Give some examples of eve96/osjuhjor8 ;kw d7fj7 lv;vryday vibrating objects. Which exhibit SHM, at least approximately?ju7o8o;;/ j7v6dr k hw9jsfvl

Is the acceleration of a simple harmonic oscillator ever zero? Iyxh0.eru 2q e*4hjc5a f so, where?

Explain why the motion of a piston in an automobile eng7sxps2m vf/h6 ine is approximately simple hars/xv2sm6f p7 hmonic.

Real springs have mass. Will the true period and frequency be lark0.,/ehujx f sger or smaller than given /,js0 .hfk uxeby 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 ham:gudhh xo0) -rmonic oscillator (SHO)?

A 5.0-kg trout is attached to the how*fwkaygx6hxe x2.t) g 79 n+qok of a vertical spring scale, and then is released. Describe the scale reading as a function of time)7w+t f9qg*xah 2ng.6w xxkye.

If a pendulum clock is accurate at sea leq,)nh6g(te 8atnn;bgpfftd 47 c9lh)vel, will it gain or lose time when taken to high altitude? Wh ghttben6t9h)87ln( g f;dn 4pf,ca)qy?

A tire swing hanging mpa; a 7p :zxlm-.ga4ofrom a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a m p g a;plzox-am:a.47stopwatch?

Why can you make water -51 y ev8uuhreslosh back and forth in a pan only if you shake the pan at a cey5 8h1ueruev-rtain frequency?

Give several everyday examples of re v 4s9p-q bqu,hs5p0ojsonance.

Is a rattle in a car evei6(nk4xm8yhdvl1 / lur a resonance phenomenon? Explain.

Is the frequency of a(8myp+h1 t1 0xmg9c eubv(jwc simple periodic wave equal to the frequency of its source? Wmxbyu0c +v9(w8etg(j1hmcp1hy or why not?

Explain the difference between odbu9rn312ex v(7 sx2fdg.hx the speed of a transverse wave traveling down a cord and thbn7su2 .ex 2rd 9xvh(x fog3d1e speed of a tiny piece of the cord.

Why do the strings used for 28av7d c8 1zm dmgfxe)the lowest-frequency notes on a piano normally have wire wrapped around the2 x7 m)88z1m gcevafddm?

What kind of waves do you think will travel down a horizonta aj33,unppn t c,k.lr4l metal rod if you strike its end (a) vertically from above and (b) horinl3,p3r 4j pck.,naut zontally parallel to its length?

Since the density of air decreases with an increase in temperatur /:dm9juyni(cy6dz+u 6r u bx2e, but the bulk modulus B is nearly inuu :n 9yyr6mcdzu+( d6j b2x/idependent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in +zco 2a0 bcq+vgdc h+5-xwoq nn.j 47bamplitude as they travel away from the sourcx+con z4n+bjw0h2cq5c+ 7 qda.b gv-oe.

Two linear waves have the same amplitude an4pos:2e( chp)g,w dmqd speed, and otherwise are identical, exceptpw,m )h4c2d eo :(sgpq one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two secw dk(p 9yci(e/tions of cord as in Fig. 11–33, the frequency does not change (although the waveleng i9(dk cwep(y/th and velocity do change). Explain why.

If a string is vibrating in three segments, are there any(1mfvf)oot d: places you could touch it with a knife blade withouf m)d(to:v1of t disturbing the motion?

When a standing wave exists on a string, the vibratk /:cn)z ,zvq4dh:z uyjd0rb6 ions of incident and reflected waves cancel at the nodes. Does this mean that energy vc6hdb)4 zqnd,ujzyrk:z/ :0 was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, howmfzua2pkk6nuh s .3i ,+ clw:+gkk h96 might we determine whether th++9 :. a 6pgukh h32iz,ks6lumckknfwe energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distan0 idvwrr :6oz6tzfj*8ce it travels in one z*r6:j z6otidf8 0vwrperiod?    m

  An elastic cord is 65 cm long when a weights fyib:x8 . sajt5)qh- of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of thistjx5-h q.ys bfa8:)is elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm wh efjxg( 2mr.lq nh8c-6eg; ad;en its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibrati6m ;8jc 2(q rdn .;eefgxhl-gaons?$\approx$    Hz

