Give some examples of everyday vibrating objects. Which exhibit SHM, fbpkx1axuse, ) j6:bg uzy0( ,at least approximatel epbu ,xg(z): f1j 6yaxub0s,ky?

Is the acceleration of a simple harmonic oscillatocjv7:rh6fq * ar ever zero? If so, where?

Explain why the motion of a piston in an automobile engi piqz6rh35g 6cne is approximately simple harp 6z3q cihg65rmonic.

Real springs have mass. Will the true period and frequency be lah9qjcu3s,ffr;x i)p ;rger or smaller than given by the eqpq3j;hi)9 xfr u;sf,cuations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic osc iz77prcd0 u9sillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then iv37e ,wmck,t 4f(k osig y 6a50oftzy.s rez,ei o0tg(c65k, okf4a7mw. 3vysfy t leased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will iijehc28n* nat k pu1-3t gain or lose time when taken to high altitude?jcnep 8h2kn1* i-tua3 Why?

A tire swing hanging from a branch reaches nearly to the ground (Fq ;yj2gwwn,l 1ig. 11–48). How couldng;ql2 y,w w1j you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth i fy/m5v* iy,sh;wo0w9fe4qq yn a pan only if you shake the pan at a certa5,w 4; v q0iofh*wyqf9eym/syin frequency?

Give several everyday examples of ks+y 0u y9dgmdo;n/nl9 )ica; resonance.

Is a rattle in a car ever a resonani 0/gfz vzp y/bjo2g92eq,1 nsce phenomenon? Explain.

Is the frequency of a simple q 2ey; 3v:i* aqthl7trperiodic wave equal to the frequency of its source? Why or why nqy7tav 3hit ;2e*:q lrot?

Explain the difference between the speed of a transverse wave tra8cc,exrbx4;3jioizkf1wxbk vxna .; q0 b- 5 :veling down a cord and the speed of a tiny px,n;;v k -5wc.fkbrq3 0z8:bbex4x1aiij ocxiece of the cord.

Why do the strings used for the lowest-frequency notes on qx(-c 1ark 3vpd y k,u tuy2f9qe)e,3ba piano normally have wire w q1ae-qfr9pktu)x 3,,ev cuby2k(y3 d rapped around them?

What kind of waves do you think will travel wf;gcee;m t ,6gcai6 0down a horizontal metal rod if you stric e ,0c;w6gi6e;gaftmke its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air dep b8ga 4i-(jrtcreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wav4 ira g-ptj(8bes in air to vary with temperature?

Give two reasons why circular water wavesbuvvhmgaf8q9gg 0 * ,x0g1jc - decrease in amplitude as they travel away ,gjua-g18 0 hqgf9x bvv* g0cmfrom the source.

Two linear waves have the same am)jnrk +( gm*etyoko 15plitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which tr goe+1m)t(k kjn o5y*ransmits more energy? By what factor?

When a sinusoidal wave crosses the boundary -v+p-g 3h appd3brh4 xbetween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velop 3hahxv+r-d34bp gp-city do change). Explain why.

If a string is vibrating in three segments, are therqizo/m 5ojet;vsy l t9spzy47.1( hf) e any places you could touch it with a7s4e1s o;(y lh/i zo 5pzy9ttv)j.mfq knife blade without disturbing the motion?

When a standing wave exists on a string, 9oycl ,m2,+glmji z,kbfuin4;mj(p7the vibrations of incident and reflected waves cancel at the nodes. Does this mean tmci n4gpu ij(+z2l f,9ko7 ;ymmb,j, lhat energy was destroyed? Explain.

If we knew that energy was beingpzo-d84oin27 zy7ecd transmitted from one place to another, how might we determine whether the energy was being carried by particles (materialo7ioe dz 7z-nd8ypc 24 bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.vg7nllu 9tk+u oi0c tb6v .4+i18 m, what is the total distance it travels+k690vlg+t iblct 4on7u v .ui in one period?    m

  An elastic cord is 65 cm long when a weight sc2z )z:5u-7hnqoog sof 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic u75ho:nzsq os -g z)c2cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm wh jz)2/ihx:alv gfdw-td8 )rf7en its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequencydvjtfig) r87a zx-)hw 2d/f:l of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3. d k9aqosx:5c)tppsh0;o42 ct6 cm when a 2.7-kg fish hangs from it. (a) What is t 2s:5cpp4otdqhaoxc 9) 0tk;she 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 frequek68v kmw7-opjncy of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 k8k6m7j -vpowkg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig.z2ehh11, gb c- fz5zlu 11–2 at times t = u2-, 11 hzc5hzebl zfg0,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 0.26in q65 eehp(xz,0zcl5 g is caught in a spider’s web. The web vibrates predominately with a frequency of 4.0 Hz. lc(x,pe5 zn60eqh iz6
(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. When9z; u0p qia-4sk3udhjfr9u 1 ckn ,n4z an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is 4k-iuc f 9dz3hjnau pq49nks;z0,r 1uthe value of m?    kg

  A 0.60-kg mass at the u6jtgi9duleg :qk. c 94rt)nx* 2qg *send of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. ):q6 ig2 lqudsjt x.t en994g gc*uk*rDetermine
(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 of a f8 8vwklf(hhuy ox(3:SHO half the maximum value?8x huf ov(:l3yh8wk( f$\approx$    A

A mass attached to the end of a spring is stretched a ziqr3yn-m1j ( pg,h3 fdistance $x_0$ 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 7n5s omyp hydn24a6o1spring 0.315 m. If the spring is stretched an additional 0.130 m and releasp 51 n6md2syo7aoynh4ed, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnesgink b qlh69+0 kh1:nf:mnvf7qy 4ag+ s constant k = 280 N/m and is executing simple harmonic motion. When the object is 0a+g+fkqh1qh yvg9n:7 bimflk6:n 0n4.020 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 xj* s2f; 6f xu/r(ro2jni5a jtbp :jr)compress the spring of a toy popgun 0.200 m to “load” a 0.180-k)xrxj2(a/j: 2s6jj 5ifrb *nr u t;opfg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to o:jj, k-8 zmud83xm k68mwqgwane end of a spu awq jx km ,-dgm88683jwkz:mring; 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 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 accorug+)er6y +yuz ding to the equation x = 0.45cos6.4t where x is in me+r u g+u6yze)yters 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 energy of a SHO half KE and half Pyt.8qhc vy*.g40/;pp v +vzhe a3klbnri7cb 6E? * q/rb8 +v7ypyc;.l0cvzebpvg hn. 43ih6ka t±    A

  If one vibration has 7.0 timetttp hr1)d lkl3 rs y.(r77a+i:fisd-s the energy of a second, but their frequencies and masses are the same, wh1:atl p7.3( ysr +7kh)tiril-ddfrt sat is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring otcy*j o-nieqw .5 l :.49vsjjznce every 0.65 s.9j4o-e z nt*..wy j qijv5ls:c
(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, e4eyzqs+qqc4q t2ssy ,; n2m+ rach with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibra +2mr4c,qsyq+ syzt2 n;4qs eqtion?

  A 300-g mass vibrates according to the equation x = 0.38sin6.q7 1mja6 lhpkivx,.r85t where x is in meters and t is in seconds. Dete87krvl.x qpa6 ji1mh,rmine
(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*l*o :p+2 sgerix3hgx 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 end of a horizontal spring (k = 124 N/m)94sjtxua)zahe,p47 g cr-/fyg.eqh6 is struck by a hammer, which u9s.,z ytj7a hx4 pa46eqgr -hcgf)e/ 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 k (qdc 7*ai: isnhax o;4b.m8tN/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium poinm7.o*sbthk aqa4 n;cd( 8xii :t (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring sty)4048u8 rgm+ubqcp pzcv 2a yiffness 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 stri0s 6vmcs6k+pp /il,b0f6 vuf bkes a 0.600-kg block attached to a fixed horizontal spring whose spri,mbpuv/li60 bs6p fcvkf6 0 +sng 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 mzgwy *g0h8g j *pdmdde9g.g)8ass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more timed gdg pgh*)g8j.89mey* dwg0 zs 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 vibrations in exactly 60 s. Whbg:av*1 o1xeb at is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly onerpx/wg lyy,c( 6/ht77zrq ji ; swing per second? (That is, one complete rht7/6 g;wzqr7y( j cyixpl, /vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, gi4 uqm/h,x3x v chkoz+*90pawhere the acceleration of gravity is about 0.37 that on3ch9,*4 qm+ oiuh vazkxg/0x p Earth?    s

  What is the period of a simple pendulum 80 cm lf v8,bqyhj/ 9(lmr7 jsg+iue4ong
(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 hal/p*s 9du9ra os a mass of 365 gld/as9pu* r o9rams, 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 pendu38x230tiq 1rtzx z0 jyhf ivm-lum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust i0 1j02-qfthzrxv8m i3xy3zt the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed tjg(mcn0l-iz f*+yz;tf ( b r8$v_{max}$ 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 released frooy) e*cnh,9 r)kd bzgoap5q8)m rest starting at an angle of 15 b qh)pe98gz*)co ,)odak y5nr$^{\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 passq) (0s4hapk3mjqyh ,m the bow of his anchored boat every 3.0 s. He measures the distance between two crest0a s4h3mym,j k()hpqq s 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 y ;rg (0-xrra+)dqz ky )uxo4*m;c ywttravels with a speed of 343 m/s How far apart are;ru()o mrk wq0xyta*4r);dcyzg+x- y the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz9kwhk9 b je x7p+s)(/fhv jc7x) and travfbxe9h /) vwps7 k(h7jxk9jc+el 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 longity,et1t7fz qx* udinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the w *jl z3y1bctw1v w8k/same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal wbztyww1 8v1l*3ckw / javes be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apare.ocdujv -0z 1 dzff) gg8-6ygt. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the other? -8 gjzv u1gf zy0dcd.6eo-gf)   s

  A ski gondola is connectec61;uge( 7e-qt yclaud to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the termc6ectulqy( e-a; ug71inal 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 t sd1kpfxih5bpsp;s h o *)28h3he sea. He hears the echo ofshxio *fbksdsphh215 3p8 )p ; the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at dif9dwlxy t6n)vao5au(4a4:l c 6as3 o ttferent speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance to9on d)y(lwas6tx 6uva4t 5t a:l3c4ao ok 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.l xqj9;tgk 5e wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually includetk. j x;lq5g9e a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an eartomi an1h+f(je3r,0:fi 3 fqy uhquakeo103j :ey,q i riafm(3nuffh+ P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an eart2ri0y0cwl,o(z9 a xbhhquake wave passing through the Earth is measured to be 0oa cr,wiyh lx 2(b0z9$ 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 tgc r,)+aetuq dc,b/ ffu9*4swhe same portion of the Earttcsafu /4fw)be+q,,r 9*dc guh, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have rb4 hx tkgizw,ysz4(u -w((d- the same frequency, but one transports three times the power owgbis d,rtz((zux- 4 k -y(h4wf the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observedoegj0y khszo4;cl). ; 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 wha;glec zooys.; h4jk0)t factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving towarduqvgwt v+;0 o9s:g7w d 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 thev+ 9 qsgu0vtog7 ;:wwd energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, w 5mcfk96,c spphat are the frequencies of the first fscf5c ,m 9pk6pour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will ;lhy vi0prod y7aux2 ah,;a(wq,it94 it vibrate if it is finger70x ;iaquwr9ptvo4,(2 ;, h idahyayled one-third 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 frequency of 280 Hz. .paap/z h. /ibatk6b2tyd.1zName at least three other frequencies a.6 .y tat1 b/bpzd zh2i.a/pakt which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency oye z*dfj-lm6btv,d65a.q 4q9:sptc m f standing waves is 475 Hz, how far apart are two adjaceb -v 9.mql,*zm6q 4fs6 c5 epadt:dtjynt nodes?   m

  If two successive overtow*p-dda l.7)l xcn wx7nes of a vibrating string are 280 Hz and 350 Hz, what is the freql*7lw c.pwx)7xdd-nauency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from thhr*jhltm dic /oad ph,(j97)/e bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fund,dja ilm/7/hjp*oh dh( t9rc) amental and first two overtones?    Hz

  A particular guitar string is supposed toz4 fkgaxba. ;v3 3zad4v h/h0eq8 d)mz vibrate 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 freqda0mghvhb z)/faxd4z 3ze4;qa8 3.vkuency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate,sxohkcuzvq8er j;x8ev/4 27 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? deceeux;jz7vcs8, o vr/8 x24khqreased by    %

  One end of a horizontal string is attacm2wsu2 k9 mhhiw+ w.fv1z-va3hed to a small-amplitude mechanical 60-Hz vibrator. The striufhsvmk 23w1 .mwai9+ whz2v -ng’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the stxnf71oe hu3 n/ring may be adjusted by moving the pulley. If the han he/n 31oxfun7ging 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 water back anddwqnw0b1fg:4 s, fu 1q forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. Whw4snf1u wfdq10, :g bqat is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikeui7 zb1q * 5q-budr8ces a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 47-rqu 1ieqbd75z c*8bu $^{\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 frv2zal ;atg0 iz52phwim:y * i.0(ndarom 2.8 m/sga iw( nl mv225zr pa* t:ay;dzih0i.0 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 traveling in warm air when it hits a + xjbme9c4 f5nnwpnmm .anxxx),0 42:dxas 8a layer of cold, dense air. If the sound wave hits the cold n0am +p4s2ame dmn 9j nab.x)5w:xf xcnx,x 84air 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 bounrdt pbou x7yk;8+,6z,+hwup;op . sbfdary between two types of rock at a 38zd+ opht bkf78s+puy xpr6o,,;bw.u; $^{\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 g +d i( ,f9snqhk 9dok)l;2ofxmanual, the dish has to be pointed 9g oofis+h xl ,;(qnfk 2d)d9kin 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 travels a21 5qxkl8wlhv cross the Pacific Ocean. As it approaches Hawaii, people observe an un5kwl1 x8qlvh 2usual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing ca-hcer a8yf7 ;sr bumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately-e87yh ;a sfcr 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a us 8nl,zhy jp +m0k t2;pwm0f8fire net 18 m below, which stretches the net 1.1 m. Assume tlmsyt hp,+n f0zpu;8mw20 k j8hat 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 pla z1 6xwr cp/2c.cimzn,ced on the end of a freely hanging spring. The mass then fap 1x.c 6znwc /2mcri,zlls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fi4 1k f4qaq3k,qqsoka;g. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the sp,sqa fkqkoa4 q q3;41kring?    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 (diametereprzo0f8r0 u 2g/)r pa 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it startszrr)02uag 08 pfe/pro to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonogrdg(tjov38l ; naph record have a wavelength of 1.70 mm. What will be the frequency of the sound emi8l;j3dv ot (ngtted?    Hz

  A 2.00-kg mass vibrates according to b8 rti)at0i6k the equation x=0.650cos7.40t where x is in meters and t in seconds. Determ)tb0 kr 6ti8iaine
(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 its3o1rbiadbq98(i)nnbh)gq a: frequency if it accelerates at 0.50g (a) gd1nh8 nbabi )r() 9iaqqbo:3upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Wg50x*e2*d tib uot02otqqh*ehen a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whilebe00q o uetdtixqo* *th52g2 *.
(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 evz)komq6 7r2wc ui1/392 Hz (G) and 440 Hz (A wq)cm u6r72 1i/vkoze).
(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 8mrnx(pi7wi. hjlol9 i85 6 vgcord of Fig. 11–33. Determine a forlgh i6jlwn 8iv8xoi (.r75m9pmula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each pro:p-q9ix5le/ kws nzf,c n. c7ung moves 5c97xunkf z,nwe:li pc-qs./ 1.8 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 harmo-8z,tawuwia v+ lq 7v) f/kkh6nic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the enk/ia w +a)lqh t87z-kv, fv6wud of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached m8kz(9 4fswpi to a ring that can slide without friction on a vertical pole (Fig. 11–57). m(s9 f4wz kip8Determine 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 exactly 2.000 s — each one4 0kr)5 jdy yh lvo xt;4q3pyj;s.d5mu-way swing takes 1.00sp o5yu;.m lvd);3jyydh4jr qkx 4 t500 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 verncsxrr( h2bbi9,* ;wtm/5uj ftical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the rxtbws9hf(;b*c 2m/ uj n, ri5period 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 stbb43jsu/ jqlj9ar/nrhg 6x7 - retched under a tension of 255 N. A pulse is genex9n74/j-l gb3 6 qsrbujjh/ra rated at one end, and 20.0 ms 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 from a ceiling by a spring with spring 9, q gnm:rux anzvk0m93(3u.dpn-c ltstiffness constant k. A penny of xzmcq0tnnkm-3 .u,9dn uag l3p:v(9rmass 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? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the ji drf() -8pfhaunkyard. 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 pr pfa)i- 8hfd(eriod 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 gives thig ols-74(0mdua)j kpe 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 vibrating on a spring, estimate the frequency of this vibration, given that thg4mk -j)sia70(udl ope shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz