Give some examples of everyday vibrating objects. Which exhibit SHM, at least d n5 yq-kyldg7)yo3(d foq8c/ approximate- kdfd8y5l3 7)qoyyn(dcg/q oly?

Is the acceleration of a simple harmonic oszx v7. f3jrd;mmg1)d jcillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximatemo1sx5nwqt115p)rah bhd)/u. gkjuux;:t g ,ly simple harmo;ts ru/15 d.:xxbm)thjw1kg q5 n,uhgp 1)uaonic.

Real springs have mass. Will the true g+9lgim rbu) x2i4p2rperiod and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massp2+b u ir4gm9i2l x)grless spring? Explain.

How could you double the maximum speed of a simplevt y5:gzz +qhlkj(o0; harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hoodl9dw i/9* k ukk/ksc0k of a vertical spring scale, and then is released. Describe the scale /9ksdd wik/uk*l k9c0 reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time whx6 fbe bg8y.8r*ufq/ gd .o 2svpam*g)en taken to high altitude? Whyabfoe qd).b6y rf8*gu8 2*s . gxm/gpv?

A tire swing hanging from a branch reaches nearly to the ground (Fig. m9 n1 k0tub8 2s5sjren11–48). How could you estimate the height of the b8nr1 bemn5su k0ts j92ranch using only a stopwatch?

Why can you make watez .bx mlqd3 bqsj58*0fr slosh back and forth in a pan only if you shake the pan at a cerxq8qdlbz0*.f sbjm5 3 tain frequency?

Give several everyday exampldkv9 xpj-n 8jigb4g .rmu9j+0 es of resonance.

Is a rattle in a car ever a resonance ph6ie9pb4 bzoqcw7zc5 6enomenon? Explain.

Is the frequency of a simple piom:os9* o .feeriodic wave equal to the frequency of its source? Why or why no so*.f:e im9oot?

Explain the difference between the speed of a transverse wave trat4qwh - bo9kvz5 *e-t-qfczf 3( ifxc3;jn f3kveling down a cord and the speed of 33hfec 4(ftt9xf-nk* k;-qcjfbzo-q 3 w5 viza tiny piece of the cord.

Why do the strings used for the lowest-frequ*g e-mfhnv*us2mvp 1 2ency notes on a piano normally have wire wrapp2vhm *nsemp2vu* g1-fed around them?

What kind of waves do you think will travel down bm 0r4ldm 8)4d 9ckyqba horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parall4mr8yd dbcm l)k94b0 qel to its length?

Since the density of air decreases wit9,;be w4ml dxoh an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wabol9;m, wxd4eves in air to vary with temperature?

Give two reasons why cir+zivqej 2v-a18h2hr xa* i0xjcular water waves decrease in amplitude as they travel away from the s221a az8 i*e-qjjrv0h i xvxh+ource.

Two linear waves have the same amplitude and speed, and otheue7,oy;*8xr u 7llgw vrwise are identical, except one has half the wavelength 7*, rveug7llu8yx; owof the other. Which transmits more energy? By what factor?

When a sinusoidal wave crossu+ od (o4n;1x7yuoahses the boundary between two sections of cord as in Fig. 11–33, the frequ;u1dosy+(aou 7 n 4xhoency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating grhbau(lwo/ )d)jrs/f:w 5;d in three segments, are there any places you could touch it with a knife blade without disturbingjg / ub;h : )(/w)rarwlsdf5od the motion?

When a standing wave exists on a string, trpfym a pi.h m57k8mzh((2z)3z c/z fphe vibrations of incident and reflected waves cancel at the nodes. Does this meaipz) 7(zc8m3p.fa2/z5 mmrhy(p f hzkn that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mighmsae.6s1 ef / 73zbhvjt we1s7j /aeve6mzh b f.s3 determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHt4my +:h5/xhcml4uuj M with amplitude 0.18 m, what is the total distance it travels in one period?+ / hyj4mtu :ucx4h5ml    m

  An elastic cord is 65 h dy8b;nie.pysc) 7,scm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” con b7e8ynpi cd),h; ys.sstant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg j4p11qccunk9v1wi6o driver gets into the driver’s seat. If the car goes over a bump, what will be to 1j1qcpu64 i1 cnkvw9he frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish ha15.gq u 2m(u7f mjvpxangs from it. (a) What is the spring st1umamqf .xu2g5(p7vj iffness 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 fdee m )oisy.fil)/ q: ,dge;(c 8siyb)ni *c0nrequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency i./( 0 i ifgeemqy)dlciy*o s,dn ie;) b:c8ns)f only 0.38 kg hangs from it?    Hz

Construct a Table indicaia- ;hgewl1h w:vh93g+ 7gt5h ppz) hzting the position x of the mass in Fig. 11–2 at times t +-phe:537ap ;lhz9h )h wg1 ztgvhwgi= 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 bdp*11dbrvc c0eq; o. in a spider’s web. The web vibrates predominately with a frequency ofbp1 e*c b.oqd0d; 1vcr 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 :vie12k;u ucd: a2dvr spring vibrates with a frequency of 0.88 Hz. When an addition2ik1 rv2:u:vd auced ;al 680-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 spring vibrates 3.0 times per second w nu ksd (7)k vyru6zhy(96-lpqith an amplitude of pzyr hu-7uk skny6(d(9 v)6lq0.13 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 omis+y so/mjy5cue+ua6* z8 i;f a SHO half the maximum vali zoyu/6 a*mess+jyi;+um8 5c ue?$\approx$    A

A mass attached to the end o(3 bi + kqc0v;m*)xwdr /6yomzjz1alyf 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 vern)d7p7j/ e e8 qfgu1zeb0zn 5mlj06nbtical 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 au nnqpb65zebm8n1jef0) djeg z/ 077 lgain?    s

  An object with mass 3.0 kg is attached to a spring g./(dunko p(-n q j8xxwith spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its eqou-n8( g.q(xxj dnp k/uilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of0mzz oe6534nxuh 5/ cpsxn f z1iu:ss8 a toy popgun 0.200 m to “load” a 0x3su6x sczzh0:u z84/ 5s fn1mniep5 o.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attachei:n02l1n o3yrhncpf 9/n2gf ad to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spr rg9p nc3/2 n2f0nhli1fyno:a ing 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 equation x = 0.45cos6.4t where xb jgw)pd)kb(f07p o*z is in meters and t is in seconds. Deter7f)kjb0gz bo)dw(*pp mine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half Kc 6t.fb:fw 8mkE and half PE? 8:bf.kt6 mwcf ±    A

  If one vibration has 7.0 times the energy of a second, but their frequenciesm00b(pta 15eb -nmc9 pwv1lgn andb c09na-tm0nw 5pgle1vbm( p1 masses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin os8fmeip ;x:z02bdbdsme b,ca jf /48j0cillates from a vertically hanging light spring once every 0.65 s. /8ed2 isz e :fm,8xb bjpa;j04cf0bdm
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs,:8at5liqkq2 5ua,jx: mt nax0 id42xe each with spring stiffness constande:x,mil5 k q5xaata i24xtuq 08j2n: t k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5wcv(/nq n rk66 *pv6mft where x is in metev ( /q6kwnfm66nvcr*prs and t 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 two examples of SHM, labeled A and l7n7nkye6ci7 jp+qh -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 fx6tnjva/rq s*),q l: = 124 N/m) is struck by a hammer, which sn6qt:a ,l /jfxvq*r) gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with sp14hfpe d(h t 5ik9te(ering stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260hep(ed4 f5t(t9hi ek1 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 sprinj *kxd.-mwgnvp *m):mg 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 tfos 0)gyi.gaxbt. gl-wj( q3nys: *p-o a fixed horizontal spring whose spring stiffness constant iwfg0bslgp-oa.( x:-tjnyy3q*sg i.) s $ 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 b( ofe6f w0kht iv+:pk)ridge. After reaching his lowest point, he oscillates up and down, hitting a low point eig( ko0w:eh)if f+ tk6vpht 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*/5kcn-cy0w/-zmp f /ve,kxd lme3v l s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it iznrnc pm8 f0un +sdy*3 i4 :om;yila09s to make exactly one swing per second? (Th 0im8in3 naf 9:n+pl4m0*ruz yds;yco at is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wher m3s vq/f26kii-0 )s+7dyxrl g ztfq.xe the acceleration of gravity i0+ti-d /x s)mz6fk 3lq xrvgyf 7i.2qss about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm ly-:j y /jaxb:j nc+/.i x2:te w+ubxhlong
(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 2tzqs(w: cls g6 ,qz.tgrams, and it is released at zs2cwtsz,.6( qt: gql 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 pendulumw pi;ybe ,pylrpxi ze/b- .17( has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjus b1li ,z (;/7yripey ewb.p-xpt the length of the pendulum? shortened by    mm.

Derive a formula for the maximum 3.imq ckutpm6 3pwc : h:eog8,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 ie aku0k5gy..dt is released from rest starting at an.keky5 a0gu. d 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 afp mn*ifye:i74 h1v x*nchored boat every 3.0 s. He measures the dismyifpni *ex*:1h7f4 vtance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of vbw4dh x)x+ 4sx)eu7x262 Hz and travels with a speed of 343 m/s How far apaxv4)+ u)b 7xxewh 4dxsrt are the wave crests (compressions)?    m

  (a) AM radio signals havucz+pco 6liybr47(1 be frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a s u+c(r b7l pi6coz14bypeed 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 longit/kq z( ;d(udfo thr)3pc9s qb,udinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus,l; c-r8jce jj6 but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what fac ;rjlj j8c-ec6tor?   

  A cord of mass 0.65 kg i/9.fdnqf5 uc+s m0epp8 f z sr5epo41gs stretched between two supports 28 m apart. If the tension in the cord is 150 5+ 9s0./nfg1f fupp5qdze8so4 merc pN, 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 oftqpppp/pl+*e7 o9 v5or qn+9t length 620 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 alp vrqt +p7 9oq5t 9pp*e/p+lonong 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 io0askm ltv5 );w(-d/y 4sndqof his ship just below the surface of the sea. He hears the ec4/)d - 5yim s0v(; noqktadlwsho 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 earthquake travel atu;r-yk,05kj j ipie,xli*; dg different speeds, and this difference helps in locating the ipxju5 ,d g-ir ;yek ji;,k0*learthquake “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 approximated by a sinusolg9); kjf;yq dzxe5o; p2v(btidal transverse wave. Assumigp o5y;2vb lx e;;z)k(q9 jdftng a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudp x ae hunccako5.--64es, of an earthquake P wave passing u h-4a6naxckp c- 5e.othrough the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured thon,o l;i/j9: ev wv/ddp+z a;o be hz9av do//l i:wojv;,n +pe;d$ 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.: q f-gxiro;iz ov6pl ng7/f; same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the twoivn :irqo- x;;lg/ o7 fzfg6.p waves?   

  Two waves traveling along a stretched string have the same frequency, but olumrjk/,tsz:re9p3t 8y2gh; ne transpo,;k3tpr 9ezluh:/y g8rmsjt2 rts three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move i2nkjc 4)om wq8b:u v7up and down a total vertical distance of 6.0 7: j8o2q mkucv)4wbni 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 toward9r skc:)pknrz k/-m+z each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at thikr 9mcz/r+ ps) kzk:n-s moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are thc5 l.t)i smkmifvt(4 h1r3e r6+ )azvse frequencies of the first four harmonicsi iavr)sm c4+.tzsre)vh t1 f 5m3k6(l?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at rns io*pe 63 m+o+goh rbt;x42294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is,+b6ip+ re goo4x3;shn2ro tm* only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates iyr cdu0p/j7w8pv9 hg9orq5 , bwubp+8n four loops at a frequency of 280 Hz. Name at least three other frequencies at which it ,+ jwhu0/c97byqbwu 9rp88vp po5 dgrwill resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency 3zi/ipi( xij zfcx xr3z-/um(nd9j7+ of standing waves is 475 Hz, howx/r3zzic(nfm-xi3j d+ 9z/(7 jiu xip far apart are two adjacent nodes?   m

  If two successive overtmbmh+2oo- +ej ones of a vibrating string are 280 Hz and 350 Hz, what is the frequency of to+-o2j eb m+mhhe fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3k9 2c0c2b3rvumh4pel 0 s ujs*.6 g. The distance from the bridge to the supk hvpcsc2e0r s42u930b* lj umport post is L = 62cm and the string 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 vibrate at 20m+03gu47 rud2f ymheg 0 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to cogue 3uf07 2m4+drymgh rrect the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate atwin3 , 7wszv6v 200 Hz, but it is measured to vizwiv,3 v6n7 wsbrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to ae6, kfoz w:o-) 7vmxz-kk fq,o small-amplitude mechanical 60-Hz vibrator. The string’s mass per uni okfzf 7)weozq,,kvmk-:6 o x-t 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 legv;z 6egiy 2m2ngth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achim6ggei2vz y2;eved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back ax ovdxks7 d03h6x*gm a60tik* nd forth in a tub at just the right 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. d*th g skdivox a0m306x6*kx 7What is the speed of the water wave?    m/s

  An earthquake P wave trau3qr:0mrg4zy ht7rigpm :s 9(veling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the bounrtm3ihsr4 : zq(g07p 9y mgr:udary 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 velocimsfpg l1:-s2xia h,slsy t 4 txq.9+il+*l)rqty changes from 2.8 m/s to 2.1 m/s If the incident wax4 ll+i:qsxrli hs1m ,.fts-l)pts+ y* q9ga2 ve crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in za- i::/xlnd xwarm air when it hits a layer of cold, dense air. If -dnxi/::lzaxthe sound 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 earthquake wave strikes a boundary between two types offd i/,n6 i-sb mw9 *ddc,qnr:z rock at a*,/iqzd:9 rm ,-i6bdcs nfnwd 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. Accok5v)l0 4p btkbrding to the user’s manual, the dish has to be pointed in the direction of the satellite, but an ebb)4 vkpkl0t5 rror 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 the Pq .omd. vv7(l;s*um iracific Ocean. As it approaches Hawaii, people obsevq(o. ulr*m.dvim7s; rve 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 a*yf5 kmj; ulmf7ta .ytpul1k+rg0 .s3 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). tajfykl7pt*0lmr1 yfu5. m +;s kgu .3[Hint: Use conservation of energy.]    m

  A 65-kg person jumps froi4 -vsmsfhn2n 2 dok79aeb (4wu v0ky,m a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves lika4 ,v kdne-k(2um27i 0nv9y hsofbw4se 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 hangingihoelx*vt d 1 .3p5rm* spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequencym3o*pvh* lri xe15.d t of the oscillation?    Hz

  A 950-kg car strikes a huge spr9jcn* tp .+xcoing at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant ofxnc9*jt+ c.p o 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 abo hxe9vnekuhhkk ou71b f01t) 2c);hw8ut 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimb1th9kehxw 0)e 7on c2u)hkh8 kv;uf1ate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm fro*ubp)6rf84 ,lm6 s)ayof bdn+1hxm ykm the center of a 33-rpm phonograph rec)bfo4a6uy ) *nml8by ,hpf m1+s6drxkord have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the eqoh/9bn5n gv, quation x=0.650cos7.40t where x is in meters and t g,ov5h q/b9nnin 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 frqu11 )a3ijq(z+dq xvyequency if it accelerjix v+)(113quqzd aqy ates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stand(jo +f1q0dmgy s on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raf+d( 0fq oym1gjt 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 musica7b8uie ,t4 fdckgsm-jry7/(j l instrument are tuned to play at 392 Hz (G) and 440 Hz (Ajcfyr(ek, ujgd si 7-/7b4tm8).
(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. 1 -m h+kvl b2/wjhg8 erapigyqs,74e- 01–33. 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 rati4h0- r hliqmw ke gaj 8yv,pe-/2sbg+7o 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 h+9bk5 b ivc8iqc) ;w bz:pld:Hz, and the tip of each prong moves 1.8 mm to either side of centericv95)lc+h :bkp:w8zq ;dibb. 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 sn e3*ybum7;y simple 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 (Fig. 11–56) will not lose contact w;snb3 *muye7 yith the board during the oscillation?

A string can have a “free” end if that end is attachnhnb0 19 han4lxi9a ,ged to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the othi 4ghn ,x9na9b0n1l haer free.

  A “seconds” pendulum has at8 cn2pm*(xbx period of exactly 2.000 s — each one-way swing takes 1.btcx* mn2xp8( 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 oscillauumz59m td* sgfcq+; u t129xkte in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the pcktqux;s 9 *uf+m z 5utm9g1d2eriod 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 p v3*x fucz0w:yb*i xv*ulse is generated at one end, and 20.0 ms later a second pulse is generated*vcxw*uz* iv:bf30yx at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffnetd6e0,zkk u*kgc,0dfss constant k. A penny of mass m is placed on top *kzk ku0d,gtc6fde0, 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 caxtc x,s5tbko c,mv(7r3 -/pq* 8w szyrane 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. What is the period of the bouncing? [Hint: Refer to Table 9–qsxvc,5o*b -m/taw7,(xc p zsrtky381.]    s

  A block of jello rests on a/didua ew 3sp4m0nh7kjf3c6d) of8a( plate 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, estimate the frequency of this vibration, given that thea0s)np/fd837fkcd e3owha(m i uj 4d6 shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz