Give some examples of everyday vibrating objects. Which 4 7 xe8oluw04c/zegfoexhibit SHM, at least approxio 4c08fz4gwu7/ l eoxemately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where/)f: vvi7 fudp2p3 jy30 jlwui?

Explain why the motion of a piston in an automo)u 7q1l*ni vubbile engine is approximately simple h*bi1lu7v )uq narmonic.

Real springs have mass. Will the true period and fre ;* ne).up etd4xfa8i s.zppe:quency be larger or smaller than given by the equations for a masuaiex4e ps.;d)f.* : tnzep8 ps oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simkf: ;ct5zlym il1p8 lumv(83cple harmonic oscillator (SHO)?

A 5.0-kg trout is attached qo1yba/q 5t tgqu) /dag5g.4qto the hook of a vertical spring scale, and then is released. Describe gu/g5a5/ q) odtq4 tayqb q1g.the scale reading as a function of time.

If a pendulum clock is accurate a/2pr gv.bx b,bt sea level, will it gain or lose time when taken to high alp.rbbv bg,x2/ titude? Why?

A tire swing hanging from a braff .u o7(g*yprl3*ztdnch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch u73 *p(g lyt dzff*r.uosing only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the p4 ffi-y m(;y0oyouem.an at a certain frequenmf y4o yuefoi(-.y;m0cy?

Give several everyday examples of resonanq-xfk)m f;y.mjzn8 woktw- -8ce.

Is a rattle in a car b g9w gm)vx():za;hlj ever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave (yel3b xf+d;9h ;mcjcequal to the frequency of its source? Whe9yc;( ljxb h;mc3f+dy or why not?

Explain the difference between the speed of a transverse wave b (,v5dq8ac4ttlv b 2ytraveling down a cord and tv,qbt4 bty(d lc2 va85he speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequepi/1vhzw(ypj y j)0,-k lpe f8w6ki(xncy notes on a piano normally have wire wrapped -yj16(kxjk/eihwy( l,w f0)8ipp v zparound them?

What kind of waves do you think will travel n5r ip/z afn1/z9xf81 ftij :wdown a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel rffz:apt i1/jiw zf xnn95/18 to its length?

Since the density of air decreases with an+85m-wq mz fom increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to +5 mfq8o-zwmm vary with temperature?

Give two reasons why c477y vu psn9kxircular water waves decrease in amplitude as they travel away from the 9p47nyvuxks 7source.

Two linear waves have the same amplitude and speed,/cv8 7)vhiqbt:/ tjku and otherwise are identical, h87q tjcitu /v b)/vk:except one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectig 7tiy;lg b938wbpan ,ons of cord as in Fig. 11–33, y,b3gl 9abtg8pwni;7the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there ankz36)bur2 2myix;tf n y places you could touch it with a knife blade without disturbing the motio)nbiy2mu tk 2fr 3;zx6n?

When a standing wave exists on a string, the vibrati3hc4yu 1.nkp qxd4vj 2ons of incident and reflected waves cancel at the nodes. Does this mea.ny jx h4dpkv41 cu32qn that energy was destroyed? Explain.

If we knew that energy was beibjt:8erg frk ri9h6:a q6w7n(ng transmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodies) 769rjqkw:(fh 6 at8r n:iergbor by waves?

  If a particle undergoes SHM with amplitude 0.18 8a g z leuy1o-j0l*ebksja8 09m, what is the total distance it travelsu 00gs8k yb*8jl9l zjoae1ae- in one period?    m

  An elastic cord is 65 cm *e 2n c(ez(igmlong when a weight of 75 N hangs from it but is 85 cm long when a mc(gie*z en2(weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 15006f **gmss,i se-kg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over si,gs*fe ms*6a 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 it. (a); q;dhqlj-0v0ffg ee / What is tjeh;- fldg eq 0/f;qv0he spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a freque0ewtt8 oe2dpla+n 0s y)4hsik 76+1p, titjawncy of 3.0 Hz when a mass of 0.60 kg is hung from it. What is i2 ws7p tiwsaito,4l+8ne htjyt0a+) d6e0 1kpts frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position nc da67xlise,.;/qms0m wkm1 tt0e o( x of the mass in Fig. 11–2 at times t = 0,q7dm00m/ xtwk c eolt(sna1mi,; se.6t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 cauhu h1gwza 3n k6,q0/.y4 )gc(ngqkunj ght in a spider’s web. The web vibrates predominately with a freque ng3u(ajw4,zqg/n 0qn6)uk h.hk gc 1yncy 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 springngs fk82h;1pg vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the freqgskhpg 1 ;fn28uency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second t. 4v vnk32ddbwith an amplitude of 0.13 m. Determi.2dtb3 dv4kn vne
(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 spjmf5sa9 nm,;heed of a SHO half the maximum val;afmnhj, 59s mue?$\approx$    A

