Give some examples of eve+v.mnci phmp bj;n*4v :jy*sg(y,z7 nryday vibrating objects. Which exhibit SHM, at least ap(np insz*hvyb ,nm.*gj;4 y+7:mpj cvproximately?

Is the acceleration of a sim cao)4 j:pwp+jple harmonic oscillator ever zero? If so, where?

Explain why the motion of a pistubxs 4qhr) z,e-6nmy 5)qhj/hon in an automobile engine is approximately simple harmonic,h5 )qjqxu /s hnbm4e-r z6)hy.

Real springs have mass. Will the true period and frequency be l by bw;;ltcyale*f00vu0l9c4 wxg6c4arger or smaller than given by the equationsc4uw 60ct; bw yx9 y;vfl40l clbga0e* for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic (+ l)xxkj; kmqgklt)mh6*-ss3p h9qfoscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and thevnv ebcy(5.-wn is released. Describe the scale reading as a function of time.nwv y.5v-( ebc

If a pendulum clock is accurate at sea level, will it gain ord r,t)*yp,02lhjho q x lose time when take2tj0rh*loy , qhdp,) xn to high altitude? Why?

A tire swing hanging cskov re-p5-*from a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stope- -ovr5 cs*kpwatch?

Why can you make water slosh back and fu2 xwyq4cj((c orth in a pan only if you shake the pan at a certjwcc( ux(q2y 4ain frequency?

Give several everyday examples of ree)g n8+s)znv ysonance.

Is a rattle in a car ever a resonance phem tmp) ./ojb9fnomenon? Explain.

Is the frequency of a simple periodic wa1lzq)p9vescz2qlk 2* ve equal to the frequency of its source? Why o )2z2l*eq9c klzvsp q1r why not?

Explain the difference between the speed of a transverse wave traveling mtwlq(b. n*b ;0 jxkvo-* 8pwpdown a cord and the speed of a tiny piece of the w; * x 8bv0np(pwjk*-blqtm o.cord.

Why do the strings used for the lowest-frequei)fq th0-cm 3t q2lxxl5 vqpk-vs884tncy notes on a piano normally have wire wrapped ar8k)3vlt0 mxvf52tp -4hi x- qt8qclsqound them?

What kind of waves do you think will travel down a horizontal m*:2u7we*ok 9q wcn .vofqdf-t etal rod if you strike q.u f*:d -to cv2oq9wf ne*7wkits end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increas6xk )7f0ywro 8lda3nue in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temran d06u8 fkxo)wyl 73perature?

Give two reasons why circular water waves decrease in b.tyvwt1p4) xgyyjv(6ptz (ucir3l4r2u0 1c amplitude as they travel away from the sougt cp(ytcvxuryt y4r3 1j2 pl41v.z6)b0 iuw(rce.

Two linear waves have the same amplitude and speed, and otherwise are* 3amqcpca ;r**7 kayr identical, except one has half the waveleng*cyar* ap7kca3qm *r;th of the other. Which transmits more energy? By what factor?

When a sinusoidal wave cross0 jui bp*f/vu/es the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocit/ b/uivj0fp* uy do change). Explain why.

If a string is vibrating in three segments, are there any places you could t*grqi*+k f+e:a4u vwg ouch it with a knife blade without diw*u+kg+*v4:qf ri eg asturbing the motion?

When a standing wave exists on a string, the vibrations of i tl+fb6b lm ,ptt3w4n+ncident and reflected waves lwtpn+,6mtb b4f3 tl+cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being tran ,5hz)bxdiq(ysmitted from one place to another, how might we determine whether the energy was q,ziy5( )xhdb being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM wb r ;z*w jme4hbq( ;,x2pzmr0with amplitude 0.18 m, what is the total distance it trav2;pebzwq;4z mwr, xbjm r0*h(els in one period?    m

  An elastic cord is 65 cm long when a weight of 7a1*knb, cve05la jvhhsiu 1 /-5 N hangs from it but is 85 cm long when a weight of 180 N hangs fhva1,ai-s/e v h0cnub k1 lj5*rom it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm whd3.ejgn 7vq0 ien its 68-kg driver gets into the driver’s seat. If the car goes over a b vie7d0gj. qn3ump, 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) What p+w3b7qqv 8 .a jgy7,x9jb wwgis the spring stiffness constant wjgjpa wq 8y79x vb, +wbg.q73$\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.g:f24 coe1fhofp s7* e0 Hz when a mass of 0.60 kg is hunefp o4oh*2fs1eg cf 7:g from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the nb6 y64d qj;x*n,nqxy position x of the mass in Fig. 11–2 at times t = 0,t =;ndy*x b4y6x6 n,nqqj $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 spi e.w(, ;5z 4(bovaccmgot0 x 0dybnpaeh,ab1 )der’s web. The web vibrates predominately with a frequency of 4.0 Hz. 0o1v)( a ebmb wpzh , ny,(0d54;oga bceatxc.
(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 w v-l b :ru+)npb4 wj9*cqxpzz5ith a frequency of 0.88 Hz. When an additional 680 -bvzcxnp 9p l+:*4)5wzur jqb-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a o ru9a.zse,6fspring vibrates 3.0 times per second with an amplitude of 0.f aeur6.o ,zs913 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 halg82s 8pfjv rg) j) 7dq5zbewpnbp2. d;f the maximum value?beg)7) rpj28sq g dd5j.p;f zw2p8bnv $\approx$    A

A mass attached to the enw4kdio cu;g).b) gv6 vd 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 stretchesg, )phnnp ( ,qejgu.phrb/*) g a vertical spring 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 againp) gnq (h n,g ep,*gjrp.hb)u/?    s

  An object with mass 3.0 kg is attached to a spring with spring stif1b9u/y pxd 2mufness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium posmbyup 1/2x9duition, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m to ppr2)qzkv7 0u “load” a 0.180-kg ball. 2q r0 pu7p)kzvWith what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionqq2wh:k9k;zjb zlvc2,- ldxk. . ,farless surface is attached to one end of a spring; the otherklv 9xl:zf ,ab 2qz.-k,kc.rh; 2 jdqw 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 tos emf m(ph33u1 the equation x = 0.45cos6.4t where x is in meters and t imhesu(fpm1 33 s in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO h5t) (we,ulqr .;+dluro:yjel e m:dz,alf KE and half PE? ± +5o r,lryd llm) uq,uj; ed .et:zw(:e   A

  If one vibration has 7.0 times the energy of a sevs5o;vk)h v ,p3iqg0 hw3daf7qglmg5,+ -zq ocond, but their frequencies and masses are thh53lvo 3va,f q,z7idk-g5+q)g ;h vmps qgw0oe same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a h djcg-w 3.k+8 dfk)suvertically hanging light spring once every 0.65.-ckgdw8f+s)j hd k 3u 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 paralvtvbw 4-xpb* 7 frfgg/ +)wa(llel vertical springs, each with spring stiffness constant k (74w -*r fv+gwbxb( pgvtl)a /fFig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t whe-zsq 8lnx (:were x is in meters and szx ln-w:eq (8t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows twe)vh7, 2qjx uno 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 = 124 N/m) is ghsg +j9cso+zy kxo-z 2/)3thstruck by a hammer, which gives the mass an initial speed of 2.96m/s gh2kzzcy hsg-+j9t/ x+o3) osDetermine
(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 witpif3htt fh1c,+h,m*p xy70 sgh spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 7,ctsmp+thx ,i p *fg03f y1hhkg 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 tw2z ix. :jnz wtjfeimwfr: 0(s/rqi+24o springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixcg nd:mhv a.j(zm0-( 2 /rdriued horizontal spring whosraz(0 /m rjncu vd.m2i- h(dg:e spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. t. os0((dvdyw After reaching his lowest point, he oscillat(sdtd0 wyo.v(es 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 vibrav(fha i--b;5qb 0tzuk tions in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per s jkdj.ttzc-fws, *3f jr,c0/recond? (That is, one completjwktf-0d/cr,.,3 r*j cfjz ts e vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What i n qtusomd*i51mn530t,fp iq/ s its period on Mars, where the acceleration of gravito0mt f*i 51 dspnm3, inqt/uq5y is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lo8ztj m y02s2mlng
(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 3659ax fd0:p6h,qa ij jo1 grams, and it is a ,dx091qjof:6 ajihpreleased 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 p2*laez4sz i8h bwm6jbsc8 9x3endulum has a length of 0.9930 m. If the clock loses half a minute pji8 c 3 s8wza2ehz lm*sbx64b9er day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speedy491h ppx q0mz/bzkru:fa zt/r, hi5 3 $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillaq ;1hhrqr+0w xuct36 ktes at a frequency of 2.5 Hz. At it is released from rest starting at an an x1qrc30+tu h;qhkr 6wgle 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 wavs oxqjw4/ry (u 4g89wee crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast aow84q4w/ urjxe(y g 9sre the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels withx em-aoh/7:76c )f4r)qc 9qlsez a:dwttu ;us a speed of 343 m/s How far apart are the wave cez tf-asx4ule;9 rt)oq7: )wua6d:7c cmhs/qrests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 160m(rk 3di23xw4 cet 0kd0 kHz (kilohertz) and travel with a speed o4ecrkik( 3xmd t32d 0wf $ 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 ky vd* /s*qu wfpwt/-4of longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulusr+egkk4 bp5d.v54:+a iy r3 /hasqczj, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be a3isaz.:rhvq+ r54+kc y5/pdgk j4b egreater, and by what factor?   

  A cord of mass 0.65 kg is stretched between twoe)hy flxw17 53za-fq x supports 28 m apart. If the tension 3qz1)fw7lexf x -ahy5 in 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 connected to the top of a hill by a steel cable of length 620ej/qrs)ip70 f m and diameter 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 retur0 7qirfp)s/ jen.
(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 x k ,v27qtf)u 86dh wesgt45vtthe surface of the sea. He hears the echo 5u,)g vd wefts87k6h t42qxvt of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthq;r0h.es mvp64 1;rr4qqygzp 7v tgd)fuake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance t er .q )yv0z;r4p 7t;1 hmfsgdrp6qgv4ook 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 approximated by a sinusoidal trg2 t qs:vxk ,a6 ;gp*,oobhb,dansverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies)od,t,g6q s 2;ha:,vk gxb*opb , what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) t1fbhr: xd9i .yqqd -u/he amplitudes, of an earthquake P wave passing through the Earth and udi/fr :-h9 1y.qxbqd detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an eadk/h0(*f s gaqjbv5t9rthquake wave passing through the Earth is measured to be jbgts( khd5*q0/a 9fv$ 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 ofmqoc /)tz(b vp1.gkmggpk3;6 the same frequency travel through the same portion of the Earth, but one isop 3cz;/kqgkpv.6) tgmm(1 gb carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequencyetgu)yjy d.p*5 )/ ut6c:em7ynyv5ka, but one transports three times the power of the otna56u ))ke5u7 :tt dj ym.eyg/pyv*cy her. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up anh5c.fey3ro6qa;v. icd 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 bug’s q;vrfc 5c eiay3. h6.omaximum KE change?   

The two pulses shown in Fig.pjgltjltt js u/n,vn)/z0i 4t6 kc/-. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few mom0tp jg/4 . lt/tktu/i-)nz,jsnlcv 6j ents later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 H/bk8f eahmk9l- al*v 1z as its fundamental frequency, what are the frequencies of the first a8-l9kfkla h*v/b 1emfour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingererj,pg p)-y8 .tlds(wbd. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, jw) brpt d(.8,psg-yl only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates i n4p;m ixwdf2l pu7,p.n four loops at a frequency of 280 Hz. Name at least three other freque; puf,xnp pw7d.mi2l 4ncies 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 the7 hc;4p9i)u csgmlwu0 frequency of standing waves is 475 Hz, how far apart iumlcusp 7)h9cw 0;4g are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 r.jm o:haw94gn g8im+Hz, what is the frequency of the fundamentaj+ nwrg 84:amo mg.9ihl?    Hz

  A guitar string is 90 cm long and has a masa. ws0 gv9lew2m90gmhs of 3.6 g. The distance from the bridge to the support post is L = 62cm and the wg2ahe.m 9 00gwms9lvstring is 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 vj6yr 6+sw-n nwo 8vrb/ibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct thwobvsrjnw86-n6r/ y +e 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 qxwg2wyrg(t1mhp.j /b0y ::w it is measured to vibrate at 205 Hz. By what percent should the tension in thyy( b1prw02mt.x wjh/g:qw : ge string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a smallj:z1v4msl* )oxbt c wos;e4i--amplitude mechanical 60-Hz vibrator. The string’s mass per unio ) sx z:vm4;le14wobi-*tsj ct 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 be adjusted by moving thi :mfgs+5y(ne e pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 1+( :ne iyf5sgm0 cm and 1.5 m?   

  When you slosh the water back and forth in a q.1 5psa gamn/tub at just the right frequency, the water alternately rises and falls at eaa1 amnpsg/.q5 ch end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within t2xnqv,7)p3e edp- 1m* ct khzg2m/hblhe Earth be e d7bvmc 2hp)m32gx /*q1n,lk- heptztween 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 chdkl zv2 j)vc.)anges from 2.8 m/s to 2.1 m/s If thzv.)jv2d klc)e 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 layer of cold, dense airzhru elztdp3:;0;3, lml:hgr . If the sound wave hits the cold air in,z;:p 3r3rh0ll: th e dmzgl;uterface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rock atr(u seblrf2;au* h9:g 8l8nev a (hsg*e rl2; n v 9ab8uef:lu8r38 $^{\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 diameth9m4 ml 2( )vdng-s9/queu+p h)hp ruaer. According to the user’s manual, the dish has t49n+pp( r2luu-hg9d )v)hmh/ qaume s o be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across thedgv( gy6g ;t m(tf)jh9 Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in thegh;(y)9 g tdjvf6(mtg 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 a spring stiffness constant of 550 kN/ g88zk od d 1warv6r,al2bf*g.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 (ap*o.rwdkbv r 8 ,fala681gzgd2 proximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a windlpavju -grqe0 m4 :sbka yg/9o c*+9ec(hjc14 ow to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves l jcm+(9u4 ag:*ackbo9lev j/pc41r se 0qgyh-ike 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 hanging spring. The mass then h9 ta9inlbj-ed 9+z2gfalls 33 cm before it stops and begins to rise itl99z jbd+ah-ne29g. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a hug7 ( gop kxp(su3b(vy5xe spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spring?3py57xo(gs ( x(kuvpb    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 ,rs8pnt en o47 up:xjb4 m,g-ycm) 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 gupb, jn,s4e -8 7xo:4rtymnp (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certaim+c34wkr h *hti+n7 jdn groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequenc7+h3cimhkrd*4tj + w ny of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the eqk 97jpbj/k 4xi:nuh 8k afp4v6uation x=0.650cos7.40t where x is in meters and t in second jp48:4v6hipnbku/kx7fk9aj s. 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 frequene g 6n b ou2j(e+q+/hthj)ol+rcy f. What is its frequency if it accelerrlhtu(6 +bqg n)oejje/2+ +ohates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Whex(ha2 xts(1jm,1 ummua*n )lmn a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whm (,(tsx xju2h1a m 1nm*)maluile.
(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 Hz enyg)uz 039kb(A). 0bu gk3y 9ne)z
(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 t2u7ek.ktz02 3qfq tmtwo-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy k3te2 qm kt. q07fz2utsection versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prj(ew:hodgvz *x4r * ovxq;,b/ong moves 1.8 mm to er4 gw :* oevx*h /(xvbqjdz,o;ither 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 s 295ia;qzjyu1kmgoq++5c0 du p d9plwa 0sy; kimple harmonic motion of frequency 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 (u 1;myq5z0sak+02puk9op i9 dq l gy5ajd+wc;Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attachedvi1 i5jq s1gn*tvl7 k; to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations o vi 1t q;*ijs7l1vkng5f such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactlyk3/dk0(b dqx ww ;p7bp 2.000 s — each one-way swing takes 1qk0/w;k(7d bx 3 bppdw.000 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 the vertical direce1i o.5fad yd(tion 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 swin o(i.af 1eyd5dgs, 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 stretches x*ljd60z(m5 b h9qxsd under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is*9bsxshz x 6dmql05 j( generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended frm ymrdu:; 7m 2j9sllrsj bkz:-y6:hn;om a ceiling by a spring with spring stiffness constant k. A penny of mass m9yz :6:2mljm h;7 :y;r sjndmks rlub- 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 the junkyard. The steel crane cable is 2mn ,gw4u z7py1(4obra 2 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hio,y14z(arp wg74 umbn nt: Refer to Table 9–1.]    s

  A block of jello rests on a pla1 w;c vd-tc*gvcdcr;gc5w.f 5te 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. cc1vcfc5;g ;g vtd . dcww*r-5In 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