Give some examples of everyday vibrating objects. Which exhibit SHM,+skr* kq +5hxs at least apprs+kq 5+xh kr*soximately?

Is the acceleration of a simple harmonic orj1h7o. v ku5vbb 58doscillator ever zero? If so, where?

Explain why the motion ogy ) ak*api:d)f a piston in an automobile engine is approximately simple harayp)i :d)gk *amonic.

Real springs have mass. Will the true period and frequency be larger or smaller x0 (y1xr:+zz:dgkbno - fstk 7than given by the equations for a mass oscilla7t fb1rk-(zxz s0gk+y o:x:d nting on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple k q3 n(ay*i3lgharmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook ojajqwo1c0-xn 1 n1tro1ymav a:- u:n(f a vertical spring scale, and then is released. Describe the scale reading as a function o1n 11a yrn:t oc-avw j-nuo0axj(q1m: f time.

If a pendulum clock is accurate at sea level, will it gaintp79i yr o .p99q5yhk xx2gp3x or lose time when taken to high alt x29r57o kiypy9.hq xp 9px3gtitude? Why?

A tire swing hanging from w c7;guq phhn292wm* dy+ 4ylka branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwyq gy2 upk+mw*4c2l nw;7 hdh9atch?

Why can you make water slosh back and forth in a pa6l.x.ht,t ydrvfq- n k3q;vw i-1 4lwjn only if you shake the pan at a ce;n6irkh3v.w lt-q1flyj,w dx .v-4qtrtain frequency?

Give several everyday exar 66fw)5bxv/gl(yz 1wtr uix3mples of resonance.

Is a rattle in a car ever a resonance phenomenon? Expk xsdpd2; utyj;o -8c:lain.

Is the frequency of a simple periodic wave equal to the frm,)-gz (asq ijequency of its source? Why ori(,a-) zqjgsm why not?

Explain the difference between the speed of a transverfw -zhs y (;z sx.8i/morb,lt5se wave traveling down a cord and the speed of a tiny piece of the cordbs(ox8hlsim-/ ;zf5 wr. z,yt .

Why do the strings used for the lowest-frequency notes on a piafhcxuqo (/l;. /i yfw)kq:ap) no normally have wire wx)(kqhwaf f ).p/;yoluc : q/irapped around them?

What kind of waves do you think will travel down a horizo :gqwwgrlac) l81r uha(/r(e5 h8kj3ontal metal rod if you strike its end (a) vertically from ajh rlgw/eaw):1qlh3 rr gocka(58(8ubove and (b) horizontally parallel to its length?

Since the density of air decreases with an increase njfdy+d x3 a4:in temperature, but the bulk modulus B is nearly independent of temperature, how would you exp:afynj d +3d4xect the speed of sound waves in air to vary with temperature?

Give two reasons why circuladken7 3-n3ndkr water waves decrease in amplitude as they travel ae3n n3 ddk7n-kway from the source.

Two linear waves have the same amplitude and speed, and otherwise are ij(v; z0+v lvw)o3enordentical, except one has half the wavelength of the other. je vn(;z olo3+vv0r)w Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cor,cjorz2 +,t yqd as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain whyo2,rzyqt+c, j.

If a string is vibrating in three-lnite).o , lb segments, are there any places you could touch it with a knife blade without disturbing the motion,.-t ei)bonl l?

When a standing wave exists on a string, the vibrations of incident and reamsgm6 lu s(reh t4,vw498jsikhgcj;5y k)+* flected waves cancel at the nodes. Does this mean that energy was destroyed? Expau ekv6jmyi rhs8*k;m),g 49w tjc4hs+ls5(g lain.

If we knew that energy was being transmitted from one plaz7r1 kz2y9g)9py txumce to another, how might we determine whether the energy was being carried by particles (material bodies) or12y ym79p9r)txz zkgu by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distanczda; x )(4: jtk)pc i+9inxlkse it travels in a; nt4:c(lk s) k)i xi+pj9zdxone period?    m

