Give some examples of everyday vibrating objects. Which exhibit SHu8pkt+d:j j (sM, at least approximatel juksj :(+dt8py?

Is the acceleration of a simple harmonic oscillator ever z kp 6:yqi/mq37 (; hvcur ,ql+xuqa(vzero? If so, where?

Explain why the motion of a piston in an s 4y) r5i:g7txb5cv/ lqr/cc cautomobile engine is approximately simple :rl y/4c/rst5c )b7qcx g5icvharmonic.

Real springs have mass. Will th j(op4 l*xp0mc g(rt)ce true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Exp(mc)j lto(pcpx4 *gr 0lain.

How could you double the mas hc7wmp9nc0:c 8 q2uo oiqjeu54(b,aximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached toxp20p8xi:xed;r3my y dq: g: t the hook of a vertical spring scale, and then is released. Describe tr8y2 :03i mxdt: d;eyxgq :pxphe scale reading as a function of time.

If a pendulum clock is accurate at sea level, willhn ty gji 2.q2z-3:.lugcsp f+ it gain or lose time when taken to high-uit+pfn: lz.y 2.ghc j sg2q3 altitude? Why?

A tire swing hanging from a branch 9:dhjqhc:n*aru,do7.h 40 b-r mcj clreaches nearly to the ground (Fig. 11–48). How could d r h7mdj4-lq9ch0 h,ccbu::o. n*raj you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back z+xjusx;bnad4 3rm6s7r68 g dand forth in a pan only if you shake the pan at a certain frequen7xsgd4 bmxanr83 ; z6+ usrdj6cy?

Give several everyday exampl+ bgfhx6 umn+;es of resonance.

Is a rattle in a car ever a res yc5ljol4d6b4x k9ub g)kai* 6onance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the fb+sz: d/pcmq qpif)rww33i3i( d:4 dzrequency of its source? Why or w: wm)zdp di 433f:pqiw+(c 3dzrs/ibqhy not?

Explain the difference between the speed of a transverse w c4 +, frxi6clk5wzu2oave traveling down a cord and the c+cuk6z5l,xi 2f wr4o speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes:99va qt)crq di gq2b5 on a piano normally have wire wrapped around th 2qgcv5):r9bqq9ad tiem?

What kind of waves do you think will travel down a horizontal metal rod if nbpv38 ff)j)l you strike38fjpl)bnf v) its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with ann7 y6hs;)uur:(a h ur16nr7y)j cbqzr increase in temperature, but the bulk modulus B is nearly independent of temp)(hbhay7 1rqu ns6 nycu 7uz;r 6:rrj)erature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrealvxv,,- bevs -0(c al*d*ot lqse in amplitude as they travel away from (d-a bx-vl**vqcll0t, veos ,the source.

Two linear waves have the same amplitude and speed, and otherwise are identica9r;/r/5nfjjmejanr g5 ax4 :cl, except one has half the wavelength of the other. Which transmits more xj nnfa/cm49g/ jrer ;j:ra55energy? By what factor?

When a sinusoidal wave crossewl +v )b9:akj0uar4c+hyzw f 2y6t2cxs the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelenccy a4+)j khu2vzwx+2 bltw9:y a6f0rgth and velocity do change). Explain why.

If a string is vibrating in thre*f q4b1yp)ycf3 ax 0ywe segments, are there any places you could touch it with a knife blade without disturbing the motifqx)p1b 4a* fyyw0yc 3on?

When a standing wave exists on a string, the vibrations h dtaw,p4 0zla/8a .p,a( ubzzz;/kuiof incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explaikz(iw 0a z, pzuhlupzaa4a;d. b8t/,/n.

If we knew that energy was being transmitted from one place to another, how m+b2q-r5.+c dbn1 yjcxk 4nq uaight we determine wh1-q4jn+ ayc 2ndx.+kqcbrb 5uether the 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 hg/x6usw.rf,vf q f60;4- trgsi 7gdpdistance it travels in one periopggq/f 7;u tr-wfrxig.f 0,h6 v ss46dd?    m

  An elastic cord is 65 cm long when a weight of 75 Np 6e-1jnuzh g: hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?g1zhn:-j 6eup    N/m

  The springs of a 1500-kg car compress 5.0 mm wq hxjd7pkuh39* ykb1 :hen its 68-kg driver gets into the driver’s seat. If the car goes overyj b h317 :kupdhk9*xq a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (*;; uin*wagsyr p3 y:h3lcj4q a) What isns li ;cy wg;u*4arh:y3qj3*p the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is hyta)e- a-vtv z55j cx3ung from it.ta at) v-j3vz-yx 5e5c What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the matj5i:emn 8y 6rss in Fig. 11–2 at times t 6 my ijtnr:8e5= 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 0a)*r gvmur+g s +;u0:kdpdc9u .25 g is caught in a spider’s web. The web vibrates predominately with a fredv)r*uak muprg ;0gd u +s:c9+quency 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 of 0.88 Hz. When an adkct3v57 fc ll 11,p eyp6yqz(tditional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of 3 (v pq feytltckp1,67yl5zc1 m?    kg

  A 0.60-kg mass at the end of a spring vibratesfpmzuyh6. j05 3.0 times per second with an amplitude of 05fhu6p .0yjzm .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 oiqf c2n5 (z:xof a SHO half the maximum value2zf 5n(cxioq: ?$\approx$    A

A mass attached to the end of a spring is stretched a dista5l k c6w bxd/2bm4bw8ance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is stretc(w3 us)e sww:nhed an additional 0.130 m and released, how long does it take to reach the (new)usn s3)(eww:w equilibrium position again?    s

  An object with mass 3.0 kg is attached top5im dlke)-v. a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 p)mi.5 evdkl-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 to compress the spring of a toy popgun 0.200 m to teg +p+es68yt 56 kztmyzb ;0b pv4om5“load” a 0.180-kg ball. With what speed will the ball leavmbp4b+;eg y o0m 5tet5tk+s8zp6vzy6e the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attasld51 b0 d:sdiched to one 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 sprinsbd5s01 did l:g 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 = e (;yxjox s4uobj:6f90.45cos6.4t where x is in meters and t is in seconds. Deto;s (:uj6bx x fe4y9ojermine
(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 ij01mx9czh p0 fxr-i1xs the energy of a SHO half KE and half PErczpj01m xxfxh09-i1? ±    A

  If one vibration has 7.0 tignetk9:idv) /mes the energy of a second, but their frequencies and masses are the same, what is the ratio of t/d:tv )9e gkniheir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangingm vd z.wtd63vd 7)i0id light spring once every 0.65ddiwz36 .td0viv)dm 7 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 parallel vertics ;iym 9kjt6 2s8wpwf+n) jh*5 aw2rpd;j3 jqmal springs, each with spring stiffness caswyqp 2i3frd hj);j twk; jmm+69*ps 2jn85wonstant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibratecq; mbr029,ye* h,itop:v .lhjortwn0 . 3rxe s according to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. ;cp.x :yqw2r.b,e0i hj0 ,vntrh3ert *o9mlo 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, lat;ewjw.)o e;ibeled 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 = 12d x5yl xqdd.gc/ ut3z0o;v/:t4 N/m) is struck by a hammer, which gz0gult /tv d3ox:; 5d y./cqdxives 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 p icvksfyd)e4*v4ennx ;e. + ybo8, x,spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes thvxvdx4sni)yonb ; e,8kc 4e .+ f,yp*erough 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 connecte(ym* * 1lo2vq;df fkr-psa3c xd to two 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 0.600llq d4a0; :l+t*;ieimlzsz9ixybq lk;cz- 3(-kg block attached to a fixed horizontal spring whose spring stiffness conl;lb(zm:3q e-*lkzyisd;tla40z 9; qx liic+stant 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 65.0y :h1mh;k kbi zgiq;s-r ew8h28k4m+b kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low pokgmh8bh8kyimw + kq bz-ser241:i;; hint eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exmr: c-hj, p4fjg1g,je actly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it)yer* xkbr5epzds0qn*.)3 m b is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 s.3k0)m.ee qb)r*zs * dyx5nbpr)    m

  A pendulum has a period of 0.80 s on Earthbmh nxw1bb8ov:o.r u lnvnm))).3wi( . What is its period on Mars, where the acceleration of gravity ii 8).xnh:nvool1w)vr w3)u( bm n bbm.s about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lonv0d-f 7fkoz/ rg
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simpyn(ujk ap)9j )(xgs )vle pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at n pu()s)jva gjx9ky()an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock loc *0ah9u3 r.a 80aopwmn4 qjqjeep,,nses half a minute per day, how should you adjust the length of the pendulum? shortened b .mpa*qe 0 8h nnrpj0cj3a,o,49ueqaw y    mm.

