Give some examples of everyday:f4 kp ar7n1su vibrating objects. Which exhibit SHM, at least approximatelup74:fka1 rnsy?

Is the acceleration of a simple harmonic oscillator evnk64ptlzk3y oqh4sv : 0tli)1 er zero? If so, where?

Explain why the motion of a dy; w(3ezc 1aiuh/cj3j+, nlz piston in an automobile engine is approximately simple harce3 nji1z;d/l+h azy3ju (w,cmonic.

Real springs have mass. Will the truef.ac a1v4 si+*wd71 pgyp3nlt period and frequency be larger or smaller than given by the equations for a mass oscillating on .f31 pv1 7ngc liay+4awtspd*the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple har2l veis1x3 im5monic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of u :f,fe qva vt5b5)kj2,fq6kpa vertical spring scale, and then is released. Describe the scale reading as a function of t5kfu,)fvt2 v efab56qp,j kq:ime.

If a pendulum clock is accurate at sea level, will it gain vli:mukj- zu7x :u8 .qor lose time when taken to high a78vj.iu kl :qu-zux: mltitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 1do u2tt-cb6h(1–48). How could you estimate the hei(t6duh bt2co -ght of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pa lzcu)z/n54vz80yw8 wrucu 1zpb, hc2n only if you shake the pan at a certain frehu82zpccz)1n uwyb4c5v0z, / uw8zrl quency?

Give several everyday examples of resonan*0h1(y aq;adios2y,/rbwv lzce.

Is a rattle in a car ever a resonance qshu ev +oeax77(cr((5gj nv+;bdu*d phenomenon? Explain.

Is the frequency of a simple periodic wave equ-)mxb ,kosk ;jg /t+thal to the frequency of its source?-,hb;m)t k +tgjox/sk Why or why not?

Explain the difference between the speed of a transverse wave trav9 (ih cx0r;awzeling down a cord and th0 9z;c riahx(we speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes ol owuz4, npof .8-yktix:y)hk : lwa*2n a piano normally have wirexi 4 uykw tl:,8n:p2-*yo.zh)fwoak l wrapped around them?

What kind of waves do you think will travel down a horizontal metxl (ek+hb,yqk2)zqn95e ndji1 keb09 al rod if you strzk92kj,hdbn+ bx 9k 1nqlei e0q) ye5(ike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but thq;:.ow6jm spxf l 5em3e bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in airxj3 6.q5fmsmlw;: oe p to vary with temperature?

Give two reasons why circular water waves decrease in amplitudep;jsdldqhh 3 -6)c2lk as they travel away fro 6cl 3jdh2- dks)lq;hpm the source.

Two linear waves have the same amplitude and speed, f2 +:cz kky.cl)6 y.p+crzr qiand otherwise are identical, except one has half the wavelength of the other. Which transmitz 6 cik++kc:.c.qfpy) lrr 2zys more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as i byh3.0yj yga2n Fig. 11–33, the freque.3ygya 2yj0 hbncy does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there ac2upuzp3w b +f:jw0 /,cqrlb4 ny places you could touch it with a knife blade without distuw cfq 43b 0l2zpcbpr,+ju :/wurbing the motion?

When a standing wave exists on a string, the vibrations of incident ax 9u5khtdid .6kc0ms6 nd reflected waves cancel at the nodes. Does this mean that energy was d0. kcxi5d6ukt m9shd 6estroyed? Explain.

If we knew that energy was be+tb pa:o2tellj f0qa.;mypv8ki, 3j1 ing transmitted from one place to another, how might we determimva1a io+2f ;y,ltpj8.pqet b3j l: k0ne whether 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 i08vr-zn/ gx))mn+jtbqfn yg h+3zga 4t travels in4n0 a)-r3g+ ) mg/nfhg xbztqj+8yvzn one period?    m

  An elastic cord is 65 cm.tms i6qnv /)m long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is them6)/s q.ivtmn “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 ml .4ec 7qhp.goaljz-/m when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what l/.eqo al4ph.j7g -z cwill be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hanx7np/ 9gvj uqc4h. g3ags from it. (a) What 9 cun 3p4jgvqh g./x7ais the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrat/1mf5kwm7j wues with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs m1f wkwj7 /5mufrom it?    Hz

