+4 ;i i/ja9 ud8e 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 cre d )l r1xbcyat/cvu:19sts pass the bow of his anchored boat every 3.0 s. He rd/1y)v1 : ac bx9ctulmeasures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a spe.n obl4w:6efrxq 6-08psvij y9j l e3led of 343 m/s How far apart are the wave crests (compressiopf.nqyi:bo96 l 4lse v8wlj3jr0- 6 exns)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohert8nv34jnr,x f3/3ni *g,n vuwa h3qshiz) and trgji nha,n3 3x*v,833 fn /nirqvsuhw4avel 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 l6o09; fcgkh0aqf. -pxzv /xgg*( atn of longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as the o 0hd oh.:vq i;vap,6bkr9 3a3ujdk ly0ther. In which rod will the speed of longitudinal waves be greater, and by what factohab p00,;h36l yvkj du9kra ivo .d:3qr?   

  A cord of mass 0.65 kg is stretched fx iqeqs80a.k 6hv s;*between two supports 28 m apart. If the tension in the cord is 150 N, how long will isexq8q6vk;* is0 af.h t 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 cable of length 620 mue: **f:n1qg k3x5 ugq+5w m.wmqtgl m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into egux5m5f31wt gl*qn:u *mw.q:mq+ kg 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 hi ige .1i4bobfm-6 -2fmssc *yus ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean flo-mysi sc4* f-.2if16egb muboor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an eat ta4 hnel-(i(rthquake travel at different speeds, and this difference helps in locating the earthq- ( 4(letinthauake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface w ) lvihl+gx) wk1d58*bn tzg5vave 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 contact with the ground? [Hint: Set the)8vg dvbhkz5t wlnx51g)i* +l acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earth* lf z2 ib,2d1q6wdveqquake P,e6 l2vb qwiq1d2zfd* wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the E -r-pa)k+tbhe arth is measured to be -)b +rhapt-ek$ 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 thyrcizye 3nz ;t,3) wu9e same frequency travel through the same portion of the Earth, but one is carrying twice the en93);y 3, criewtzzny uergy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string haveds ujxqy0 t13,( lri7l the same frequency, but one transpor,iqljyx7s trlu1d0( 3ts 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 to move up and down a total mrfcf7t3fyl l1)x1zgb))f c 3l/vd /f vertical df/1cb1)l fztyf 3 f7mlv)xlc d/) 3frgistance 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 change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (ezzl h 8o+x1i)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 pulses pass each oz1zxe+i lh)8 other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrats:d+vml +t c/gy5 dyy+es at 440 Hz as its fundamental frequency, what are the frequencies of the first s:mvgcl+td y+yy+ 5 /dfour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrapm,+ ujjn3ong 1f 8u4s;b5sn ates 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 string vibratf ; un n4jponma18j3s,sb5+gu es as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at k08e sl.go0n/is(vgk least three other frequencies at which it will resona8/iv 0ses0.gol kkg (nte. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If 9nuc d y(v xp6tn8d3,s8jg iip-w h*0dthe frequency of standing waves is 475 Hz, how far apart arvgdc8*8 ppinhnu j0x6sy3dw i9, t-d(e two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hzov/s q.a48b2tq-iy sy ga)tt5 and 350 Hz, what is the frequency of the fund qv4tgati)b8sto -2ya 5s/.yqamental?    Hz

  A guitar string is 90 cm long and has:m* 8 qxp1 gcni0kj2z/r yd27v6d tetc 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 8e2v:17irgy6x q 2tj* pncz t/ kdcd0mthe frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string i8vs77,o-uron4/lli2ja onu.n+n p ux s supposed to vibrate at 200 Hz, but it is measured tox7 . olnl7-a2o u8+v,/unrosj4nnipu vibrate at 205 Hz. By what percent should 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;*8zl6s6 gx zso* 9qm2i; cqdh/tl tbg vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed q ls/6;lg*g9t xshd6oit82*qz bm zc; to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-6b - 7rsd7xdffsk3 g1hamplitude mechanical 60-Hz vibrator. The string’s b h3f7g61sfr7d xdsk -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 lennakx 1)f+cuegyp g 8:98w.l pugth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave pattex1 g8ny cu8pf ewa)klup.:+g9rns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back andivga0 fk kba:es75hyp 84m-(a forth in a tub at just the right frequency, the water alternately rises and falls at e:70gki 5 -a(smk vaebhap 4y8fach 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 the water wave?    m/s

  An earthquake P wave travelingl tzt 81+n5 wr5mhixy9 at k.0 km/s strikes a boundary within the Earth between two kinds55 izytmw 9t8hxrnl 1+ 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 un gzlyfd3oq19g ;)bx7e derwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a 1x qloeggz) y7f;b3d934$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of coldkofqaj s.5, 4a, dense air. If the sound wave hits thes5,qaf 4a k.oj 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 strikes a boundary between two typeskylnuvvr(8 jpo3m(mk(er :+: of rock at a 38mk(vouy+ e:( vlpm:k8jr(r n3 $^{\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 k t42;.v)qh:dash ay. f.zdbu z 8dz*wto the user’s manual, the dish has to be pointed in the direction of the satellite, but an errodh;z*akz u.:4ddfv yqt.w ba. h2)8zsr 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 q1o 8v4u 0l f9 zsm., xlc-ub:cjs4(rj qfs:ev750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during ts4oj lc0u: lzbs r,vuf1c84ev9:ssq x.(m qj f-unamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant 9e:oykh,mlqj t bt)26 of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservatio2te 6jhmlyobt k9q ,:)n of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m bel6l oqzb-g69 huow, which stretches the net 1.1 m. Assume that th9bzgh -l6o q6ue 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 on the end of a freely hanging sprih gf,se9,rtu meu:8tgj(m3 o2ng. The mass then falls 33 cm before it stops (ej,hue,m3 t2:ou g9 smf8gr tand begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a spoq18l+ hb64eypro4av eed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stif rb6vp+4 oloyaheq 841fness 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 coffixcy2v x q:cfvaxm -s;7e.9c5ee (diameter 8 cm) at just the right pace of about 1 step pic.x v:9 x7ce-;v2 x afymq5scer second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from then: pw8 ,pw h5y5d)-08w vvrfc oq2xckv center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the fwk fvhnx r )dqvcp0,co25v8: wy 5-p8wrequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equatil orw(2,3aqzoe/c t6xon x=0.650cos7.40t where x is in meters and t 36,o rxaoewq/2t cl z(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 witd:p t.+zwi hqjr+ oakzy/ ;9x/h frequency f. What is its frequency if it accelerat9xy+;t :i+ zhzkaop.w/ /rjd qes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft float q j-s-:rmrfahu.9bb.yb5ah .s on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raf9h:byuj-.r. b bm fa5r.q -asht 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 Hz (G) and 440/u /o7yud/w 5 pf2qohm Hz (A)dpufy/ w2 um/oq/h7o5.
(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 trakoe:b j 4fo/hlz1g 5ba-*s3gpveling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or kosf/ajbp -g4o :5l*bh 31gezthe lighter?

  A tuning fork vibrates at a frequency of 264/ 2cc4q.m5cliadqe x / Hz, and the tip of each prong moves 1.8 mm to eithe4.2c 5 mcl/ aqcqixe/dr 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 ey v+n/srmor q3w 0g9 uoi4xr:7 0uo)uwith simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which tws+uoneyg v3/ rquu0r 0ro7x9m)oi4:he 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 5qmb (v gin-e4that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string win gb(e54- iqmvth one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — ea42hk 1qrnizc-g j,eg+0p)c d gch one-way swing takes 1.000 )2i41-rd+g c egg n0hk,qcpzj 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 sprq a;2a *eqec bny0)tgq+c) o5uing can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, theqc+5a*q g ;ueanty))eb02ocq 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 12yaeq-srz +u4 t 7rv52 c0dwkp83 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ckd 2 0r4p8vyt7q s-azw+reu5ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended;7dw lzhq/ yto1 gkj,ote .)1p from a 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 just stay on top of the block/p1 ;kygt jh7d)q,1owtl z e.o? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crgfpx;rks x5ky ,e .:h .zzr1t2ane cable is 22 m long and has a diameter of 6.4 mm. A breet 2r,:.hp1kxefzxzs r g5;ky.ze 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 shrlhi;2eujn6z**,hu y own in Fig. 11–58 (which also gives 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 to a mass vibr*z,u l;6rnhiyj* 2e uhating 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