  An elastic cord is 65 cm long when a weight of 75 Nq+r8)f(h ere u8dl9cq hangs from it but is 85 cm long when a wedfe q8ulhe+)8 (q9r cright 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 ge +a( usym*s5ab(en5cfts into the driver’s seat. If the car goes over a bump, what will be th5 n*5fu(sm(+acyaebs e frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3jd/jacb* 1r9/t 1tf xk*7vx:9 nhiu me.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness co kbtv1mj9 i/ 9ntu 1:/dfxrce7j*h*x anstant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.6cz +x3m3q;ybv0 kg is hung from it. What is its frequenyzx+vb3mc ;3 qcy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at tic:;l5v dazh5w 1e-y 26u1txgasrhf v5mes t = 0,t = e51rs ;6ag y2 d c 5vvlh-zu1wx5:htfa$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 6wig0j- oauk5spider’s web. The web vibrates predominag i6uko05wj-ately 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 d 4gjw ;z .lbu5bn5z-,xwrj. fan additional 680-g mass is added to m, the frequency is 0.60 Hz. What is rlzj; , xd bwbjufw.z.n5 45-gthe value of m?    kg

  A 0.60-kg mass at the endeiy/0k9/t e3 5it/pu ry0ggd l of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. kdu eg0/i 0ip5t/r ely/ g9y3tDetermine
(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 e: pu-xfaod2oz0c2vlzp +h8 eq 4sux26xvpq:0 quilibrium is the speed of a SHO half the maximum valqpz: s+p-0 l0 x86oevxhoc24qp2vd2x:fu u azue?$\approx$    A

A mass attached to the end of a s (g olu,.rg+moa,qb l(pring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If (ccao3l.b2y ,l2 qxczh4wv5r the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibriumb(,v5aq cccxzo3l.hyr42w2 l position again?    s

  An object with mass 3.0 kg is attached to a spring with spring 2t a*zu k+zsv98 eu0l2i14mb/qu fpmd stiffness constant k = 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 0kf1udzu +z2uilmt 48*bv/p9q2 smaespeed 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 Ndy klokmj 5xx /66;/wu to compress the spring of a toy popgun 0.200 m to “lomx/6k/dw oxlj6kuy5; ad” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal,g yr/-*gq3y sr )x-mkw frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work i y/-)rgx3-my*gwr ksqs 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 equation x = 0.45cos6.4t b0xz8 q/rudrq*eggqu-xkc;8s- -bk 5where x is in meters and t is in seco *k;ebu sq d-rqx05g8 czkugq/8b-x -rnds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and half s/c4-6pvgt)wg di.u5rh/o w ePE6.cp4ro t5ue gs/gw)wd hvi- /? ±    A

  If one vibration has 7.0 times the energy of a second,tq4zxrto,m) dd1 n+x 2* a2yes but their frequencies and masses are the same, what is1d2dsn+ t4*ey)xort a, mxzq2 the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every ) o dack:t*klfeb/oj5 7xm-:t 0.67bf xa-ctkj* to)5 k/mo:: lde5 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 vertical springs, each ,rybuze - nu*.iq7xd-with spring stiffness constant k (Fig. 11–49). What will be the frequd u-i,qex rn 7b.yzu-*ency of vibration?

  A 300-g mass vibrates according to thecm82a8wu3;a 4yqb kqlj m:l+x1g3g nc equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determ4lm:wmc8c+ lknxbuj3g q2ay;g1 a3 q8 ine
(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 eachk b nen is5cj1lpr13pt:ea 19/, 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 end of a horizontal spring (k = 124 N/m) is suxoviyun9y u+1nz -*5truck by a hammer,o- nz9vu+5 1yn*uu yix 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 with spring stiffness constant 305 e0g xk/b.3se y;(fbhtN/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The massgb s3(.hf/ yet b;kex0 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, z+lvjcj8w f(pr3y 45ywith spring stiffness 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 attached to a fixed horizontal sprin/x7 3k81 qziou m6pzczsyw-z, w80hn cg whose pqc1zukshxz wn z0,3o -6/zc8w78i myspring 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.,mv9;cf xbdhl377iqv After reaching his lowest point, he oscillates up and down, hittid,vx 7 mci9l3qfh;vb7ng 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 vibrationf52x e:ef6;jy htegz+s in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make +saaj vx-5 dc6z7ikpd9n:et5exactly one swing per second? (That is, one complete vibration takes exactly 2.0 s.) p5ak 96tdcs-ven:x7 zi5j+ad    m

  A pendulum has a period of 0.80 s on Earth.. t/p:zs5z8mzqyz)ikpn (v0j What is its period on Mars, where the acceleration of gravity is about 0.37 that om 0(zs8 t.zpn5)zpy:/kzjiv q n Earth?    s

  What is the period of a simple pendulum gt6b0p+d4yla ig 1q/u80 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 j*qx39-cxnq02+9xwp o+wkd 5c x jmmfpendulum bob has a mass of 365 grams, and it is released at an angle of 12x+9pwq f9j od-5q jmx n2kwx*+cc0xm3.0 $^{\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 pendulem*laq d-d;8 j/.ja z 5gkfc/dum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the leng/d /-5dkgje8j a*zqd;a . cflmth of the pendulum? shortened by    mm.

Derive a formula for the maximum sp-+us b ,ypiw6weed $v_{max}$ 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 rela s k3ia1*w21t2j:uqudpdrj ) eased from rest starua*a:jqs dd wtjr u 1k232i)p1ting 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 anchorejpt2)q l(gy(chb1 lzy -ih+5b d boat every 3.0 s. He measures the dist2bchi l ( j)y5z(h- q+glp1btyance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air ha9xfz iy n -(1yq61dfbas a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressiz i-f6f1xn1 dq y(9ybaons)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (x*5l/ qci(6 io ;kf oq;lujd:ukilohertz) and travel withuld f/i;q qix65:lo c;kj(* uo 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 longitudinx) k +ncxa4/vz l8uec( 5ke/vval 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 densebgy+s99o:( r:gir s r3w zc0pl as the other. In which rod wils0c9wirr :sl(9:+ g3 ypbozrgl the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kgv;mtdswt8in)fth/9b )zcw;t-f bu-h3 w* 9ep is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to th/fw )f99c )8tn-uwt dz b3t-i;s bh*vm pewht;e other?    s

  A ski gondola is connected to the top neo/2z 8 ) vzwzn5x+usof a hill by a steel cable of length 620 m and diameter 1.5 c5onw82xv euzzz/ )ns+m. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea+; 2aoxp-j 6ddcumk 4uwbte:d;,o e9te/ga *j. He hears the echo of the wave reflected from the ocean floor directly bpukc e: be -+/*aojeuwj6;modd;tgd4 2a9x, telow 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this diffeg*ouhbj72r+*q+g;t d+ wdlq mrence helps in lodt ;l+*rg2ug dbh mj qq*w+o7+cating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoiwi1smg+pz pmg-jw b9;36 xh6n dal transverse wabs+w;96hp6xzgmnij - wm1p3 g ve. 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 acceleration a>g]    m

  What is the ratio of (a) the intensities5f( iy 3mbscm-e)u lind/2re8, and (b) the amplitudes, of an earthquake P wave pc) ds/eibu-f(i m8e5my n r3l2assing 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 thro5abbrjuzp9gb-n5nr 1e; mp/ 6ugh the Earth is measured to be 5rjr6p nb9mgp /zuab -1b;en5$ 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 same22 kp9k/r rzxw3xwc2u portion of the Earth, but one is carrying twice the energy. W k/w3kx w2uxrpz92r2 chat is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, bs;dw* (2t;1wb0 /tdae-dozk m hp mkk-ut one tra ;;0dkmkwthd/w sdzp*-1teo2kb- a ( mnsports 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 lpw.d/3ulf- mwjs6s4ux: k j- is observed to move up and down a total vertical distance 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 4-l -j.3fksujwp :lu/ xd6mws KE change?   

The two pulses shown in Fig. 5ta85a yy3u k1x 9cqqfjh-qs.11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few 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 mom hyj59t3- yaqcqa5q1f.ux 8 skent?

  If a violin string vibrates at 440 Hz as its fundamentalp *xnhu4fbxhs)9 r *n6 frequency, what are the frequenc b*4f6 unxr9p nhxh*)sies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what freor3 l:)4h; 8enzr nhzzquency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-len)z8;:o rn4hhzrz3 thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of088qlm0qttyb :js ml - 280 Hz. Name at least three other frequencies at whicmsqj8b0m ll:-t8q y0th 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 of standing9/ms4 pegf r +cppm4 9,tyimu. waves is 475 Hz, howp/fy ,cri. p4ps mm+4tme9 g9u far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating stz)ui *okmvlqi98i ksv3:q i jz /(1r4cgwtx/ 6ring are 280 Hz and 350 Hz, what is thj)9/slzoutix6i3 wv1mkq vq*:4gi i r/ (8czke frequency of the fundamental?    Hz

  A guitar string is 90 cm long av xekek)d (xq)1 3*jj6pxfw1z 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 fundamental and first two over1x13ejwx)jdkkpqvx)e ( 6z *ftones?    Hz

  A particular guitar string is supposed to vs et q7lg5p5(eibrate 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 frequency?So the three fre teq l(5g57psequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, b /vzh emv q3f y6u+d)8j,8zmisaw8bqa wf2+d,ut it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct th83f+ b,mw w, szjyhqi dvmf)6eqa/avzd28+u8e frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 6rp(;r ;jm;4 lhhi1p9dyw yx x-0-Hz vibrator. The string’sdr9wix-m;1jhypxy; l (p;4r h 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 bryqc pru4g- 42y moving the pulley. If the hangp y-qr4r4ucg 2ing 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?   

  When you slosh the wate-jn66k31i2y sb;wdl vm k(qrx r 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 1d2mbi; 36 l(kvj6kxs- wnqryto 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 traveling at k.0 km/s strikes an agpsnx ) , :je-mx(vxpxp*3+zpok4. boundary within the Earth between two kinds of material. If it approaches the boun 3z4 -pnepx+.)xp:j k (psv,g*xmoxandary 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 uf-() xk7bpd-cmpe6m znderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If th(d-cebxf )pmzpk- m7 6e incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travxg56*bimy ypye;o.*e eling in warm air when it hits a layer of cold, dense air. If the sound wave hits thegm 6e.ieyyy*x*o bp;5 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 strik*j- emtfa f.j/es a boundary between two types of rock at a 38 *.e-a/ mjfftj$^{\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 user’s z-b-t;n/* (k * jqwe5*nrmonqh fy/dl n ci71pmanual, the dish has to be pointed in the direction of the(fnqd/*ne -lrmiqj1c-h7ky 5op * nb nt;w z/* 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 try3 l-u0z+kem pavels 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 hk - mlyp30uz+eave 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 bumper has a spring stiffness constant of zugwd/-fs * g.:*c s6xizg( qq550 kN/m Find the maxisf/( qgdi .- cux*g* zq6zsgw:mum 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 conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below lsk0lyh*+ipii. 4xy4 rji (+u, which stretches the net 1.1 m. Assume that the net behaves like a l+iius* h riy 0x+yl4p4i kj.(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 ha8 sz* v-ol k13spp4tvunging spring. The mass then falls 33 cm before it stops and18v 4lzusop-*t3pv k s begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at ahx.zi6c5 q(da speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m z.6xd5hcq(ai . (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 (diabx *0,r b*rm+xpy.tr7uf ou3(ox *qhymeter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffepxy r 3uq* bomy,7buhr(fr0o t*x*+.xe.    cm/s

  The ripples in a certain groove 10.8 cm from the centerocia o.5h-1kh of a 33-rpm phonograph r5 h-1oa. ickohecord have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates a3;8ik umyl2o c) hjt1sccording to the equation x=0.650cos7.40t where x is in meters and 8li )uthy 2jsm1c; ok3t 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 ql/(wup (xkg 5is its frequency if it accelerates at 0.50g ( l/(ug(kw 5xpqa) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When apcg 3/ttjj s xx2-6a:t 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the rap:c 6xx-tjg/jt sta32 ft 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 td v.d) dnn .lue.4i+nto play at 392 Hz (G) and 440 Hz (A). u.).4iv ldd+ . entndn
(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 cqv5eai 5*:q qdord 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 dqv:e qa 5iq5*of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each(xu v2,ivovi + prong moves 1.8 mm to either side of center. Calci2v,u+vi vo( xulate
(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 frequency 1.5 cycles rigj j . 1rtn:,r,-hngper second. What is the maximum am hn trn:g1- jg,rij,.rplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that xng 7y 39wky4 b( *ai88hzgoonend 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 with one end fi in4g7wkooh3y8zb (8xa n*g9yxed and the other free.

  A “seconds” pendulum has a period of exam4oh s *zjy2h;ctly 2.000 s — each one-way swing takes 1.00jy2 hh*s;m4z o0 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 oscily/ajua :qo y7g )hz7y-late in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the periogh / jy7 a-)auy:zyoq7d 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 d fq w6d gs802hqy* ;qp/s8uekmass 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is geq8eds q0dh ; k8*pq/wfs2u6gynerated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring wit5 sthyd wgk :+7)liw:th spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum al i w:td:gw57 +)ythksmplitude 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 a/5f lpa:8 w.dclpqt5d(nf d9pw)mg j1 jlg,5x t the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hin qxpj15l.w5jp( dl tngm9ald:8fcw g5f ),dp/t: Refer to Table 9–1.]    s

  A block of jello rests on a plate as sho 4: b-s y5gi7,u03ci) zilgauht y,rbcwn 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 vb,gybi)0 5i7ci4 utu :zl a-chr ,s3ygibrate. 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