  A fisherman’s scale strdp ivzs0d3k0+ etches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is ti0 s3p+zkdv0dhe spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates wizr1p. zio-xv tu+v ii3.5 hmo0th a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from it? vum5oh ox-r i z .+t.ii301vzp   Hz

Construct a Table indicating the position r vs1gsgdn-) vktl5)kn 58ej5x of the mass in Fig. 11–2 at times t =tk1 ) -le5vdjgsn85 5k vsn)rg 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 in a spider’s we.bj)g; a- 3fgkc pq:feb. The web vibrates predominately with a fref.)3- jpgfg; c:a qkbequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency o0q+r(lxwv8k e03 k8ryhqocc1f 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the valuexk(+kr 0lyw8c 0qhv83ceo qr1 of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an o(e-r9 6qvk tgamplitude of 0q (kre-vg6to9 .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 fromver6:p*v tvq vohj2*ax) x) 8x equilibrium is the speed of a SHO half the maximum value?o tav:reqx 6v82)x v)p**j vxh$\approx$    A

A mass attached to the end of a spring is stretched a distand1wp9 *jcpq a7yu 1kb3swn)t; ce $x_0$ 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 strt1pz5(u ,i ) doo7zuftetches a vertical spring 0.315 m. If the spring is stretched an additi,(u)pz1ttz 7u idoo 5fonal 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spro q +nvk433ryzing with spring stiffness constant k = 280 N/m anorq3z +n3y4kv d is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N t 9;g. 8yvbux*3 *z9 amkxdvvkqo compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave thvayz9vdgv.* b 83; *ukq9kxxme gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to o h z 1)8b3h0kps:njtxrne end of 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 s )1 j xs0th:p8nhrzkb3pring 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 x jf0md2pe5d u )is in meters and t is 5pj2md )u0fe din 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 half KE and half an3 /m rxybh y:,01pwwPErw3/0w m,xyb ay:hpn1 ? ±    A

  If one vibration has 7.0 times the energy of a 4ze /(w-)gj)m+z30a1- +nnaz dkqtufd hfhcnsecond, but their frequencies and masses are the same, what is the ratio of their amplit/4)ff j+kaz-(zchnhnqem-ug+d0 3 aw)z n1dt udes?   

  A 2.00-kg pumpkin osci;;whyq0.dch (, egv ekllates from a vertically hanging light spring once every 0.65 s. deh( c. h kwq;e;yg0v,
(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 identil oze;b z8d*-qcal parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the fqzd*o;b l8-ze requency of vibration?

  A 300-g mass vibrates according to th hv7(yey;.w9fgj7z9bf j 0 nwojg l:8ze equation x = 0.38sin6.5t where x is in melb j9 f0e 7n(jf9.:7yzwgovyg;hzj8 wters 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 twoi wiyqfunu7v:.v( : x( 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 horizonrdd y0z,u(7/obvff x2tal spring (k = 124 N/m) is struc0bdxuf2 dr 7 fzovy/,(k by a hammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with ;k-4y/ wt bl-tgpyv u(,d8ep*gdnl5d spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point el d*dgvt g4-;5 d8wtynpu/by-(,pkl(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 spe: 9k9estg q2x5jzse *lnb ,n(rings, 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 0.60h9xm 9+ nqcw8j0-kg block attached to a fixed horizontal spring whose spring stiffnesw9q+xm89ncj hs 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 maqq/jzsm i:ccy/ g; q7/ss 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillate/:qsgjcmc 7 /yz;/qiqs 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 vibration.b-tqp, qa gjgr6/cz2mh u0w,s 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 pert1ipuxe5v 3n4 second? (That is, one complete vibrativ5i1ex n3u 4pton takes exactly 2.0 s.)    m

  A pendulum has a peri0fqtr, q m)x 8/xxzqpso:8 fa5od of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Ea:x/ 8, 0pq8)s oftxmf qrqaz5xrth?    s

  What is the period of a 3lzg4 )pxtwew qoghv 7 4e)9,asimple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob sb+-b:n fm agqth*,f;u9 mrn,ol)/ grhas a mass of 365 grams, rfo * ;ubtf,smg)q+b9g an-h:nlr/ ,mand it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clocxf j) xi:z: :.vzqw;bgk loses half a minute per day, how should you adjust the length of the pendulum? shortened by w:zjq ):fb:x.gix z;v    mm.

Derive a formula fors 7z ;hy)::fsws 1icbj the 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 oscillates at a frequency of 2xv7 )q 4f /dv-edxbh6l.5 Hz. At it is released from rest starting at an lv h6/x- qed)7xvfd4bangle 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 wavek-yb,55ikhq 7c-hb (us3 nwxx mon/7e crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two (7 -i 3sk/- yonuhqh,n5bebmxxc7k5wcrests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travel rr j/mw), :,rd:qiozhs with a speed of 343 m/s How far apart are the wave cresthj d ) i:,r:wmqorzr,/s (compressions)?    m

  (a) AM radio signalsunj0-h5bje sb 0km7l4 have frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a sjmsku7nb5jbl h00 4-epeed 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 longitm++zohdwd :ssyle l b6mk3487 udinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as thl)tgvddv)3ofsx29 q+ d a4n4oe other. In which rod will the speed of longitudinal waves be greater, and by whaf)sa v)og4ldqt9d xd4 +n o3v2t factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m quf 7eg 2mfkz+ saa7,-apart. If the tenszfga, -7aeq7u2ms+kf ion 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 l3 rpwh) atu0;s 6-lkkbength 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sendkbkt6rhl )-03; aps uws a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of 6(mysvb brwcq+jjunalpwj10. 77-p ;the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep isj +6 cjayb17pv7r np-b0ul ;qjsw .mw( the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, agx+ ugl2ubfuyu w34o*/l2rt6nd this difference helps in locating the earthquake “epicenter” (lu22w*+u/ 4xy6buur3lftggo 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 sinusoidal transverz3+jch3wm;-rt2pls im. ( xlg aex0-p se wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contacttmxsm3i0l p2 zrheapx -.+-;l wg3jc( with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) thenzgi ewc6i26j5 g-hj w7+h 6gb amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and h eini6 jc67-6g+ggbj2wz hw 520 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is meqq a38/ y-.zzrdujn z6asured to be ud8jz ny.q-z63 rzq /a$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same pl. ncr-;- i lesesu0dnq.*y ,hortion of the Earth, but one is carrying twice the eel.n*ld cr0s-.-qhs y; u ine,nergy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a strt 0vjecn5h ;1i1gc:dgetched string have the same frequency, but one transports three times the power of the other. What is thh0: 11 nt;cj iedgg5cve ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total verticax)xh8g . ,unoil distance of 6.0 cm, fr uoix,hgx).n8 om 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. 11–52frd +dm:7 qv(e are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of therde(m7fqvd+ : 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 at 440 Hz as its fundamrxe f3 /l hf,-ukt+a1cental frequency, what are the frf-xtuh l1e+ /, 3frakcequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will iu+ tss +*yz; r*8*pppao hu5iat vibrate if it is fingered one-third of the way down from the ensyz*iao+8husapu*p5 pr ;*+td? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 283r;-iuw8vq iw 0 Hz. Name at least three other frequenq-ir ;u8iw3v wcies 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 the frequenm+27qigf s:ywuq p7b 3cy of standing waves is 475 Hz, how far apart aup:q7fqs 2y3 +7b iwgmre two adjacent nodes?   m

  If two successive overtones of a vibrating string ar,jk8 zp8 apiuf*fu8x 8e 280 Hz and 350 Hz, what is the frequency of the *,8fx ziufp88a8 ujpkfundamental?    Hz

  A guitar string is 90 cm long and has kf kc8.3+m clp*tbkj; a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtonekt;cbf l8 *k+pmc kj.3s?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but 8y8:3c)qi/f tda ygn mit is measured micdgtn) /y38a y8:fq to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibratj3 vzvvk zr i1622k6ote at 200 Hz, but it is measured to vibrate at 6viorv1zk 6 2tz23vjk205 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 ar3 r12 dkno*:*pjlpaottached to a small-amplitude mechanical 60-Hz vibratoao *1n* pr:d2o3lkprjr. 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 be adjusted by moving the -gi3q g x)9ldepulley. If tgdi3g)ql- e 9xhe hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the wh qy9scy /r66+nqy 0vlater back and 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. What is the speedyn09l6/qs hvcr 6+yqy of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within thvqf88 ns12xlqje5b1hd k7k0s e Earth between ts7xql8b 1n5khe01v sq2f dk j8wo 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 veloci. wcuy n) d50+:nwoasjty changes from 2.8 m/s to 2.1 m/s n w50d+a:)sj uncy.owIf 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 itgl)f4cz0z c 9u hits a layer of cold, dense air. If the sounf uz9c4)cg0lzd 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 wcg3gj( h* w,3fg 5boirave strikes a boundary between two types of rock at a 38 (5cfw3,hr i3*gg jogb$^{\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. According to the user’s maw+ c*0 msizmo(nual, the dish has to be pointed i+0w s* i(mozmcn 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 the//tjs ;amcw7 f)s sfh- Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsuw js-fs7 tc asfm/);/hnamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffnem 3bjh-1pyzemx-vcxd:hi + //6iodu .ss constant of 550 kN/m Find the maximum compression x- id3m:by//mic1 x evz.hp6 hj-+oud 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 conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18a,*m4xp4ve amrvuj2 ( m below, which stretches the net 1.1 m. Assume that the net behaves like a simple s ev4x2j4 a*mm prauv,(pring, 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 masewk4fxc6p1 t0 s then falls 33 cm before it stops and begins to rise. What is the frequentkxe604cp1 f wcy of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s f kq0v hkqyamk)1k2*w) af x89(Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness c*)1 qam9 8kh 2kwxq vayffk0k)onstant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the r(sadb .,dxo oexi;j ;;ight pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate th d x.(esx ;,ojb;ioa;de speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm e(lpddcrz7sfg(6h9 8ms-a p/from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the ff6h zreg(9m-a/sd dc8s p(lp 7requency of the sound emitted?    Hz

  A 2.00-kg mass vibratt.ycvk 4s83c jes according to the equation x=0.650cos7.40t where x is in meters and t tcsk4.ycj83 vin 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 frequency if imh gqaf+ 5k/qewi)z:(t accelerat5+h mikz fq) (we:qa/ges at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man s 0y b p)ox-nw;ln07sthtands on the raft, it sinks 4.0 cm deeper into the water. When he steps off;hpx0 0 on)b-7lys wtn, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) anlq970nxsf ddvd kwn39; e hz 8sz,w-.jd 440 Hz (x9 0 ezv w7dkjnld9 q s,f;n.8zd-3shwA).
(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-/bx,v(ux 0. / xesvtv-yls cm.o;1(fpm yd br/part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength gre -(x./ / msbxp0exysy b m(tcu, v;rfdvl/ov.1ater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each pro7av:n0ow ..w/-g6ir9e mdviq0p nrq lng moves 1.8 mm to 70 re9iaw :r m.pqd0vnvw. i6gqn/ol-either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cyc.mz gqdp1uh 31les per second. What is the maximum amplitude with which the end of the bo1pqhgu. z3 dm1ard can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that enlqy+6qv7 jmg8 d is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such q +vg mqly76j8a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exac- 2 yqv4r ;sos7k 5dtvch0wmu2tly 2.000 s — each one-way swing takes 1.00s4d5yuv-2; q shm7rvw2 kto0c0 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 q .shmv(g8(gpmk4c/ g spring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amou smk(gmgqph.g c(/v48 nt? [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 25br;crrjdu3q jh/ yq19z: -ne2 5 N. A pulse is generac; byj1e/-:ruz9nq r 32drj hqted at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with springebe4z0k fx z+/ stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that w z/4xe+0kfzb eill allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg zg8xdo9r-knvbg) 3e y ,p( 0d:alz eh*car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the carz*xb,gd a 3 9 hkd:pov8y0()lgenr-ez bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives the dlli) : ty787qkxsjs/wimensions 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 vibxl :8 q7wiyjts7 )k/slrating 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