Give some examples of everyday vibrating objects. Which exh.qkf 8h2 vgfb8ibit SHM, at least approximaf8h8fgkq . bv2tely?

Is the acceleration of a simple harmonic oscillator ever zero? If s1 pnak(low 3an5u7 ww(8mr kj9o, where?

Explain why the motion of a piston in an automx 8:oaq f.4cdvet.i; tobile engine is approximately simple harce:t q. 4o8fitvd. xa;monic.

Real springs have mass. Will the true period and frequency be larger-tu.buab5-n hkukd uvj2jsm*6 ;* k4b or smaller than given bya t; vk*unsuu65bkdm4j -hbkj*b.u 2- the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic osua1 /izliq go)x(a k18cillator (SHO)?

A 5.0-kg trout is at*h. 1 yxcuyrs0tached to the hook of a vertical spring scale, and then is released. Describe the sca cyxryh01*su.le reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or los4n 6i, 8d jjfd5yo 3)ik+qic rn:yau.de time when taken to high altocik d6y adn, :f5.d+ iijqu )r4n38jyitude? Why?

A tire swing hanging from a branch reaches near8cfbe gqzmv u2nu46aq .d s-gg5/9mp-ly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a st4b6qf.gnum9/ -zecmd g2su-5gva 8 qpopwatch?

Why can you make water slosh back and forth in a pan only if you shake the pan a z2uv xo 5ys-:21gsnwu/rono3t a certai:osz 5-1o/vu3n2s yrwgo2x u nn frequency?

Give several everyday exa sf3(e1pvtlrf -n.b;aw(ppse-cc7 t0mples of resonance.

Is a rattle in a car ever a resonance phenomenon? Explaine)2iuxx3h. sx.

Is the frequency of a simple periodic wave equal to the frequency omdu792dposj ;x 0vc 8hf its source? Why or why mo7098v;dh u xp2djcsnot?

Explain the difference betweenb9r c 1ussln;- the speed of a transverse wave traveling down a cord;9b1 ns-ucl sr and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally hav 2+oclnbc7 uo1e wcc+b 2l1uno7o ire wrapped around them?

What kind of waves do you think will travel dontde0m6f.51k n rh1a/ o q-hqawn a horizontal metal rod if you strike its end (a) veo/q1 m .htrnaq0a51f6 kh-denrtically from above and (b) horizontally parallel to its length?

Since the density of air decreasetk:l ;nc-, 3 hf)iienys with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how w: n f,hnyl;ikec3-i t)ould you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves znb4k4 g 3co0cz2n ac*decrease in amplitude as they travel away from the source 2cn*4kcznc3zb og4a 0.

Two linear waves have the same gvxo dvwo/8 wc-8*vxw41 s; rmamplitude and speed, and otherwise are identical, except one has half the wavelength of the other.x/1r-8 ww8 ;gvvdwc 4msxvo *o Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of corq.h-3x8w 5 hlrmvt bu8d as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain h3-wr85q.vh xb8mtl u why.

If a string is vibrating in)ugs- lkzc jci/5wt/:bze(3 n three segments, are there any places you could touch it with a knife blade without disturbing the-cj5bwzc:3lg skuinz/e / t() motion?

When a standing wave exists on a string, the vibrations of incident and re5s,2jvgrw *2ej :xxtm flected waves cancel at the nodes. Does this mean that energy was destroyed? Explain.vt emx x:gj2,w*5jsr 2

If we knew that energy was beiresg80. paza;g1f2q tng transmitted from one place to another, how might we determine whether the energy was being carried by partic2ag8 rsazg; 10 tf.eqples (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total dig)7czg9 4h)y nnn v fj(m4s9sqstance it travels 4v) ngn74( z9j qf)csngy9s mhin one period?    m

  An elastic cord is 65 cm long wh jq co:0sz.8wqen a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is j oq 8:wqsc0z.the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm wj: 2v83kib4t(5myevrur + tmyk,r*jj hen its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency ofvykj*jmrk,t m3b2t+i u e4y: vr58(jr vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3. wa*mp f/dxy+16 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffnaw*xf+1 y/ dpmess constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of erzc jait-*hmwwk* ; 7 n.-i3z3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from it?hta;j -3z.ekc* ii7*nwzr mw-    Hz

Construct a Table indicatitg hhg+ *g1 du:jaz,2;sb*bn8+uzbop ng the position x of the mass in Fig. 11–2 at times t = 0,t b**zbauto h g;gu j,z+p1+gs: 8dhb2n= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 we(, tcfi, q,iaeb vibrates predominately qiea, (tfi,c ,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 frw36a0(2;zr xhf1b / j:bqmmlvb,k hgl equency of 0.88 Hz. When an additional 680-g mass is added to m, vgk3bl bhqw2 /z;b:,0mjf rm6 (xhl1a the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per secon.gd7 o,i gy2oq* gva0kd with an amplitude of 0.13 m. Determine vkaog,dqg7 i*oy.g20
(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 maxiz/t/hek9 fd4rmum value? d/h9fetk z/r4$\approx$    A

A mass attached to the end okgs99 qlx,z ehlq .n*;j)lg+ jf 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 kl3z.g k1y7 ud6tkv*ss -e1xlspring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position agag y6kldk*1t-3vx z7su1lse .kin?    s

  An object with mass 3.0 kg is attached to a spring with s5 5qmier sgdfer 0x,6,9oyp8jpring stiffness 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 0.55f r,egde0r ,o5qx9856p yjms i 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 com1qaom:l rdq)v8wn p45lomy7 (press the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what nl5 my ) oa:8owdl417v(rqmp qspeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end ogz(k1 w8 ebc:r +oggtf9/7wbu nk 8g(cf a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the efkcoc8(b9 wwgg+7k/(r uz8 tb g1: ngmass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.32w y7sk whxarl(-h.b45cos6.4t where x is in meters and t is in seconds. Detywh2b(w x.-7 3sh rlakermine
(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+uwc2 */ yy qr/c/ueau a SHO half KE and half PE? ± ucqyw*u /c2/eyu/ar+    A

  If one vibration has 7.0 times the energy of a slw1mqjs9h :cfd 3bfh;-s . kd0econd, but their frequencies and masses are the same, what is the ratio of th.- wlshc 01s9dfdb; m khf:jq3eir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring oavq-.x md jp-*q9df:dnce every 0.65 s. p- jd.dvf-*:a qxm9q d
(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 supportf 7cs9 sy diy-489awsced by two identical parallel vertical springs, each with spring stiffness d y8 cs 7ca9yfs-9i4wsconstant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is om gr rgnj7)jlfd8 p s q)(*8c5ep8d-din meters and t is in sec-dr erd5 jj m)p8sp cgf*dq(no8g8)7l onds. 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,( ftd+ xla jjd:2asj+3 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 6tx.) uor2 axos:mr*xspring (k = 124 N/m) is struck by a hammer, which gives to xsrxx:*6.2tuma or)he 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 stiffness conl yis zzln0tge1 m16 xyu9)36zstant 305 N/m vibrates with an amplitude of 28.0 cm n16eyl9t 6z0z1y u3zimxlg s )when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with ;64pde30ll/mj pk ay0ugfu,a 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-kr7 y. h,a:fo)fv fais;i1hq *whz0p -kg block attached to a fixed horizontal spring whose spring stiffness con-zip fsf.r0o)v,yq1f7 khhw:a ;* ahistant 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 breau;6b t8e5fz a0pn 4hidge. After reaching his lowest point,ba65ee fhu 048 ;tpanz he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. Whr;c4bish m6 ,nto.yq, ehr+*nat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exacf6(g1l fnldzzhf .-8 jtly one swing per second? (That is, one comzdh6f(-81jfgfl.l n zplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What isxi;t yx76i,fjb -s0 jo5ftmk- its period on Mars, where the acceleration of gravit b-7fj jtxtoxi-s 6i m5ykf,;0y is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long ,ny +lm.mn/j,0 ue) qqwo v7in
(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 3.)t*mr/0l nq:l1k-u hr uvhuy65 grams, and it is revqh/-)u:r. kt0yr hu1 llunm *leased 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 lengthub5gr(3hfax , tf-n5wj0fuz, of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pen5x- agtr3nuf,h b5(uf wz f,0jdulum? shortened by    mm.

Derive a formula for theb 9fwbm6/pj;8zxr qdc r 6p)y, 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 oscilu qk4v16*mq l3fz/oe klates at a frequency of 2.5 Hz. At it is released from rest startizvm*6oeu flq qk/k3 14ng at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every3 k b ochuzzi+w.2w61wf)n6jw 3.0 s. He measures the distance between two crests w.zwzbfo62 3w6 nc+wu) ji h1kto be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travef 8yu 8c6nm15 brati9nls with a speed of 343 m/s How far mrtbnyn19 8ia c5fu6 8apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and1ub(;ocf n6o3v eril 9 1600 kHz (kilohertz) and travel wi3e nf6coul(91;ib o rvth a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of lcbx/rhncm - y0v (d3(0 x.a)vig*vyzn ongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but g,3bn -npux: d9uk0e zone is twice as dense as the other. In which rod will the speed of longitudinal nb3zg :kd-90 xpueu,n waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If t; j) (avdq: d(sbcwzv;he tension in the cord is 150 N, how jd )vazs b:(cv(;wdq; long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cau qb6q.z/g;k2uh aj0i ble of length 620 m and diame 6.02j qazhgu/bkuq i;ter 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 8a drq 3(n(i9duhl, 6 wpt;ysrside of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly belowwy ,ntup (3lrrds 86;(qiad9h 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at differen 9kkjj qnxrb+/b23fhaut: w54b,haab+ p a.4 at speeds, and this difference hh43+q4 k,bfr b bxa:5p9bk naju/ h. awtaj+a2elps in locating the 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 wavh: df)h*e 6gqze can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hfhz*g: hqd6e)z (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intens(uyvi6.azuf: p7lh o5 /0/dnlzynsz3ities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the sourc.dpus/nl/uh y ( 6i7zyf:35aznz v l0oe?(a)    (b)   

  The intensity of an earthquake wave passing through the8j)4i3mr pka-2n;rlx fq rj 5z Earth is measured to be rpj;8qf- k mn35) r2j4zi xarl$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same por gf67xx wc, fsg+wk*v7tion of the Eartsg*7wwfx, 76 fkv+gxch, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string fmbw;;jx 4.tg+wqy;r have the same frequency, but one transports three times the power of the other. What is the ratio of the ampl m+4rfq.ww ;; tgjx;byitudes of the two waves?   

  A bug on the surface of a pgvt 90c:orfj 4znph 0t+ri3+zond is observed 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 does the btr0rinc0 z4oh pg+ 9 3fz+:vjtug’s maximum KE change?   

The two pulses shown inhiu0k :8jyb oso:jb ru4,9s.h Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch0o8 hs yk.:s94b:ohui ub,rj j 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 nu 7oc 82nd24vdd.fvpt5woi; at 440 Hz as its fundamental frequency, what are the frequencies of the first fodp;vvc.ntd5i78n f2 w4d2ou our harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what icye1;5 sd jp0frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave. cep;siy1 j0d5)    Hz

  A particular string rfs+l3nr j q6w*esonates in four loops at a frequency of 280 Hz. Name at least three other f3j+fw sr6lq* nrequencies at which it 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 tirq +amk c.w(1f-qsksb-i-y*he frequency of standing waves is 475 Hz, how far apart are two adjacent nyr-fcmq*ksa -1.siq-ib +kw ( odes?   m

  If two successive overtones of a vibrat1kn)mgoo 8r j2ing string are 280 Hz and 350 Hz, what is the frequency of the fuo1 n jm28ko)rgndamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dy;os8z-3bqm mu*ge:q 5r;h mvistance from the bridge to the support post is L = 62cm and the string is under a tensi o qh;5vyqsm;b3uzmer 8gm:-*on of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is sb6f*y .kh-fjb:tifm4z 50nq xupposed to vibrate at 200 Hz, but it is measured to vibrate at im. bft 64-k0zyh:q b *xf5jnf205 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 vibram,k7 x2olp/u*sgbw 4 mte at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the te2/bmp xw,mol4sk 7g *unsion in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amp:f 8 p9l9lm 6jerm(vox:ewr-papl+)alitude mechanical 60-Hz vibr(llm8r6mla o w)ep9j+a9 rep p::fxv- ator. The string’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 bifc,e.c1vogh9 ro o-c0z h06ze adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by06c zof.egzvco c ir,-hoh910 varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right no7chvz8+ 5n9eanq jo b (6ic:frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the spn9ijn:o6(ce+7n8oh ab vqz c5eed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earth f 44b,jh+fp uq)ig:xobetween two kinds of matef ) 4juxgipb :qh+f,4orial. 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 velocityu(;*x7rqsjv +jvz w1(vmh. ow changes from 2.8 m/s to 2.1 mohzq(jv 1uwjs;r v x7m(+w.v*/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a la,s(e h 2hwrzj.yer of cold, dense air. If the sounh w2,s rezh(j.d wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquajn.x/j .h z-zkdrl y9 ;a9qqx/ke wave strikes a boundary between two types of rock at a xq9yjz q9 -n/jrx .d alh/z.k;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. Accordingrwblc7miw43xq/ m ,9 d to the user’s manual, the dish has to be pointed in the direction of the sar7 qm 9dwcmxb/liw3 4,tellite, 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 velocit kt9yjf6syuw2z n2m;d ,jo* t,y 750 km/h travels across the Pacific Ocean. As it approaches Hawaio j6ktj2 ,9 y;z*mntuy, 2swdfi, 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 boats.)    min

  An energy-absorbing car bumper has ca59; hcl)ip jrmq3(czs; op.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 conseh;c(;zaojs 3cr95pqmipc ).lrvation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretchexkzci. 67z rj1zj2e i1s the net 1.1 m. Assume that the net behaves zricz12j1.ixk76zj e like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely haq3(ke) np1 scvnging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency kv1cq( s3 )pneof the oscillation?    Hz

  A 950-kg car strikes a huge sprin1t-w s z,fug3f(,u *s+jxvph ug at a speed of 22 m/s (Fig. 11–54), compressing the ugu13+( w ,h ftxufpszj *,-svspring 5.0 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 (diamkapvu6v(0,i 1wci2 d beter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estupk2d01 ,iviwcvba (6 imate the speed of waves in the coffee.    cm/s

  The ripples in a certai-r b25,qz+yyk z1r 7+gi1x uxdf( xpt my9k(vgn groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be gk, yfm9ybvxy( i u1z 7t -x 15pqdzr2+r(+gkxthe frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where 56l wgkq00m (l7nd jswx is in meters and t in seconds. d k5slgm70(lw6wn j 0qDetermine
(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 frequefcbk8dj rc7 /b)9phy 0ncy f. What is its frequency if it accelerates at 0.50g (a) upward, yp7jk8fc0 c) /bdrh b9    f
(b) downward?    f

  A 220-kg wooden raft floats ov j+ -n fh2f3s.8 xyal mrwofk(w5f-.ln a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, lm af-j fw(8ov.- kn5 rfxw2hl.+s3yfthe 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 instrum olbs;loude1a8 4o h8)ent are tuned to play at 392 Hz (G) and 440 Hz (;18ao4obled lo)8su h A).
(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 st s;ipku; eil;,retched 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 wavelengt;iu,l esi ;pk;hs 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 prong mr oza -qprmp;* o//:ihoves 1.8 mm to eiizo p/-rrh*a m:p/;qother side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cycles a7k22daq z h .5vtg8piper 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 with the bkpizdt72h.5 va q8ag2 oard during the oscillation?

A string can have a “free” en73g bf4am+:epqyi zy8d if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resona3a z+ q8ey4p:gbm7fyint 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 ts+3teb ehx: 0xakes 1.t ebe:+h0x xs3000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in th20++ slcs4)ubi ineife vertical direction or can swing as a pendulum of small amplitude, but not)sl20icu+ + bin seif4 both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [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 isw z)a+k6wnd5e stretched under a tension of 255 N. A pulse is generated at one n+ek 5zwwd) a6end, 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 sprinv5n9oh.y / 3 3vhqoewng with spring stiffness c3h5./ e y whqn3nov9voonstant 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? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at thka:-*fe6w tok e junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. koak:tef -w*6 What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as sdim : f;tyhcz,lt.;32cb9g f ohown 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 spr;c,fhdmfbotli 9 zt: 2y3g ;c.ings 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