A mass attached to the end of a spring is8ub/ 4fgwc bj61r9pjooh7j -v 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. Ipozxi1kk. 8dh,f8o1oe9jv/* wi p3hmf the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium positiv1oi ihp/8hkmz 8dfk,.eo 9oj*1pw 3 xon again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnessi8r:34w x zj9j*+dwekig6xeg constant 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 0ix9e3*kwjzd: +8xigj4r w6g e.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 t)f e-0s, 5g:*zi zgz m:qqbiv s6f;gwoo compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leavez0-g*v: f qembg)sz 6iisf;g ,zwo:5q the gun?    m/s

  A mass sitting on a horizontal, frictionle),v 7wy:u suk:lnqdg;ss 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 q gn) y;ul: wsvudk7,: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 e,v+akjxnk -:t2i x 10-ljs6xob uirz;quation x = 0.45cos6.4t where x is in meters and t is in seconds. Dxo2s;l kib -i nv1,60k:arx-ux+ tj jzetermine
(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 :d e8;hi+a7d xwgenz4)siw o7a SHO half KE and half PE? ± 4 +:7zhiw7n)de8 so; giedxaw   A

  If one vibration has 7.0 times the energyaiou95c e *-sda lb* x*k8z,lb of a second, but their frequencies and masses are the same, what is the ratio of their amplitude zbo8eu -bs 5,a*k*lc*aidl 9xs?   

  A 2.00-kg pumpkin oscillatesk)l2q-bj qp+sf;c sn b,e1o+ c from a vertically hanging light spring once every 0-bqpbkf s) 2 l+js1c eo;,cq+n.65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is suppor7keq fv7ppf(py51 )epted by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency o(epqpf 7v 7y1fp)p5ek f vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where xx9j .kvc.o78i sjns. r is in meters and t is in seconds. k7nx.rs i9cs8vjjo .. 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 tw9c+j gp1 n/g9yef zyx6o examples of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124xua0(.qm x :kh N/m) is struck by (ukqa0x :mx.h a 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 withqu x pp dw;xu2c3f8:3c*p5 vfp-oe9gb/ 2 lfud spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equili8;p cdl :uvx32pcop/ 5xwd* f-3fub9 p qgefu2brium 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 spr25dvpev fqh,n3 g mir -5d:i,aing 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 bl,cp)67fo;i)m ;:w-kgi ee png2wgswuock attached to a fixed horizontal spring whose spring stiffn;)c n2iwo,f gm7i:eupw 6egsp-;)gw kess 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 jumps from a high bridge. Afw6yqg g. yw06fez(r, yter reaching his lowest point, he oscillates up and down, hitting a low point eight more ti,e6yq0f. (ywy6w r zggmes 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 vibration)jxmq f+8omh(; a8cwms in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be il1dl zh(gqmr (u,f6f.f it is to make exactly one swing per second? (That is, one comp6flz, 1f q udh(g(.mlrlete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.:ka:4 kn s3iil80 s on Earth. What is its period on Mars, where the acceleration of gravity43nkiial : :ks is about 0.37 that on Earth?    s

  What is the period of a simpl8kluuq-e:8-j7 y p,x ptj hiu8e 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 pendulum bob has a mass of 365 nrx0o )o7jh+qnav n((g9fuc 7grams fvcnqr(hj7)0 +n (7 aou9gnox, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock losesl5 mbbx8 0oxrqa6(g q4 half a minute per day, how should you adjust the length of the pendulum? shortenedgxm40orxl5 (bbqa8q6 by    mm.