Derive a formula for the maximum speed 2bour0gi zp69$v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at lc upi0.k5l bcltr4iks1k7+ + a frequency of 2.5 Hz. At it is released from rest starting at an angle of 1ucp5 tliirk4 kl7s.b1k 0l+c+ 5 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every 3.di3x) aes0hot d.-c,i0 s. He measures the distance between two crests to be 6.5 m. How fast are ic ,oe di.xt3hda-) s0the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed ytyp1l x0 kizx4 zr/n5wt//n3 of 343 m/s How far a/tt zr03i/ynzxk y51xpw /l4n part are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz a+wost;wx t 7e1nd 1600 kHz (kilohertz) and travel with a speed o7+x;1 ewtowstf $ 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 lonth t-j p)2k1 pzd + sepuw.lr2( *7lctlomrn16gitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same e*fc0g 2tnor wc,fj/6 plastic modulus, but one is twice as dense as the other. In which ,p 2f60g/ccrn*jw oftrod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is smb/lc2n 3uq 6trwb,dtl0 h7 7wtretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it ta bqw2htlw3/7r tn6um7 0cd,l bke 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 620++q fne9 suns if)8m-+rsa fu- m and diameter 1.5 cm. As the gondola comes to the end of its r+ 9ei-a) 8fmus+nfsrf-u q+n sun, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. 74sswans7a ,:j .uhtwHe hears the echo of the wave refle:.7 4j sh,s7awntawsucted 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 at different speeds, and this d hd5y alhsni l0tk2t1.**h5bjifference helps in locating the earthquake “epicenter” (where the disturbanc*s5li5hty h t kjlan210h*d.be 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 e5jlki:6r1 ts0t gs4i approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects ge6li:4 1ttji 5rsks0begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensiuc e k)i/oa2 z(aatf,,ties, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from t,o aa2u czkeif (a/t,)he source?(a)    (b)   

  The intensity of an earthqawiavqq*9c hb amy *y.1,n l8,uake wave passing through the Earth is measured to be mwb1 qaaai9qc, ln, **v8yh .y$ 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 xvh( dx*l0 :lamp43tn the same portion of the Earth, but one is carrying twice thxnh* 0 xap: 3ld4vltm(e energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string v+z.(7 eu5ycjm m1fsl have the same frequency, but one transports three times the power of the other. What is the mu+c l(v y7z j.e15sfmratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total vertiep5kv*(z n0 geg4s3gy cal 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 maximum KE e g(4gznp3* y 0kgsev5change?   

The two pulses shown in Fig. 11–52 are moving towa lu fp/zpt-8j4q1oc* mrd 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 this moment? - m*fzjt/pp 8cu4loq1

  If a violin string vibrates at 440mfl-p-i4 ;ke q Hz as its fundamental frequency, what are the frequencies of thefimq ; --4lekp first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unj 6/8yvdcnf, efingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as an/c 6yj8 ,vedf standing wave.)    Hz

  A particular string resnpd i+dd+z(mid3t w63onates in four loops at a frequency of 280 Hz. Name at least three oth33pmzw+didd n6i(t d+er frequencies 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 tgnln46txk8; x he frequency of standing waves is 475 Hz, how far apart are two adjace;xtnl 6kx4gn 8nt nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350j-i* jm ij2n.,a:d ll 4yt9xl.y g.rxn Hz, what is the f 9xlgyjnjrn* -d ii2ltl:..4ax ,.yjmrequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Thddrt 7xh23 w jm *vbe;s.hf+x5e 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 ovbdfhv2t*mjw +xs 73; .erd xh5ertones?    Hz

  A particular guitar string is supposed to vi q.qmzq hu+e7ve1/cg,brate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tens7. c +zv,qqemge1uqh /ion 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 suox0r)v75mekptoxjlpi 0u, 0 * pposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By whpoiot 5kvx0e0)*mu plx,r7 j0at percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attachedhb28tbeth c)2j0eh4h ma l3c7 to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit lengtt 0mhb ceb4 l )8hh23tahj7c2eh 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 stri8p5-smxr4scn ng may be adjusted by moving the pulley. If the hanging mass m is fixed at x r4css5mn-8 p0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the w9:z3us6k5yby6y un jsater 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 standiyssj63 buyzy9:u nk56 ng 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 travelinmijtp8c 6 qpc99(s+gy g at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an iict gcpjyp+ q96 9(m8sncident 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” wher9qm8*owoj.kf6v y9 oye the velocity changes from 2.8 m/s to 2.1 m/s If the.kmy*oj6 9vw oq98 fyo 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 o k yze9*od6bq+o:ok 5h aiua73f cold, dense air. If the sound wave hits the cold air inq6 kbaoo i o+3u:ey79ah5* dkzterface 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 betweenjsp0gn,ct *v 7 two types of rock at a 3gt7 , csnp*jv08 $^{\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 abou ls);vk zgdr1p2-luu, -)z kgot 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the directiov2u k );gul-,odrgkl z 1pz-)sn 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 vel.omuvw/w0qro2 z ha/83s2 vtg ocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people2w23r omo/v/u q.gh tvzsw08a 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 co s,oc6 ruw)o5oly x+s0nstant of 550 kN/m Find the maximum compression of the bumper 0o y5 ,l sc6ooxwsur+)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 18 m below, which s+u5 z*zv +tdg.unrd z-tretches the net 1.1 m. Assume that the net behaves like a simple sprind* d-5u +gzrvzu.nz+tg, 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 spritm0uc91 92br o+lq(uc( hzbjcng. The mass then falls 33 cm before it stops and begins to rise. What is( hqu z 9lc90b 2t(c1+mbuocrj the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sprqwn: l9 3ohbtcwsgcr/v 53 6f)ing at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffnesshls)c53ww9rqg:n c6 oftb3 v/ constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace 6;5/lqmftdx:fxjk dv* aa,x6 of about 1 step per second, the coffee sloshesxd*ajk v6;,xq/6l tm xfd fa5: more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.o-5ko )ns azj* ikq)fp8dq 25g8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequengi2dfn)-* oa5kqq o8jzp)k s5cy of the sound emitted?    Hz

  A 2.00-kg mass vibrates according tou;mzgtzs 4gvr/ l-t-1fjzzd 0 s;h3g) the equation x=0.650cos7.40t where x is in meters and t -0 ugzmh 43/ t;)ztzvr sjgfg;1z-ldsin 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 fr 0vpnhsc25wt 57r:4sch qi)qw equency f. What is its frequency if it accelerates at 0.50g (a) wnw5) r4 qvqc t7s 2chsph0:i5upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Whm mfw1jd-n :xal4xin 8zv.96 ien a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, inxlm:jd-f va61mzxw8n 94i .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 H5i*p ;os;ogwfz (G) and 440 Hz (pif ;o*gow5s;A).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched t1(m-wyic-)ls ddsm 0f wo-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 fwm) -s 10m(sl-ydci dfrequency 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, a+j+ fz8 -g/iq cf5ky sm3.whglnd the tip of each prong moves 1.8 mm to either side of+zqg8 g/ my3.fl5fhi-wc+s jk 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 freque;xvri+l2 jf c4ncy 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 rfci; +2jl4 vxwith the board during the oscillation?

A string can have a “free” end if that end is attached to a rn5h s3nw+/j*uoikgo1. x: xdo.lghq5ing that can slide without friction on a vertical pole (Figlx:+wg n5j *iguh ooqs13h5dx/..nk o. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing tabs :zacxo5zb, il /1)ekes 1.000 s.5:e)x zioz b1/s,cbla
(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 oscill. ;76ilht3nbebv o el4ate in the vertical direction or can swing as a pendulum of small amplitbl6;eoth. v7li3nb e4ude, 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 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 pu:j4jhw :vnlxg6-r yrmr 3 1.27db yekklse is generated at one end, and 20.0 ms later a second pulse iwb 3rr4y m7knjgrdy6-2ejhk::1.v xls 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 witm8reh; gf. ee(j5otb 1h spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will ale g5o1er8;m. b(tehfj low the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 12a 73 myt9d2fjb00-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is mybd327 fja t9the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in 6viw(gf :uker:y)k8 x 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 vibra8igr):(w k y:fu ekxv6tion, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz