Give some examples of everyday vibrating objects. Which exhib)+wanyd t5j 6kit SHM, at least approximat5+) ajtyw6nk dely?

Is the acceleration of a simple harm:s 1ldkd)epmex1/u6h onic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approxipg5feoj s:kq;/i v.h9, lc2gg mately simple ha; pfqi/9o25:vjcsg khg g.,elrmonic.

Real springs have mass. Will the true period and frequency be larger or i*6hs*u4 vd fu4*. rlsjnmu7r smaller than given by the equations for a mass oscillating on the end of an idealized masslesli7snv.mu4us6*4u jf **drr hs spring? Explain.

How could you double the maximum speed of a simple harmonicyr7 u/k jyck:wof 5-r8 oscillator (SHO)?

A 5.0-kg trout is attached to the hoi/gyzdjf1m7pg+ 7v6w ok of a vertical spring scale, and then is released. Describe the scale reading as a fungz1i v6 +wydfjm7 7/gpction of time.

If a pendulum clock is accurate at sea level, zqz 5; 7cv(jx ,y3a6,,k-ho uotiao onn drx3:will it gain or lose time when taken to high altitude? W6;d,qnyotzv nkr,a3oxhu3- oa,o5i(j7zc:xhy?

A tire swing hanging 9fnhg pr(i/9 hfrom a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using oi ( h9hfrpg/9nnly a stopwatch?

Why can you make water slosh back and forth in a pan o9sjle xo+a2,t nly if you shake the pan at a ce+o lj2 st9,axertain frequency?

Give several everyday examples of resonanc 3dh:z3z ym:fce.

Is a rattle in a car ever a resonance phenomezlqlv01lx+7 c non? Explain.

Is the frequency of a simple periojqdn84wbcck8; re1s 2tu. c/ddic wave equal to the frequency of its source? Why rkbnd2c 1wcq 8ue ;djt s/c.48or why not?

Explain the difference between the speed of a transverse wave trpi4xwrxe:9 1qw .efi6aveling down a cord and the speed .:wf4p6qex riwiex1 9of a tiny piece of the cord.

Why do the strings used for the lowest-frequency noteswh5r tn;68b 9meinsye )+w(jo on a piano normally have wire wrapped around them? iywhnn 9swj8+b65e)mrt;oe(

What kind of waves do you thinki.0w s9osxw qandg: -e7ru g/4 will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b)9xs us4:g. /og-a7 qrdeiwwn0 horizontally parallel to its length?

Since the density of air decreases with an increase in t+qq3*kqnl;p8 o fjw*aemperature, but the bulk modulus B is nearly independent of temper;3pk* +lqq oafn8*j wqature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travelpi tm4 hy:n;d iff.(p5 awm4i:t( ppffd.i ;nyh5ay from the source.

Two linear waves have the same amplitude and speed, and otvq016 zpv 03vn;f7frjjp mf3dherwise are identical, except one has half the wavelength of the other. Which transmits more ener3r j01dzf36fvpfv;m 07nvpjq gy? By what factor?

When a sinusoidal wave crosses the b/salp4meu dh,idk:* )5w5f eyoundary between two sections of cord as in Fig. 11–33, the frequency does not change 5f,i*mpy uda ld:)/ s 4kwe5eh(although the wavelength and velocity do change). Explain why.

If a string is vibratiau1s +qxrwwl3e+m/ /w/:iq oong in three segments, are there any places you could touch it with a knife blade without disturbing the motiqu1owm e q/+ 3/i+x awwr/l:oson?

When a standing wave exists on a string, the vibrations of incident a9qg cs 9;tjw44-elh 4xr+kpnynd reflected wavelqsn tk;h4w g9jr -px4 4y+e9cs cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how m(eheb3yflh/o tc akx).,x,nz9 g-7dm ight we determine whbfomg,nt ,y( -exc9.3k/adx 7z e)lhhether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance it/ghoq:0 k7 thg0epp:k t:otge70hkghp:p/ k 0qravels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs frg:3d r/ncz tsb3 lbg+9om it but is 85 cm long when a weight of 180 N hangs from itcrbg+dt 9:l z bsg3n3/. 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 1i+:xgsoyzgyg;doo : vq wc4(0ip)0z 68-kg driver gets into the driver’s seat. If the car goes over a bump, whag:) g+qyyoiizv dzx(wg41;0c o0so: pt will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fi)g.xq8ckhkkx1 2sv;3 aedr.ish hangs from it. (a) What is the springg;3sk81v2 kq.ixx)d hceak .r 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 60t35s cgayl* fujhvzcv9ph 3 5s:ym4a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequenct jv56 a*hyv3l4ug9ym3cf5 psz0: shcy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at t .bv.xm1.n qeqqy v6vl n:.ea)imes t = 0, ynm1nq..qx.6qev) a .elb:vvt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 7l5hc(h:tqi(fwh8mi sn: d 8n in a spider’s web. The web vibrates predominately w:itq:fwh c(78dil nh8( 5m nhsith 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 ao1h2l9p ( vc: + k2buso0avg.l jl)myk frequency of 0.88 Hz. When an additional 680-g mass is adhvjpl 2+ s:b cmok)1yka0l2ol. uv(9gded to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an amsy krim276e 9aplitude ofk6a7ime9sry 2 0.13 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 frvubva .,3cxls;ru v h,d:j6f9om equilibrium is the speed of a SHO half the maximum valurfuj,:lvc v.u6bv xs ;d,a9h3e?$\approx$    A

A mass attached to the end of a spring is stretched a distance z2yor a+qd;: w$x_0$ 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 stre7o apxmh*+npq7 v f,*llxxrr 4) rk83ztches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equi7ohlp frar vp*+mx8*x) k4xq3,7l nz rlibrium position again?    s

  An object with mass 3.0 kg is attached to a spring wip;1 f dnbeq 6p6lht1h0th spring stiffness constant k = 280 N/m and is 1 fh1n6td0 q6epp; lhbexecuting 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 poyhln j * *e-nvxth.k.7( 6etm+0b mfrppgun 0.200 m to “load” a 0.180-kg ball.m+pv h* h m7lt.n.t0-n*fb( exe 6kyrj With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one endzz ;j 6 ;(jsg /ka6:duq fifzkygr90w1 of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If thgrf;;(ji 66z9 s:yfkjgkzu dz qa/0w1e 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 wheiutu3le:jp) 0 thl 1a5re x is in meters and t is in seconds. Determine 1a) j uhp uilt0l5e3:t
(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 ouirctqwk q*-: sxe58 ar 6dpdx t**5t,f a SHO half KE and half PE? *axr8xt6- 5 5,tsqd qprci ewd*t:u*k±    A

  If one vibration has 7.0 times the energxhsc2runh6g w, r4 -4cy of a second, but their frequencies and , ghc 4s-unxr 64h2cwrmasses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanginga,x /bh-ws ,ije5bj gx8v6n f :0leh4z light spring once every 0,,xhes:w i a4v -zlj5x e jg/bhfn8b06.65 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 w)84naei s hfyx*:tu4vertical springs, each with spring stiffness constant k (Fig. 11–49). What wiu4*8fa)yx4inwse :t hll be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x ,t w);, ds-y1nrooe*cqt,fl5 9lofonis in meters and t is in seconds. Determ,lo-1 o,sefn o;*)rcwlytn5qf9o d,tine
(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, .bsap8)9x x 0cniq 9y*9hdomklabeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at re1xmg2p 6 +9rqb; n)ule;)r psoh4uwolst on the end of a horizontal spring (k = 124 N/m) is struck by a hammerw62xqn smbl9hepl)+);p oo4 g ruur1 ;, 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 spkmt*2 c)vwos8 g4 l9zz15rnwf ring stiffness constant 305 N/m vibrates with an amplitude of 28.0 g cm94 nvk zw81rstfl wo)5*2zcm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness cons:68ia10zssf3bmb h f ttants $k_1$ 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 spring1 iyqnqi ikbel*szth5r sbt)4(; r/fa4.u4 ,b whose spring stiffness coift(.4a,1q)qunl 4s*rbbb5y;r tk4 iz i e/shnstant 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 ma/iccd4u x:2 m)kw;sjzja2 g3qss 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m becu/ cj3wdigxmz4 :2j q s)ak2;low 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 exactbcf3bkb l(7)r9 cyk6qly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one9, gyh nvbm*6p swing per second? (That is, onvy hmn6 ,b*9pge complete vibration takes exactly 2.0 s.)    m

  A pendulum has a per08f-;k;akyo*v * 6km.n/zlkt3*trk gck hef hiod of 0.80 s on Earth. What is its period on Mars, where the accelerati-*tfkkzmae*/fntk .kk*o3r;h6k8 lcghy0 ;von of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulumfhn3bk*q2 q1;1fbwkp . njig: 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulul8)*gwd ia,ggm is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an anglei lg wa8*gg,d) 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 clockavvt1z2ur2*-j dxv2f brp) z9’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how shouldvx2p91 rdjvf2zrzba- vt* )u 2 you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum sr wlu9t+0 joq/peed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is release qfhf*.otb,a1tms 2r) d from rest starting at an anglabr* t ohm)fq,tf.s12e 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 lk+tc k;z390bm- (yj+ufzna ncrests pass the bow of his anchored boat every 3.0 s. He measures the distance between two c ak+3u0y z cznjmb-(+ 9lktf;nrests 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 trav gb*d1or;c /kiels with a speed of 343 m/s How far apart argc;*r/1 kob die the wave crests (compressions)?    m

  (a) AM radio signalsfu(f)kte k7 ,gv-hyc; have frequencies between 550 kHz and 1600 kHz (kilohertz) and travel witcu7-;hk)f evyt ( gfk,h a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves insu jb(ab 4w4(ukqkz4.
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have thwk5j ok 8(c.hoe same elastic modulus, but one is twice as dense as the other. In whic j.o c(woh8kk5h rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two b7qk2 w*;dylb supports 28 m apart. If the tension in the cord is 150 N, how long will it take2q k; yb*7lwdb a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill byig/-+/org1x1zqhit v a steel cable of length 620 m anvqx/ g/1tg-o1 rhii +zd diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It 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. qook j61gh6/6a6dw)xos u f 6zHe hears the echo of the wave z1sox 66 jk6 6wa)f d6ogo/huqreflected 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 :xx/o6oyg 6hsat different speeds, and this difference helps in locating o g: 66hoxys/xthe 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 sirok 4y-:+zrfz nusoidal 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 acceleratz 4orr-:y z+fkion a>g]    m

  What is the ratio of (a) the intensities, and (b) the :l9e h/yg 8acaiq7h ;aamplitudes, of an earthquake P wave passing through the Earth and detected at tw9yqagi7e; cahh :8 /alo points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth ibl 4op8c(wm)7li z et.. zx+sws measured to be esoci..b 8 zx w7m lpzl)+wt(4$ 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 sagjyw-i b1 wjum.4g(hk2fl ;)snj9h 0bme portion of the Earth, but one is carrying twic.1 jjy-swlu(g);him4j 2wn09 fg kbb he the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string habh u d5jr20zi:ve the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of th:jd0b 2izur h5e two waves?   

  A bug on the surface ;o g*akr+ey m5*ewd:tb .0sljof a pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the higw+ 0.;dkg o5ymtbals* er*j :ehest 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. 11–58 s u+6a9ybp ;grfc2g4*fwihzvp1 mj+ 2 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b)c+ g z;gp81pusfm9 y*2+bwr jha6vi4f 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 moment?

  If a violin string vibrates at 440 Hz as its fundamental freq6iwfbx// jh +gik7uu-wx(7 cjs rj/p3 uency, what are the frequencies ofg-/7is 73p(ikj/wj j/ uurf6b+xwcxh the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfing9 p5xn9nwd a- k4do)ydered. At what frequency will it vibraten aw4xyp 9)dn-ok5 9dd if it is fingered 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 rew/jh z2eayu-j wdis,g ::xn.4sonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will resoad-ygn j e,xsu.w:2/h zij:w4nate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If jz ggx280ip av8 t:4 ;ue-gbxzthe frequency of standing waves is 475 Hz,- 0xpugvz4i 82z t;jg:xe ag8b how far apart are two adjacent nodes?   m

  If two successive overtones of a vixjuhr6faui ,cxva2,d0 + : zb. dbrx13p ,nsq(brating string are 280 Hz and 350 Hz, what is the frequency of the fundament31+x i,b ac,psqaxjun x:,d0 rrvh(z2df 6.u bal?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from th()9ghoq/gz +vytl33v dsk zhcp +o6 3re bridge3v kvspc9) ly 3ohd6qzh+oz(/ggt+3r 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 overtones?    Hz

  A particular guitar string is supposed to xuxb79p e ck:6xtn 7kv *vke4*vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should th n6e4pexkcu:k t7*9bxxkvv *7e 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 stc,, cm03cby- 5mbs;vsn t;zgdring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tetbydcc0,bm3s5 ;v- s cmngz,;nsion in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to bt e mxs9ar(,;b7dp:d a small-amplitude mechanical 60-Hz vibrator. The strinamb e:7s; pdd,9(txrbg’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pulzriq9rj4 n; g)q7a(ul*fx)zy:pbpnji id(/ ;ley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patternsg9y ()z p;iq pru* rlfnai)jd:q47/b;ni xzj( may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in ao,e:x7lx (w4rinnf )ae3) /h2x n kyht tub at just the right frequency, the water alternately rises and:(7n4xnnh/e )efaiykwlo)3 x2tr ,hx falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary with asct2:t:zpa9lw-q ;uin the Earth between two kinds of material. If it apqal- t9 w:2szp;utac :proaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where th7dozi- hy rk5*uzav6 *56tcv ee velocity changes from 2.8 m/s to 2r* -*uvh5coz6t z7 e dv5ay6ik.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 layer of cold, dhro6uxb-st p qt u,8sa::t /g 3w6fn)kense air. If the sound wave hits the cold air interface at s o::6fkrhna xqtsgt/6 tupw)u, 38-b 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 earthquakeb(x b964jyncb9b6e bf wave strikes a boundary between two types of rock at afj (ebbb6yx4b9c 69nb 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. Accordin +y nce: ff+7r6qhm(fng to the user’s manual, the dish has to be pointed in the direction of the satellite, but an errorhn rqn6ffcm+e7 +y( f: 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(;nbns)kqnjzy83k 9(y b0 4i.uha qf m 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 tsunamis, some of them attracted to the shore to see stranded fishes9f.) y;y8ik4 nu0 3(q zmqb(nna shkjb and boats.)    min

  An energy-absorbing c39u4mw i(:e 08mdqysykgzx; k;og,tdar 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 5 mi/h). [Hint: Use co 9xem;d 8kmutw;0idy qsoyg(z3g:,k4nservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which streto.w3ymgg ;ewyqv;jdd0m,o a/af8. 0 3ba.a tdches the net 1.1 m. Assume that the net beha8vw/ 0.;yg;baqa3yd0oa ,a fmjdgodt3. e m.w ves 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 (,vw6vbor,c-xx wms5 a freely hanging spring. The mass then falls 33 cm before it stops andvow6(cr,w smxb-,v5x 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 (Fig. 11–54), compresh q.:txgl /is(sing the spring 5.0 h.(sgxl t:iq/m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at jscmrp: q .2ms-eprl;9ust 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 speed9- lcmq:r.prp2m ;ses of waves in the coffee.    cm/s

  The ripples in a certain grq o+r+.o2 p b1v+tzkasbjo1u;oove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the soundr++ 1;osz 12qb+.bkuapvotoj emitted?    Hz

  A 2.00-kg mass vibrates according to thf r mm2+k5 faoq8y4j.ee equation x=0.650cos7.40t where x is in me q.ky m4fmfj2a8r+e5oters and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if il 3fl ymf+ 0ad6(7zoy,f+sggjt accelerates +d f fa36y(s ,7+ggymzlojfl0 at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands xvadi 032o1al on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a i2 a0v 1olx3adwhile.
(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 ;-7wq s4uk2a7bbwv/t4 kngfa tuned to play at 392 Hz (G) and 440 Hz (2kat bgb7q7 - 4/w ;wav4suknfA).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 11–3awaje+2 *8 3h2w tjmfv3. Determine a formula (a) for the ratio of the spj22mfew 3+j w *ta8vhaeeds 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 of0 7nrjkh.v b,l*d7 c4py1jgg m each prong moves 1.8 mm y*khjc1mdgb7, 4lg0r pj.v7nto either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic ms5m*5edk cyg, /f;xgu otion of frequency 1.5 cycles per seconc;efug/sy5x *gm kd,5d. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a j zck)ui 2ltk4r37n0iring that can slide without friction on a vertical pole (i7 r c 3iuklj0zt)4nk2Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2fmf4: rc0 f +bqxp)r4bqz4np-.000 s — each one-way swing takes 1.0f mzq 0cb)- q:rr+x4fnp4pb4f 00 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the verjr9i p87a2 +-oh )+skgd yeipbtical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which o9i+is da p-bg+op8r)2jeh7ky ne is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched undecb /my q0tn2 qcr9k73rdfq/5ir a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is gene2 rq/y9 7qdtrkicncq/350f bm rated 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 vp8ls (kif;3v with spring stiffness constant k. A penny of mass m is placed on top of the block. What iikp( ;l8s3 vfvs 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 c0t yl,io )8opgo;5mg pjnx+6sar at 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 ; j8 5yxi,ppo6 solo0mngg+t) period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in -tsy+m/2 zlyx x fmp54o6:sbbFig. 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 vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 52f4 xzs/ slx5-b+ 6oy2:tmypmb0 $N/m^2$ and its density is 1300 $kg/m^3$    Hz