Derive a formula for the maxim. csz85xilmuh ron28 :um 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 Hz. At it is releag1 qo u(e4 aq+blxg:+esed from res+e q xg4e+u:1 (qgblaot 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 hilb * )+x+ mv wrecop4smq+36cns anchored boat every 3.0 s. He measures the distance b++vco4q rms6 x3p)* wmen+lc between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency 8.1zcosvkyk1jq 8c9 lc6m9 olgg0k u:of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (comprek l:kz86kv. s y9cjqo0g1c mlug9c81o ssions)?    m

  (a) AM radio signals have frequencies between 550 fvbh4b- xr.2atb l -q.2c u9mbkHz and 1600 kHz (kilohertz) and travel with aaxb2fl h9-v b4-bur.mc q2tb . speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed ofcj c4y9q,zt sge,+n s3 longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, +:qzm8ojedu 8 z)+c qos*vc8 qbut one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what qu8 8+qd omsqe)+j zocz :vc8*factor?   

  A cord of mass 0.65 kg is stre1gct-:gcvrja 4456e g,uok n mtched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a prc6 gu oag1mk 5 jtng44,e-vc:ulse to travel from one support to the other?    s

  A ski gondola is connected t /gi1ub5he3k6myk5ex c 06sxkyt 7,vao 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, it3e/kc,5 g5meit 0 k6hyauk 61xsyv7b x bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. He h-+1pvz/pq(y w8 g /q/ tqhllsnears the echo of the wave reflected from the oceanw81y /(vthq p/ gq+-zqlsp/nl floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travelnfm 9kjrxb,-* ; tffr/ at different speeds, and this difference helps in locating /tbnx*r9f j,;fkm -frthe earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be appro*c2dy7)z yt eoximated 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 b 2 yodcyz)*e7tegin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensnhx5 uze5u)jb f3j v.:ities, and (b) the amplitudes, of an earthquake P wave passing through the Eartjuh vb ez :5.3x5)ufnjh and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through theamnf ceh/ske ae r-/:m;(/el) Earth is measured to be e)/eem/h; ak/lm:r ce- fnas( $ 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 frez6ui (jsus u*gw8kah 4v/: v8yquency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wav w kj :(u/is6uy ha88*4vzuvgses?   

  Two waves traveling along a stretched string have the same frequef+yx.rp-snz:) sbu k0fv* x3 lncy, but one transports sffnyx)pkv:lb*x+s. 0z r-u 3three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a p xn1jqu,yp12vyh 4+furl:11 c)7zwqyalxe m) ond is observed to move up and down a total vertical d)1c4lelqq 1vx,pf7:zwunay1h2 )y 1mxjyu+r istance 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 does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each oy4y;1gd9jwalg4 w cj 3ther. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments laterg1jw;4ya j cdw3yl 94g. (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 a,,y 3ujn z) ;orm9wf-u8udvoo re the fre,m zu3udv r,8 ;)oyu- wjf9nooquencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered.j3 xk)oc)ouz7 At what frequency will it vibrate if it is fingered one-third of the way downou)j)k coxz37 from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four :evf( ba(ng4y+2p3keczne p*loops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonatevea pgpfz 3nck (:*4neye+b(2 . $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency o:-j),r9jk 7vy 2f gdo)knv d ayao(sb9f standing waves is 475 Hz, how far apart are two rk:ao2s9jv,day 9()gb dyj)fvokn- 7 adjacent nodes?   m

  If two successive ovizw6-q3mcs+ kgjo + v4 sr**vsertones of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fuqj*rskg v+s3 o64ivzm -w*s +cndamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fviuc, 0). la5vknse 7rrom the bridge to the support post is L = 62cm and the string ilra0esik,vvc) .u5n7 s under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is meas)*du. v d1 egof-spf(4gj(qfu ured to vibrate at1)v.dq g-(4 p (*efodfufujs g 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is mefi tu7l)m 6fsmpq 3d8:asured to vibrate at 205 Hz. By what percent should the tension in the string be changed to corredmqt fslm i)pu36:78f ct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mec6m oe :eli8ettlm 2)gt3 dlt+2hanical 60-Hz vibrator. The string:eo 8 m)l tll2tditt em+g6e23’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may bsd b.mgsqaanbawr d:23 1855p e adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patt5swq8r mnb5g2daadbpa 1 3:. serns 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 fdvk6(,0 r synirequency, 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-cmrv(k0 ni s,d6y-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling(vjwda.o :.5e r u6yix at k.0 km/s strikes a boundary within the Earth between two kinds of material. I.ui(e.xo:r5j a y6dwvf 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 a 4ka m jm o:a3;+,cbloj)smn)sn underwater “shelf” where the velocity changes from 2.8 m/s to : oma4;s )j)c bk 3anomsl+m,j2.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it ze l(+-)g tbz i5;1yrznpv b*vhits a layer of cold, dense air. If the sound wave hits the cold air interf5vtzvl*)zeb-p ( +biygn1r z;ace 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 n: y*onkkn4y. j(jju:x-kng7+ eqq:a strikes a boundary between two types of rock at a n-g jyk:nkjn: .uxq(ye7ao+*j4k qn :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 +pr*m 9rx2xahin diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite,r2x mha*xr9+p 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 velocityq vpm*t78dl 4y 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 absenpl7my8 4 vtd*qce 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 cf .lgbdr-zkj ; :mek+,ar bumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservatiozr; .jmke,kd :g+bf-ln of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whichr u pr:j.n;(gi+zi y 3/i9wb7ypcx8mb stretches the net 1.1 m. Assume that the net behaves like a simple sprnm ;r7.px zucy/i3yi8pg + i(9jbr :wbing, 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. Thxg:y8mg b z8)ye mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation:gx zm) g8y8by?    Hz

  A 950-kg car strikes a huge spring at a speed of 2t2iv o 7hs:6d3 cuhm.g2 m/s (Fig. 11–54), compressing the spring 5.0 m2g t6 midhsv7:u.3ho c. (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 right pace of w ll-m6 1i50iazqsfb-about 1 step per second, the col6a fwsm0-z - i5i1qblffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the cente.h we kuipx3i/7k5 a8gr of a 33-rpm phonograph record have a wavelength of 1.70 mm. What wkkx 8iwp./ 3gi5e 7uhaill be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the eat4 b:4l) xlskquation x=0.650cos7.40t where x is in meters andtasb :l)l4 k4x 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 f3 o09l9g5l5bextxtp 9b1y pmorequency if it accelerates at 0.50 xb gpmb39 tyoplelt5 5x1o909g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg mana*a( )scd) mtw stands on the raft, it sinksa actd)ws)*m( 4.0 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 are tuned to play at 392 Hz (G) and 440 mia/u o; iek**tzz8c)+2 tsuxfk+9xm Hz (Amit2*k/c zk z 9atimuu)8+f e*osx;x+).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 11–31d2), ru *, npmo ifk94igzt5vpej ug)3. Determine a formula (a) for the ratio of thi,zd* )oj5p ,e puu1n9g 4ktgi2fr v)me speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the f *dlxyehb+u7elp o-gp7 -nz 1i)+(hztip of each prong moves 1.8 mm to dh ()x1n7uo g 7lppfihe*--zz elby++ either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonicfvbo4 rh/+ 3nsxam.0mbf tg6) motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the enfx)m.vgm hfn43rba s/ob 6+t0 d of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end i+uiqdt,kw d 2;.fiv7 of that end is attached to a ring that can slide without frictiktqf;. , d w2+d7iuoivon 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 eqdp)e3 2g4l*t:ey zk of exactly 2.000 s — each one-way swing takes 1.000 s. 2 pze):tlky e*e34dgq
(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 oscillgb5qwq.au h9+ate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longewquh a 9qg5+.br, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pul :xec5fvakf1id; ,ko4se 15i:efo akfd;v ,xk4cis generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sprinr+ y+rnvl*c tawk/ 7o5g 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 just stay on top of the block/kno*ltr5ayw + rc+7v? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg ca pifkc-( u)i8nr at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A brek (uifn8)-piceze starts 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 plate9eu6i +oogx ql7 ag5.e as shown 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, estim7g+ aqioxl5ee96gu .o ate 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