Construct a Table indicating the position x of the mas(o.wvg)my 2fv rvi2+n 4es1iws in Fig. 11–2 at times t = 0,ts(4gv i.21)vvo2+mi rwwneyf = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 s0wfif3szx qa)mu: y*7-vs6g .25 g is caught in a spider’s web. The web vibrates predomi:qxgsv-3 * z 7fssw ai0f6muy)nately with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 3*n9yw d-e ug4 dim*68kjxp niHz. When an additional 680-g mass is added to m, the frequencyk* 864ndngwpdi*e -3uxj m9iy 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 secok9os/hhz+ k (jnd with an amplitude of 0.13 9o(h h/jksz k+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 from equilibrium is the speed of a SHO half the s8z rvmv23.hmc8kr44ob 2 r egmaximum valu 8k.bh8 r2s4r romvvc2ge4mz3e?$\approx$    A

A mass attached to the g 1.rkyj ((docend of a spring 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 stretc3u vvd;u9vkh7tph-n 4heh vkun94v7tvh; 3pud-d an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0aqb -hnh 4.36lqymdv: kg is attached to a spring with spring stiffness constanthqqd .l:a-nb v43h6 ym k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a 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 sxvxw7,njwkg: j*1,on7 ki1bppring of a toy popgun 0.200 m to “load” a 0.180-kg ball. Withp,:1bxkno,jwgkwv 71x7n*ij what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfaco2d(: ti rf7kgpv8 dy,e is attached to one end of a spring; the otp kyt7:o(,gvf8ddri 2her end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equatioz enw ;sdrh0z(l-fi b n*z;4+in x = 0.45cos6.4t where x is in meterzwbhflr -z;zie*i0+ s4nn d( ;s and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the ee7l/i27r lrm7j i lp06clyp7c)onzd2 nergy of a SHO half KE and half PEi2llr 0jopccmn77d7ryz ep ll72/)6 i ? ±    A

  If one vibration has 7.0 times the a4; bbja 2ry/oenergy of a second, but their frequencies and masses are the same, what is the ratiorba4 /;2 ojaby of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a qq/lu :iyy.ui2mi dp/v7 ol5pbxqz/+60d (ajvertically hanging light spring once every 0.6+jvay/lx5mqo6/0 /b pi i 7u idq(p2:du zyql.5 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical 0)eewhv 35c (nep 2rtjsprings, each with spring stiffness constant k (Fig. 11–4c3)venp (wjh 2re0 5te9). What will be the frequency of vibration?

  A 300-g mass vibrates accordid ju3.c7st vg9ii b9yzr:v1y (ng to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Deter(1u7v9y.bcd9 y zi i jv3st:grmine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what iotkh -i84 jt(j v8f;-ejxakh- s
(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 restg +as,lx axt;4 on the end of a horizontal spring (k = 124 N/m) is struck by atl sx gx;+a,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 witr.hggc6 5m ft9h spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The m6 h .rgtf5cm9gass 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 fzp i.b,8f7v4uug7rk 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.zetb j7qt.lmw1 r2sg0/ w 3*sbiwvb49600-kg block attached to a fixed horizontal spring whose spring stiffness constan v 3m* wwq il7b2rt14/bgs.0 jtesb9wzt 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 jumpb4/ -sf 6:b iord 9u(rugah7 ssjfkc,/s from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more timesu 7 9,rg f6(k/acbd-:i o4sshsbfj/ur 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 vibrat c b(:acrnh3p/ions in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendyy /1dmm,,+y+s vv 7k:xhggvkulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 7yvd+ ymv:,1+ k , /yshvmgkgxs.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Meidu* ,,3wofk ;* *-lolzv +jbbrauw7ars, where the acceleration of gravity is a,*bk-v *j ieoow,+afb3 ; *7llzurduwbout 0.37 that on Earth?    s

  What is the period of a simpfl o8dar )vb:wab(+p- le pendulum 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 m, the pendulu a2n- 8yewanx8osdq43 m bob has a mass of 365 grams, and it is release xned2 wqyo38aa48ns-d 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 hau:vyau qa s/dru72q 2/s a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortene/2 2 y uuq7ravs/a:duqd by    mm.

Derive a formula for the maximum / x/f ;3(nv fogtpdg:zspeed $v_{max}$ 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 fr p w5xv/ 9;ube a)57cuocngf/pm2fop+ equency of 2.5 Hz. At it is released from r;pgp9 w7v5c/meffp n5u +)ubxao o/c2est 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 1q3 ln5iuu-,hc-xp ai;8dn0 e7 qpzu npass the bow of his anchored boat every 3.0 s. He measup0ui51,3uiqcpn7 el xh-nd zu-8qa; n res 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 w5f0:. 2 mzf pmqqiy 44upk7)tz ks*1d gcgfz(bith a speed of 343 m/s How far apart are the w 7 )c2u. bdpgimt zq:4 1kskqp* yf0m(5f4fgzzave crests (compressions)?    m

  (a) AM radio signals have frequenciesdl614.t rn-mwxqw(d8+o dk oc between 550 kHz and 1600 kHz (kilohertz) and travel with a speed lwnd+(-r xd18qdc m.w64k tooof $ 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 long(zz9: g qyb tgzpu*r.jre,1v: itudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as denl: ii pt5g wvm;ezb981se as the other. In which rod will the speed of lonlp8m5 iet:91zibwv g;gitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supbl 8;h ,xkhfn/ports 28 m apart. If the tension h hxkb8;/ ,flnin the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is conne vy *vk5:5tjxccted to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and*vk55 :yjxvt c 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. ))gk4 9 dgh4g*z3 yfgbwy8dxgHe hears the echo of the wave reflected from the ocean floor directly bg)hx 4gky d*)4w8bggd9 zfgy 3elow 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, p)jjlvxlc k12l ;o)8pand this difference helps in locating the earthquakej8j k2lo1cv plxl)p ;) “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 bekcu)5m f;yblbm * a5 /9e(yljsm3jg0z approximated by a sinusoidal 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? [j5s0j* kylblmec; )a(ufy/9 gm5zbm 3Hint: Set the acceleration a>g]    m

  What is the ratio of (a) thejr2ca+cwlotg t-9 7nzlc,6ie- s nu :yqb:*y4 intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at t:t e6yn oc wuas4*:jltr -by9cq i, -n72gcz+lwo points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth ispj*o j h+qga,- measured to be jhopq,gj +a*-$ 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 tu72dkl 9kf9h ihrough the same portion of the Earth, but one is carrying twice the energy. What79ukd 9kf l2hi is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequcc//dlw37c:c;yijq y -g0 ot uency, but one transports three times the power of tcwutj0 ;c/ l7g y cdyc3:/o-qihe other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed; y h1a ffd(*0ya.wbpz to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor *b(f;f ayyph10. wadz does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (aw4czhpn5 x- o f47a45wkb*gfk7ndl i6) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the ene7bp c7dwk*hnnk4aoxzg6w fi4-5f5 4l rgy at this moment?

  If a violin string vibrates atpjvecc zio-4 l:b6k.aw6gc+8 j;zp (g 440 Hz as its fundamental frequency, what are the frequencies of the first fw;gc :6czp(zc+8pvg. - o6 4jlkbaiej our harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. A0dow-ecoty.id4mk +ru f3o/ 2t what frequency will it vibrate if it is fingered t2 o0oy . rfk+3m4/i-euowcdd one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name a ws23+x lcl7hit least three other frequencies at which iiwll32c +x7sh t will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing wav1eta .*9o4mlags.z knes is 475 Hz, how far apart are two adjacent nodln. 4.seg9*k ao1 azmtes?   m

  If two successive overtones of a vibrating string are 280 Hz -3 -4aq:mafws frjl1jand 350 Hz, what is the frequency of the fundamenta 1fj 3-4lam-jr:w afsql?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 8/9bo j6ad y;khgku e3g. The distance from the bridge to the support post is L = 62cm and the string is uhjg/;d 869eaobkk y3under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is su9+bquet7xhcwim-,z v,o- ,u cpposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be chan,owm- t vb-cxz hq+97,u u,iceged 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(k6k21h fzdj z 200 Hz, but it is measured to vibrate at 2056hjk2(f1z kdz 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-amplitudep q:kkd2br+a1/jv e: d mechanical 60-Hz vibrator. The str/rbk dvqkdp+1e: :ja2ing’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 th i5. kgb(a vn27l2c)hk1hm sgve string may be adjusted by moving the pulley. If the hanga()5nh27mv.gk ic1h s2g b vkling 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 justbrh0unk4/+x kx j5;n t the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the centet+ /;u4nh 5nrbk0jxk xr. 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*5 r8xyr ce/ yjf;j4fo boundary within the Earth betweenoc4f8 r; xyef5/jyrj * two kinds of material. If it 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 underwater “shelf” where the velocity .o9g c( n3bxtnchanges from 2.8 m/s to 2.1 m/s If the incident wave crests make a 3(xn9. 3 bnctog4$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelenz2wo itf) dj()b0 k.ing in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of ni(jobd2e 0zwkf) .t) 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 b3x q7pkh6 a2b bamxxjb1tz2 v6h8u5k0oundary between two types of rock at a 3x03z6b5xa 2k htxk1p7j q abbm6vuh828 $^{\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 a) dixcu )1q4k:wctuy z*t1m+qbout 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction o t41 yc)1ick+*)qxudm: tzuq wf the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocn c+ivp(+ ycb2n+lin3ity 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 oiipc +ln+bvy2 nc +n3(f 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 stiffnes/ggg 8m9 zggchs46y w3s 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 (h g63w /9gzggsy g4mc8approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire na 3 *ce8+tb azblfy4e/et 18 m below, which stretches the net 1.1 m. Assume that the net/*lc t4faz+8ebb 3 aey behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end s(7jaw*fv1 ar of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What isasjwr1fv *7(a the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54)5eeb; -/t 4k*eoia08zs qyhzdpoj /o/, compressing the spring 5.0 m. (a) What is the spring stiffness constant ofdhqoz oy-t0ij;beps /8ea zke*5/o/ 4 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 q; 6kiqk ;jy3acm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in th;kqyja6 ;ki 3qe coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-r5;eo7 *fllcjv pm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the so5e7v; o jfll*cund emitted?    Hz

  A 2.00-kg mass vibrates accordingw,b2q 3mza e ax,ynj; a)0us1l to the equation x=0.650cos7.40t where x is in meters and t in seconds. Deyanamb)2q;eu x0,z 1j alsw,3 termine
(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 frequencyh;ih t/vn)ufl u(6egy .tmm-) f. What is its frequency if it acceleratht /it mg).ufueh; -m)(n 6yvles at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75rv/t zsvq.k5v5 eu,*td 0hug+-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while.qt0 k z 5,ue+rv5dvt /hsv*ug.
(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 arapjocazz *he:; nt( 3m.qnnypc- /2, fe tuned to play at 392 Hz (G) and 440 Hz (Aechz*moz-a /;fc(j.ynn,ptp2a :q 3 n).
(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 d8 yq:jo9hn l,;o 8ewuyown the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavi;oneq8y:j8 hl9o, wyu er section of cord or the lighter?

  A tuning fork vibratesy12c(nrya jcnmd5mzfzmgggr 7 141:6 at a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either s rdnc zy:g71g 1n51ac grm6jzmf42m( yide 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 motion of frequ4o g,6c1pu8z):uwpwbhcy w o9ency 1.5 cycles per second. 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 w:p,u1 4oocc y)uww8g bpwhz 69ith the board during the oscillation?

A string can have a “free” end if that end is attached to a g9o05p rfnn44h .pksr ring that can slide without friction on a vertical popnh kogs0r54p frn.4 9le (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 2.000 s — each one-way swing takeseb6+ +it 2zlf 1uwzofbt41jp- 1.0zbe t++-bolj 6wfti fupz211400 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 oscillase;, ff(2c xpv8q nr.vte 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 sw(fvx,nfv.pe;2 s cqr8 ings, 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 r 8xvkrc 3q:4lis stretched under a tension of 255 N. A pulse is generated at one end8vr 3 4klqx:rc, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spr 2tz3vo cp,m* f e:wi*ly.f;nping stiffness constant k. A pe *fp2v;3:lcym tez.nfp wo i*,nny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car d::7uzb+x cw uat the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze s:xzw c:d+ub 7utarts the car bouncing at the end 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 shown in Fig. 11–58 (which ud 2uug;(n,hg 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 modhgg(n 2u;udu,ulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz