Give some examples of everyday vibrating obj0rld qk2x0c 5xp.ol t/ects. Which exhibit SHM, at least approxi5r0d/xtllxkq 0p2c. o mately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, whereah j ;,)ftv0amcqk(2j ?

Explain why the motion of a aj-5- zr x3e,6ad)gc rr2kyps piston in an automobile engine is approximately simplr rc 5ja 2y)ep,6z-g-ar skd3xe harmonic.

Real springs have mass. Will the tru5jy y l9u27j+ 5qgcnpme period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Expl jjm9q ulp5y+n2y 57gcain.

How could you double the maxh 6pm53iuju;q6v4d4 im 9iy 4uzos1cjimum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, ar-rg5l4u3 lo(.n jcvl pn5md3 nd then is released. Dl(5j n-r d343ov.mpu5nllcg rescribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or l vnz up;pa-4f n3 7sd+u:fxm7rq 7(zmlose time when taken to high altitudxr +dmp4z73z7fv:-nus lnq;m( fa 7 pue? Why?

A tire swing hanging wrkb* -ks:5gesnzg p . b8oy83from a branch reaches nearly to the ground (Fig. 11–48). How could y w*8 3.g- e:p bzkr5bosns8gkyou estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in+deiph3v0 vczpm*ds5e1yo 5 5 a pan only if you shake the pan at a certain freque dese5od 3+zi pp*mc1hv05vy5 ncy?

Give several everyday examples of:ke29k6 sslvgz ukf99 resonance.

Is a rattle in a car evr 4ym;v 3x1u z p.v)cawr0zr9xer a resonance phenomenon? Explain.

Is the frequency of a simple perrp(fch i;d5 jev o/zc4+6v yn:iodic wave equal to the frequency of its source? Why or why nev+6:hi 5nd;4y zvccr(f o/ jpot?

Explain the difference between the speed of *lezmayl3i-0+m+vj i a transverse wave traveling down a cord and the speed of a ljl+m ez*3 iy+ via-m0tiny piece of the cord.

Why do the strings used for the lowe7z km 4nvve (+ bs,vc2jz1jn.tst-frequency notes on a piano normally have wire wrapc .mt,jkzv+sz41e n2bnvj 7v( ped around them?

What kind of waves do you think will travel dow6 n0. :zw qqsjd.(enfwn a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel tow: fwje(.6d0qsq. zn n its length?

Since the density of air decreases with an increase in temperature, butr8 l8(lxz2xcg o(4hnh the bulk modulus B is nearly independenrhl(2zgnx co(8 h48xlt of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water wavepn-1r 5mxo) ve39fovn s decrease in amplitude as they travel awo1npxnrmov- v5 f)9 3eay from the source.

Two linear waves have the same amplitude and vkzjbv7 2i8z4z)(f uo: lhxd,zs+, h kspeed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what fac,)zdjzi hkk bzx8vsf72z4,o: +u(vlhtor?

When a sinusoidal wave crosses the boundary between two1 jl7rc52hb bd sections of cord as in Fig. 11–33, the frequency does not change (although the wav7 h2bdrjcbl51 elength and velocity do change). Explain why.

If a string is vibrating in three segments, are therelks 4e;dzu70d any places you could touch it widl0e;7zud4s k th a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incide wsx+cwpd wk.+t+ -0o1*cxpysnt and reflected waves cancel at the nodes. Does this mean that energy was destroyed?wsyo++tcwd+x- .sk0*pc pxw1 Explain.

If we knew that energy was being transmitted from one place to another, h3- g t-emk*sbpow might we determin*b-smg3tk e-p e whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0 eglcia: pplhe12i37/ .18 m, what is the total distance it trcl l7e1phi: pa3gi2/e avels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but 7 jwew 0;qo9q+:heffzis 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord? f;7w+ehj90: efowqq z    N/m

  The springs of a 1500-kg car co/ :b 0w)lz,ub2ce)eu .et emf/: vlnwxmpress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what wilu)x buv w,mzwll./:efct :bee/) n20 el be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) W1t 3 g otzpnnq-9wc2d:hat is the spri:g twq1dc9zno p-n t23ng stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mas5w78+ d;i3us veyhgh xs of 0.60 kg is hung from it. What is its frequency if on35 ys7hxd huew+g;v8i ly 0.38 kg hangs from it?    Hz

Construct a Table indicatnb r 3qe;8d0gg1opo x/* pnw3ting the position x of the mass in Fig. 11–2 at times t x r0t83/3n og ;e*wg pp1obdnq= 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 hn kqh0:8/cru;sth7b-p l:eqg is caught in a spider’s web. The web vibrates predomikr bqph- n0:eu7lqhct /8;h: snately 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 woxud . zspcs ;49j/5kyith a frequency of 0.88 Hz. When an additional 680-g mass is added to mdz;9 .5 osysjcp4k/u x, 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 seconbvvng ;6i2ghrox/2w;hk kr30d with an amplitude of 0.13 m. v rwbxrk20gh32v6 ;io/; ngkhDetermine
(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 eq - ,no;pxw7vetuilibrium is the speed of a SHO half the maximum valov en,wxp-7; tue?$\approx$    A

A mass attached to the end of a springtln c/qq-.kkhjis:.. y;d9 z c 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 the spring is stre3tec-2yvv:/k pvz jm4tched an additional 0.130 m and revz3t2 : /kemvvypc4j-leased, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 bpc7a/3 7x3ixetnp s8kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the ob7i xpat37s 3xneb /8pcject 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 popg q65 (q1q8pnsanqb+wf un 0.200 m to “load” a 0.18qaspq1wbn8f 6n (q +q50-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, f4oyid.p:/bxp6d c-kzj 7sj5krictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleras:kk yi.p d57xb-/4c 6ozpdjjtion 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 wb 3mjjjot6n/m4 bmp99g wy+a/ here x is in meters and t is in s 9ojj jb9mnt/6am/ bpm y34gw+econds. 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 fromqz9a6iir5k ayk8a ,.y equilibrium is the energy of a SHO half KE and half PE8yiar 9 ka5.6kaz,iq y? ±    A

  If one vibration has 7.0 times the energy of a sejfo-op6kb; o 1qzdi9t o,*ky.cond, but their frequencies and masses are the same, what is the ra*q .otdo,zo6o;yk1jf pbk-9i tio of their amplitudes?   

  A 2.00-kg pumpkin oscillates fromf ik n:;q,hl yvsk82q4 a vertically hanging light spring once every 0.65 s. qv2nk4l,s8h :fq;i yk
(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 p4e o,*dvib un5qgv3,qj/b:zwith spring stiffness constant k (Fig. 11–49). What will be the freque,iq*/4dpv j z5,n3uoe bqb:gvncy of vibration?

  A 300-g mass vibrates according to th6wcgd*; 81ofvg(7 s r.ebhfthe equation x = 0.38sin6.5t where x is in metef( *8shtowg1g r;fhcbd v 6.e7rs and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A an4w( fwj 14fsfg -8(zy( az-vya-1cfqbr lol/l d 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 rej/v8l,u/(nt32vk u ijmc7hmz st on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass8n,(mc/7 j2z /i3v hukultmvj 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 witj11c a 2ff :m;h lho3vgw61ykjh spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass pag6 hjy1cwkm: h2 ;1vlf3 1fjaosses 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 springm*ck *wt6j shv,qxq77m 47 kki 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 6h2 5 54x8uzguarivw rblock attached to a fixed horizontal spring whose spr25ua 5uxzwvg 46irh8ring 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 jumpstuoc8; lk dqyl: 6,pvq2 a8k6d 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 below the level of the bridge. Calculate the spring stiffness constant and the unstretched length8: ,6 dvo kk;lyp lq6qtuda8c2 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. Wk: *p 4kevtar/hat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be u9 /0jwl yt9mjq8uc:uq gg9/b if it is to make exactly one swing per second? (That is, one complete vibration takesucbt8u0q9 g umw:qy9/g /9jj l exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. Whagxjf+. )zs 9xkt is its period on Mars, where the acceleration of gravit9zkxxg .sj f)+y is about 0.37 that on Earth?    s

  What is the period of a simple pe6uyyt*lvr- 95 znwbp5ndulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple petxdv; +7crye md.miez 9 );v1nhhuv 96ndulum is 0.760 m, the pendulum bob has a mass of 365 grams, dyeh ti)zh 97mu;9mrx v.n+;1c6dv veand it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock wp01, :ilzsvwv19tclloses half a minute per day, how should you adjust the length of the pendulum? shortenec ls9v1ip,wv:tw10 zld by    mm.

Derive a formula for the maxmjzor ;- r7(e+2v hayjimum speed $v_{max}$ 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 ;:ayh19fus qgk/z ulbq-t89p Hz. At it is released from rt u:g fpz1;/q9asu8hq9byl-k est starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boacoj. r*og*+ yru d,kn2t every 3.0 s. He 2gcj+*,koo d. urynr *measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels w6mkl)c tia.j.v8s es dq vr g8595e4qeith a speed of 343 m/s How far apart are the wave crests (compressta)sq8 8me .5 vs6.ki ec dvqgejlr495ions)?    m

  (a) AM radio signals havewg2fd9 b zo;.w frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a spee.o9bzgw d2w ;fd of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in ,1uy srikf0f3o07 m,7mv za cu
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is tw6ign)*6taz(9f.tcfzkwl 3 k/ by gq*v ice as dense as the other. In which rod will the speed of longitudinal waves be greater )b/ntt*wc iz kl 6qvyf9*6g 3ag(z.fk, and by what factor?   

  A cord of mass 0.65 kg is stretched betweeh+vsghoa, 30c ve0h9m;)w,v wf-nddyn two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to trave-o,a)m;n w0+s hgf9 y0vddvcev w,hh3 l from one support to the other?    s

  A ski gondola is connected to thejgkj* 2qm 4y58f f1dlw 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 inyf25q4wjfj1k 8l*g md to 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 hh0-ur:,e l,nhpa ru z4is ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this poeu:u ha0z,,hnp4 rlr -int?    m

  P and S waves from an earthquake travel at different speeds, a40esy hr 44vrw9q-njjnd this difference helps in locating the hr0s4-j yw qr9vej4n4earthquake “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 wavr-eu2tt917/rh 3jrj vqj7kude can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of fre7rr 1jq uv-h/rujd 7tje9k2t 3quencies), 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 dfeee* f*0+vzamplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and v+ *efd*0zefe20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through thopu0 mf(b* x v, pt369uqiorn(e Earth is measured to be u3on9 0pqv( *rtpmfui obx6 (,$ 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 * oaw8:scguy 8th/ ,91q+eb9kdccnbwthe same portion of the Earth, but one is carrying twice the energy. What is the ratihqa1gtny/*98 +bwbuck w 8, eocdc9:so of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequen2- -u c *n.4gur zq*nbblfhqv+cy, but one transports three times the power of the other. What is the ratio of the amphz*n +vgcr-lb2*u-u 4b.f qqn litudes of the two waves?   

  A bug on the surface of a pond is observed t679*z m r4dz)7bcnif chhyp27yffl2 eo move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If t)czf6e2* pm z2cr9yl hhy 47dnb7ff7 ihe ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (adfps 0rwb6nab/c+;jc, j f0)a ) Sketch the shape of the string a)a+ 6db;0 ,csc0fbanrwjjp/f t 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 moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what 7q*zw)l* jtxk8b2dl mare the frequencies of the first four782x* *)bdzwjlqkmlt 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 vc; t- buc6jp-wl8 4fnwill it vibrate if it is fingered one-third of the way down fv -6cwjp8f4;nu tlb-c rom 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. Name 8f: jx(by 5dlaat least three ot( 5 xf8byldja:her frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves q 5ugbs3p3 q-mon a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart smup-q35 3gqbare two adjacent nodes?   m

  If two successive overtones of a -xj fi7 vz704ss cq2+jt2 f6rmci 0wszvibrating string are 280 Hz and 350 Hz, what is t scfrc7s0sjtm04+q26vzj i wi7-2f xzhe frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The )(mlam-y a0+7e9bvm,v rzd ncdistance from the bridge to the support post is L = 62cm and the s9v) mr7yaabzel-0vm d,mn (c +tring is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar stk*flajp9 oj n2rft *ei7q4635pd(yg kq/qbv7ring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed jpt*j72nq(p fbk5fvgiyeko d7 ar64 /qq l3*9to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar s 3h3 bbyhlmd, j0bhdn rzj2)//tring is supposed to vibrate at 200 Hz, but it is measured to mb0j 3b2ndjhlhdz3hb, ) / yr/vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60-k n.5(h5im jfcHz vibrator. The string’s mass per unit .h(i knc m5fj5length 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 thf4kddc qz- 9;se pulley. If t4;sdzf -qdk9c he hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right freqlv 4sig eq(8n.z j27ikby 1)6n3hwz uvuency, 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. What is the spee74w)zy. sh6v 2 b83i g1 znuiqlnvek(jd of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary oc ) pjvd*(9jlwithin the Earth between two kinds of material. If it approaches the boundary at an incident angle ofo9dpj * c)jv(l 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach usug4wr(yoat,u 4 w .m;s/ ht.an underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident was;,. su 4rw4tuwyaught(/ .omve 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, h41;od6rt4+oz9hq hwo( n meudense air. If the sound wave hits the 1e44hzh qh;+96owtor(unmod cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types oi;*-njjmy su /f rock at a yn* -ju/smj;i38 $^{\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 manuald :xlxqktlx /s47/5a y, the dish :7 / xx t/kl5x4qdslayhas to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelen,xe tg2 4/ w8fwk)ywj4 g7fryjgth 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Aw4x)y/k j e 8w ,74fgj2gtrywfpproximately 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 car bumper has a spring stiffness cyyhcgmpu j/9v,8v4q qx u+ os.2 t6r2ionstant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 150.x9qg+c 4qov,yuyhr j86i mp2t/2su v0 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, which stretches the8 eay8ak-g sv* net 1.1 m. Assume that the net behaves like a simple spring,kvaga y88-e *s and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass tr0xpzqd ij8.9 ,b6n5xgy- lup /kyp6xhen falls 33 cm before it sp0z6q 5-/n 8dx.l uy b yxp,gxpj9rk6itops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sprin;+ y ndmwf71ojftx/z/g at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is thfzn y/1xo/jtd+m7f w; e 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 (le au6.h 1qjs:z 6yfw6)m 7z0y hu+bpediameter 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 ol:z) bqzya p h17m.+6jeweuhsy6f60uf waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33l7-5*//ii voaasqb g r-rpm phonograph record have a wavelength of 1.70 mm. Whi*qb-v /i5rl/osaag7at will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accoa+s9 u,ahlm5 ds4 e;dgrding to the equation x=0.650cos7.40t where x is in meters and t in seconds. Dusel dh4s5 a9dm+a;,g etermine
(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 frrfgso9yrv5w9fk7bp )1f/ (ctequency f. What is its frequency if it accelerates 7or5(g/tfy)sv wf1frpb9k c9 at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats vrt -;jq4q.6l ed4-fkw qp+p uon a lake. When a 75-kg man stands on the raft, it sinks 4.0 qj+qkpqf44w;lv- u-p .6tr ed cm deeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument areyas:w(75n gwj5 un tc*vh; *kr tuned to play at 392 Hz (G) and 440 Hz (A). (w wk jhnnr5**:5gs ut;7ayvc
(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. 15:ds ;qyo5puymqsc6ha+ h -4o1–33. Determine a formula (a) for the ratio of the speeds of the wave in thephy-+co46q5s5;d uyo ms:a qh 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 p+x.;ptt vb;th e;dr o2rong moves 1.8 mm to either side of ;d+pxeh r tt2;.bv to;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 moti (npyn6q+m6hut/w cda5 pow38 on of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the bop8m( n+ / p5othnucd6 qw36wyaard 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 ring that can s(uzz s(h(f 7z7awtfv i6vz6f,lide without frictionzfzvz(( , (z6vu7as7fhf 6 wti on a vertical pole (Fig. 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 2. ndwe(0j t1esvyxcas8)63dl / 000 s — each one-way swing takes 1.000 s 1d) y3sd(aw8n clj6esxe0vt/.
(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 uj98y:qm/p hk8cx*bd spring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hid* ku8b: hqp mcjy98/xnt: 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 qhwk1+wfru) ozh+5d( stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Whhzr5u(q wdwo h) 1k++fere will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stify j9n.ib0fw1b0umpm7 +z 7yvwfness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillatio+j y10y9buz b770.imf wwpnvmns that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 12dctf :1(jtsbkkn ja20(2/eaiy sc5i *00-kg car 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 jjki*d2 (f :/ye nit52kt(a0cssac1 b of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shpus xu.hj69nwr df1)b 3q ie*c(*y(f5ark*ig own in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of je)xiu* ha9(r*kq ( w gfpni 3yj1bfsdr6eu.c5 *llo is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz