Give some examples of everyday vibrating odql *4nm;eu m9bjects. Which exhibit SHM, at least ap q dn*4eumml;9proximately?

Is the acceleration of a simple harmonic oscillator e2ab ,xi: yys/xw d7;cdver zero? If so, where?

Explain why the motion of a piston in an automobdh9 8qbrd7qc3,wm 0l 4c qjw cph3 tt,i2*uhm+ile engine is approximately simple ha ic whlqc,d07,mj+r3qt3wumt4 qdb c*9h h 82prmonic.

Real springs have mass. Will the true period and frequency bexv6 h -4 ff,p qyt78fnwvogk7p e3g+k1 larger or smaller than given by the equations for a mass oscillating on the f- wyxpft fke 6hpovgk 173,8vgq+7 4nend of an idealized massless spring? Explain.

How could you double the maximum speed of a simpleisv:b wd ,(0c- ibzyy3 harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a verti+w*ds8rlkum7w (i;ttdg na+qn 44, gpcal spring scale, and then is released. Describe the scale reading as a wrw (n+t84;*gup+ ak ddnt,qglmi74s function of time.

If a pendulum clock is accurate at sea level, will it gain or lose t(i qtrhrv8j (t-e /+kweu* zz*ime when taken to h-8(j*zz+i qvurwe(ekr / tt*high altitude? Why?

A tire swing hanging from a braar v0xty*:id 5nch reaches nearly to the ground (Fig. 11–48). How could you estimate the heigh5ai0vy: d r*txt of the branch using only a stopwatch?

Why can you make water slosh back and fortm:mx+e * eg; prtuv/s0h in a pan only if you shake the pan at a certain f/0 gr u tpm:;e*sxm+evrequency?

Give several everyday examples ofjzs/s6 5kb 008r(o1rig vhjw k resonance.

Is a rattle in a car ever a resonance phenomenoq3ajcr ant*8 ,n? Explain.

Is the frequency of a simple periodic wave equal to the frequency of5 .x v-efdg k8uqyt+lf)0+ydksbvn) 5 its source? Why or whygk5l80y de5vbyxtd q vnsf.)-uk) ++f not?

Explain the difference between the speed ozrrh*e 1pz 5/7bh7jdwf a transverse wave traveling down a cord and the spee/ re1pjr77z5h bhwdz*d of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes ons)r,ke zhkkkx*ul/e; a y.956 8uuyye a piano normally have wire wrapp*/ua,h;z lk r5se e6u9 uyk.ek8yy)xked around them?

What kind of waves do you think will travel down a horizontal metal z;p+ h d,ixq(arod if you strike its end (a) vertically from above and (b) horizontally parallel to ii(aq;, hpx+zdts length?

Since the density of air decreas*lhmb4j; *qfa3:arzh5sq 6a/u(fbi 1b7wazx es with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air touq7* mqbxr4h as:a i/fa;b* 3azwb165jhfz(l vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel m*pit) ejr+1 hawayhim+r1*)t jpe from the source.

Two linear waves have the same amplitude and speed, and otherwise are ide4azxt9:/o9unfwu epws 9uy /24d2j epntical, except one has half the wavelength of the otez w:p929 uw up sdxy //atue4nf92o4jher. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two /abjx3u v -w(tnf; 3-o,cj qby*g8zlisections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocla,/nvbi;3wx f bcjqg 8-z3oy (*u tj-ity do change). Explain why.

If a string is vibrating ,tl bxf0dhw1d2y1 v )min three segments, are there any places you could touch it with a knife blade without dist twx0 f2lmydb1, 1d)vhurbing the motion?

When a standing wave exists onpqinb2r::: lr a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was deslr2qn::irb :p troyed? Explain.

If we knew that ener,*kzgykr 7vw pp8b *z-gy was being transmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodp,bw- *kpg7y z8*vrkz ies) or by waves?

  If a particle undergoes SHM with amplitude aqlpza e(gg9s147v4eg2en k10.18 m, what is the total distance it travels in one peri1elq (1ega4gv9sp 7ae k4zg 2nod?    m

  An elastic cord is 65 cm long when a weight of 75 N hang0t4njh03 (yl tdv n m-+mqs8cr2awxtn lm z/2/s from it but is 85 cm long wszln-tj// 4t2+2l x8 armctdm0mhy w (vn0qn3hen a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm bp n, dh(ni/(hwhen its 68-kg driver gets into the driver’s seat.,i hp h(dnnb/( If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from i5f;hjqv (1p nqogq 68zt. (a) What is the spring stiffness constavn (ofzqhq6gj pq8;15nt $\approx$    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 w :n91haw3soj, ll;mh iq9a 7vjhen a mass of 0.60 kg is hung from it. What is its frequens h, l39wa;7jl vma jo:q1i9nhcy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position aa1w t hz9o/u*x of the mass in Fig. 11–2 at times t = 0,t =* a/w91uthzao $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates prm,;0xpia*g5 f zxmml3edominately with a frequency of 4.0 mp03 zgi*f lxma ;x,m5Hz.
(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 ovbea 46t7nt8 )ksy,(dfx rsy:f 0.88 Hz. When an additional 680-g m4:asxy(,yv6fkd 8rts )t neb7 ass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the endgr t: en0uln,.*3kasb of a spring vibrates 3.0 times per second with an amplitude of 0.13 t e:nua.s, r0nkg*b3 lm. 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 from equilibrium is the speed of a SHO hal*)yb2 . qidocz c8n3qsf the maximum val*qcidn 2 z)yob. sqc38ue?$\approx$    A

A mass attached to the end of a spring is stretched a distance wov4 x))s k+mnv(higwa0 a z /z683uwd$x_0$ 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 stretc5-6wsl d 7*kzup:f dsehes a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and re:du es kwl5dp6*- 7fzsleased, 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 stiffness constghl;0j+j z z6sant k = 280 N/m and is executing simple harmonic motion. When the object jzzg0 ;l s+h6jis 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 tod0he-w.usj +e compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will esj wehd-u0+. the ball leave the gun?    m/s

  A mass sitting on a hori-6m.rv f8h abml 4jt/rf 8as* ze(kfw5zontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of workfbtke4m wjlfr5 v* s6.8(m hr8 /azfa- is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to thmjuc q a5;56h6j6 xurge equation x = 0.45cos6.4t where x is in meters andx6 q5jcaur; hm6gu5 6j 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 halp 30id n4hr(rdi 9;qlbpe(cnlz ,w*v )f PE40 iv,p9r)nrw b3q (lech pdz* n;i(dl? ±    A

  If one vibration has 7.0 times the energy of a second, bubuq5 6um n*hl9t their frequencies and masses are the same, what is the ratio of tm*6nuqb95 luhheir amplitudes?   

  A 2.00-kg pumpkin oscillates fr z lr;4h)p9d7pu8dyfvom a vertically hanging light spring once every 0.65 hz;d7 y u4dr)8pp9lvf 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 verf. :oepjt7 :mgloh )s7tical springs, each wis:o tmfp)7:7og l je.hth spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t wx:g nr.oo0tqgrd:m d 8/* fg9ghere x is in meters and t is g*9 oodx:rf gdr08/g ngm: .qtin 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 and B. Fofo*ttfqu p+fp eb;j.9j,y t*vu(8 sb4r 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 vli+6fxbxs-n4)eklxz;2.m5hscb8 k = 124 N/m) is struck by kkmfsn+l)x ebs2clbzv.8i6 x-; 5hx 4a hammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stid v8g9lpzh2rhna 0) 1gffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.26rd 8n0v1g92) zagphhl 0 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 lu/.-a . nzwinto two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_1+k_2}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attace f o rm+pwz7+(t:02rexzy5ey hed to a fixed horizontal spring whose spring stiffness f r zwrym7:p(ex+t 5 2eo+yze0constant is $7.7\times {10}^3$ 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 masso::j wzs(lm3 f 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low poiwlsmof3 j :z:(nt eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrav w(-np(rkz q 3+u s8swjmht73tions in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing pergv( )i qgrk2n6 second? (That vi2k 6rngg q)(is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth.3bswkroia s .r *xea/hfm oi7+ ,em47+ What is its period on Mars, where the acceleration of gravi,him37 aak xf7m oe+ r4+ sbw.eri/o*sty is about 0.37 that on Earth?    s

  What is the period of a simple phr+ .hsll(n.hqv(3k nm11oj v endulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 mto3a:n62r +,by hdyrn, the pendulum bob has a mass of 365 grams, and it is released at an angle3r,: r2dbayno 6ynht+ 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 0.98 f(h* 3tyzg(t*ef nm9gwvar e7q1iw,930 m. If the clock loses half a minute per day (hff(3tiw, w*zr*a8 egtv7 y9ng1mqe, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the d hwoaa:m*-o 8lflfc+hh0 s;+maximum 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 freau q ,nk52sg,xquency of 2.5 Hz. At it is released from resxn2,ga u5kq, st 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 o,p+2opw hrs :y7* 6yp wkyij7the bow of his anchored boat every 3.0 s. He measures the distance between two cre2hw7oypw : r6o+p, sjypi7* kysts to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed ofty o48c)k9j itd 8(afa 343 m/s How faf(c)8jat9di4 8toya kr apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz)v2x+f66 09(1farem2byfsh cwshs *k m and travel with a speed oh2mcsswkvb fa0*f m1 s+ x62e6(hrfy9f $3\times {10}^8$ 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.a/p9b usnurycxue:1,da 8e0-q ,kjg in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have thvwgoqh7ljz* 1- r5k 3le same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal o5*z qhl7wvr1j-l 3kgwaves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betweenb x.nk1sf p7y.zjl i6( two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse .j7n1pl s 6z byki.(xfto travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of le,h:0u 3d4ln bekeqvv/zam(n4ghm+u 3ngth 620 m and diameterl3uqmehn3 ng+vv,u(/:ea 0b d z4 mhk4 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 oom1am;v 4. ecyf his ship just below the surface of the sea. He hears the echo of the1 cyvoe m.m;4a 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 traeae;2qeqb, . avel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took pl;,e .aaebqeq2 ace).
(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 si5 yy )pp4vg4ls/ 7l0u n)k 6zhxo +6s)gwjonuynusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthgpskyly vg op6l+yj)zx6w)4n7 ) o0 s unh/5u4quakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensiti zbvw; r3z ag43,npp0xes, and (b) the amplitudes, of an earthquake P wave passing through the gz0pz ;p43b,r anvxw3 Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Eapdv35vssu96o(ko1e j rth is measured to be s( u s9voj6veod5pk 13$2\times {10}^{6}J/m^2$ 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)$\approx$    $\times {10}^{9}W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $\times {10}^{10}W$

  Two earthquake waves of the same frequency travel through theay9*y3yr si5c same portion of the Earth, but one is carrying twice the energy. What is the*s 53ayri 9ycy ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but one7x(vmn*ok n 7v transports three times the power of the other. What is the ratiox77(o vknnmv* of the amplitudes of the two waves?   

  A bug on the surface of a pond is observety sk;hw/c69p d to move up and down a total vertical distance of 6.0 cms t/c;96hkpyw , from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other.:06.lue,t muqn /j e4u/ hsrhn (a) Sketch the shape of/jh,s0en 4e.hun:rt6l/u umq the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 44/2e tp*lve)iiwrf+tqz (o :q .0 Hz as its fundamental frequency, what are the frequencies of the first four harmonics?r .: o(zqwil )viq2t/+ *etfpe$f_1$ =    Hz $f_2$=    Hz $f_3$ =    Hz $f_4$=    Hz

  A violin string vibrates c5 /py3wfhg o3s.rkphk4 +p9iat 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the wa3w5ihh rygko 3k9s+/ p4f ppc.y 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 freque9az0 j4*y h mhuyof3a/ncy of 280 Hz. Name at least three other frequencies at which it wi4zaf9ohuyyj*/ h 3 am0ll resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  The velocity of waves 1:d /avuq(ak7 wbbc ,von a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent nuk qwac/dvv1:b(,a b 7odes?   m

  If two successive overtones of a vibrating string 512djymk h,enff. me* are 280 Hz and 350 Hz, what is the frequencyef .*jek,5m yf1dnh 2m of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The wbqdx. n:t.9y distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. :yt.bd9w.xn qWhat are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposedc-ml( +e de5no to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in lce5o(-mn +e dthe string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 y-eqjb0d4xn45 cik4/ uhm: qw Hz, but it is measured -kxmj u5 44bwnce/h q0d4qiy :to 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 horizonta* x)sw2n nkn6,18evqfp-s hmnl string is attached to a small-amplitude mechanical 60-Hz n-ks,ns1n*8w npvf)m2 ehx q6vibrator. The string’s mass per unit length is $3.9\times {10}^{-4}$ 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 b54 3ngw9j;bqa4n zl fmay be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different;wn395babl 4fnq 4gzj standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and fo+gh n63ab3yr r weg cu60zzi5-rth in a tub at just the right frequency, the water aluz w5+-abg0 h nc3 63eig6yrzrternately 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 speed of the water wave?    m/s

  An earthquake P wave traveling mcdii8jn)1 xy yh.8)eat k.0 km/s strikes a boundary within the Earth between two kinds of material. If itex.8yj))h diicm y 81n approaches the boundary at an incident angle of 47 ${}^{\circ }$ and the angle of refraction is 35 ${}^{\circ }$, what is the speed in the second medium?    km/s

  Water waves approach an-xqe.d xmp,d t.9ck su* f:q3t underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make e-3sq. xt9dck.: *qx ,ftpum da 34${}^{\circ }$ angle with the shelf, what will be the angle of refraction?    ${}^{\circ }$

  A sound wave is traveling iz70zq n2c5eie0o ze/ in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at a 2oq0/zzzie e cn7ie05n 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 bo,k u. aj256prr+s, xh5qfdphe undary between two types of rock at a jh2 pkshup,x d.5,+6 erfrqa5 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. According to th3q wu54 k/jrbr*g*v2nh q le7pe user’s manual, the dish has to be qv/3r42hlg* 5n*7br w uje qkppointed 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 wavelength 250 k7tn .k kjtfm pmf1jh9*jw.(vy -27hib m 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. 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 bo*nj(m h7h.7jj9kkp-w yfb mtfv 12t.iats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kyo9b swk::xp+N/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collidw px:sk:9ob+yes 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 tip sm mnonc26-2 oo19fhe net 1.1 m. Assume that the net behaves like a simple spring, i1n ops2mcf- on9m6o2 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 enfqo 0nqy 3t4tbhc /2.qd of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the ff2tqytq .q43/ chb 0norequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/sqfo+92r;fv oq (Fig. 11–54), compressing the spring 5v+qqoof;f 29r.0 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 just the r(ea:uy3ns i7mr s h3y;ight pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the cof3mhu(sy;nia:7 s ye3 rfee.    cm/s

  The ripples in a certain groove 10.8 cm from the cemj a9nv6;rcyk0 c evqkwq(; ( 7l,ehm)nter of a 33-rpm phonograph record m6;v,w9 k) aqk(m70 herel;cq cvny(jhave a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650co0ths 8oe3ep gtsfi -43phfe2 j z8ti-+s7.40t where x is in mespoht-i z4is+g f 3t8 jp3e2-eh et8f0ters 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 free t .4p4czig0y6ta4o8qw foz7 quency if it accelerates at 0.50g (qpz t tg460cw oyz.4ao8e4if7a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floa :j;;*akts *fs1ljm gc3wlxsv *s:ww5ts on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he st1 3s;l m 5acwsjl:;*s :f*xt*wkg jvwseps 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 musicalqcvawk(g c/ 5npv07k8 instrument are tuned to play at 392 Hz (G) and 440 Hz (A /7vna08wcc5(k pkgq v).
(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. f y9bf+*mq ld(11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section*yf +mbfql (9d 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 q;jynqyp4 cu kb /p3+q).6tii prong moves 1.8 mm to either side of centyntpqu; )bq ij .y+ip6qck34/ er. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates w uir89pyg sr3o9l: r,3 cq1ijmith simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate i 1m g9lp9q,3 ijsry :c8iuror3n 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” e bpied qup47m+ddmj+nf4l556c3ng u2 nd if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determi 35n4+ecj2id 6fl+pmpm4gduq 7u5n b dne the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a perio1g yn+y1uqm7urbiq d- d7y9u;d of exactly 2.000 s — each one-way swing takes 1.00mb;n -yq1yg d1iyuu9r7d + 7uq0 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793{\mathrm{m}/\mathrm{s}}^2$    m
(b) If the pendulum is moved to Paris, where $g=9.809{\mathrm{m}/\mathrm{s}}^2$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62{\mathrm{m}/\mathrm{s}}^2$    m

A mass hanging from a spring can oscillate in the vertical direction or can swin-rk39vuc87 e7lo gfghg as a pendulum of small amplitude, but not both at okf -9vlr78ch7 geu3gthe same time. Which one 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 $\left(\begin{array}{c}k=130\mathrm{N}/\mathrm{m}\end{array}\right)$ 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;u w r.aas41vf mass 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a seconavfr1u.s4 aw ;d pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M iswvpx5fib-bz f8(u b49aql66t suspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to jb(f8vx6bt5 6-9 l bfipwu za4qust stay on top of the block? (Assume $m\ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable itnyldza- w. :7s 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [-z7wa dn: l.ytHint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also qa,,et 94wi gjgives the dimt ,4ea,qiwj9gensions 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 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz