Give some examples of everyday vibrating objects. Whia;y b6 gw56g n c4b2oft9svv.ich exhibit SHM, at least approxt5;as2vngv ybb.oc69f 6w4igimately?

Is the acceleration of a simple harmonic os,k .iexs9, vy7r6 t zo zo2k-th+cub,xcillator ever zero? If so, where?

Explain why the motion of a piston i;t:s 2b:ofmx c;su e.pn an automobile engine is approximately simple ham2stsb:e c.fop u:;x; rmonic.

Real springs have mass. Will the true period and frequency be larger or smalled6 7f4m9scl+t lmrjo.r than given by the equations for a ma+fmtojsl6.dl 97 4mr css oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of 5ai.quho a c44a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attachey ,neqs+, :o*vgs9p hbd to the hook of a vertical spring scale, and then is released. Describe th gbvps +n9s: q,e*oh,ye scale reading as a function of time.

If a pendulum clock is accurzr)8.4vm s onae 7y2gyt)kzg7ate at sea level, will it gain or lose time when tak8meg7 tvo.anz7)z 42)rk g ysyen to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). H. gee6ura2 wbe8k:)vta gf,r/ow could you estimate the height of the bra /tearf k6.g gw2:)bereu 8v,anch using only a stopwatch?

Why can you make water slosh back and forth in a panr42vb( +xjfw eboqn+yk*, e i9 only if you shake the pan at a certain frequency?x(i49vwfr2++ bek ,nobj *qey

Give several everyday example nqp8xkbf 64mtzspm( gm s+7p //bq)6js of resonance.

Is a rattle in a car ever a resonance phenomenon .kr.k(y1ltm;t exv5t ? Explain.

Is the frequency of a simple periodic wave equal to the fnzh jx:6l g /k8//grhirequency of its source? Why or why noi/gl/hgx8kn:/zr6 hj t?

Explain the difference betwe0w4a hp+ zh vc.i27udn26oxv oen the speed of a transverse wave traveling down a cord and the speed ofwvuhiz 7d26ch.a4o n2vp o0+ x a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally hal i88j3vaqr; sy)me 9qve wv erj9)q8ml ai ;sy3q8ire wrapped around them?

What kind of waves do you think will travel down a horizontal mbqeo o+yoj60zt4r z/ (etal rod if you strike its end (a) vertica ozoyo0b ezt/q 6(r+j4lly from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperaturejx7b,qyr4 h+sx;ier9 , but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with tempjhqy9i 74s,x;xebr+r erature?

Give two reasons why circular wo7n x +0(tqz 84ouj.od/wsbujater waves decrease in amplitude as they travel away0 8 b(q.+jsuu owo7tzojx/4dn from the source.

Two linear waves have the same amplitude and pq .2n 5ax.mp5qpjal- speed, and otherwise are identical, except one has half the am -qqp.x5p nja5.p2lwavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of conh ww; lork,xi-7e /t( u4hb;crd as in Fig. 11–33, the frequency does not change (althougeuh,ih4k xn;b;t/ 7-c(w rlwoh the wavelength and velocity do change). Explain why.

If a string is vibrating in u(, encl/zq/xy*) vtuthree segments, are there any places you could touch it with a knife blade without disturbing the motiotqclz ve,* (/)y nu/uxn?

When a standing wave exists on a string mi*(qsr,::ej1mdz0) e sws9(jeaq xx, the vibrations of incident and reflected waves cancel at the nodes. Does this qj*idw( a sex0m1(s)s:ejqxz :m9,re mean that energy was destroyed? Explain.

If we knew that energy was being transmitted frfn9 ujs2+ kp;d:+3gqvjyj/tm om one place to another, how might we +;:jygkj +nm dtufpj/s9 2v3qdetermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoesgps ,k34y ur-h SHM with amplitude 0.18 m, what is the total distance it travels in one perhs ,u-grpk 34yiod?    m

  An elastic cord is 65 cm long when a weight of 75pfxd wk ehks*7q- v/ys(/ v0h2 N hangs from it but is 85 cm long when a weight of 180 N hay/ p e* hkv7wfs2kdvh0/x(qs-ngs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car -se a ,:fkt5ogcompress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibrationso fage-t5s k,:?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-k(w500m(: kcj t wzk tdyrfv93og fish hangs from it. (a) What is the spring stiffnkv wr(:z9 y0t0d to5 3jwkc(mfess 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 ((b zb hyd0*jmn+new *7kp8kxgb0az60.60 kg is hung from it. Wx6dw7y kzebnmp8n g 0 ka (0bzb+*(*jhhat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 1*-bdymtbgct 5 9+c j+e1–2 at times t = 0,t e5g*+y-b9 dcbjmc+ tt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 spk1w )uvx qh/: jz/(kszider’s web. The web vibrates predominately with a frequency of 4(/ kvhuqw1 j/zkzx): s.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 vibrate tj52e mda. yyt 4njotq3.(c5umq+6r zs with a frequency of 0.88 Hz. When an additional 680-g mass is added tem( q4 5 5qaod+t. .tutry2nm6jzj3y co 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 sa yd4as: h;hp xc:lgt.v 40xc,econd with an amplitude, 4; aahg4:l 0dt.vxcp y:hsxc of 0.13 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)o2h)ftu-i)ttqr l6-q h- wjz speed of a SHO half the maximum valuez-iht )utrqt ho)2l- -f)q6wj?$\approx$    A

A mass attached to the endh vgub bs,hcb9g)c p*n; 7q8p/1kg/ ew of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vermsrz 6k 7.sp)l4h bfb/tical 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.pmkss7f6r4z/lb ) hb ) equilibrium position again?    s

  An object with mass 3.0 kg gc7 +6/ptxypb is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motiy6/7txc pg+b pon. 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 to compress the spring of a b t vf;1(.xr3i8ccrojmp+8 setoy popgun 0.200 m to “load” a 0.180-kg balvm.tseoc; x jprf8r3 bi81c+( l. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfii nokg/:5 asfk)lc v.5x* ejc93dyj.ace is attached 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 spring cakjljv..*sfgcox5i: di e5 n9 kyc/3 )ompressed, 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 wherea8 xh*(:.qtjqc8xj p k x is in (8xt: * qqh.pxjak8cjmeters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE andng6 0 (rox-jmac+mv,x half PE? ± o 6gxrxjvma+m0 -n (,c   A

  If one vibration has 7.0 times +aq rb.b6dn-wxlv ;m0the energy of a second, but their frequencies and masses arexlr -bbq6amnw d+;0.v the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from 5lqc8,u .xnbou(ora(zoy4l r q .1 q)xa vertically hanging light spring once every 0.65 snxb) y.qoz ,5uqxql o(r(1ur48 oc.al.
(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 1 r2cf ohi;j /4pfrqo2vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrpojhc4fi1r rf2 2o/ q;ation?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in mf3bszb01bgbcz*ho y* *5wqk: eters and t is in seconds. Determinhy0kg1s *q wb zob3z5*b*:bcf e
(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 B. For eajndyj2k) /h ;3hq6eziip2u/ gch, 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 = q87q;6 ib ncnd/sikl2 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Det c/6n;n78 qi2qiskbdlermine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with an ampxzsyt+ q: dsy x*t20:nlitude of 28.0 cm when 0.260 kg han:tszy x:dt+ 0*ysq2 nxgs 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 spring stiffn3yipgs(qd- z vhy6)d;,v +uqness 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 tm z7u n9kb2jd9cqjufac3 y0s* :m*: tqo a fixed horizontal spring whose spring stiffness constant j:*y ubk9972m:3*jmc0t sqnud zfcqa is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After rejb n q8p-y;6-foa:y hbaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and theq -- pnb: fjay68hoby; 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 vibrat56f ;q8ngjb atx bd+s;ions 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 perm)wqkng.k :4qrb; -; hjm .bzx second? (That is, -m4.km)xbhb.krgq:; w n;jz q one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period onuyr28( tk)w2 f cmtd*sh*mdx. Mars, where the accelerw*kth)(.*yrdxc md2 2stmfu8ation of gravity is about 0.37 that on Earth?    s

  What is the period of aupux4.u b09b h simple 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 pe *wc)gavb/;)z8j*kcn fqmnzh2j ; 3mnndulum bob has a mass of 365 gramzw)/k*czjn gm *j mc2qh nb )vna;8f;3s, and 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 clock losesv.lz3vrbo *,k 2 6sypb half a minute per day, how shobkb6r, sv2 z*v3y.lpould you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum swn.y0 whzbj; (9xo7 hm*vdvn: peed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates aet4)ebummt 9; vi24zz t a frequency of 2.5 Hz. At it is released from rest starting at an angleti2u z; mbz )et4vm94e 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 creqyp,zh ffy,,+fr gr7f u u1a/2sts pass the bow of his anchored boat every 3.0 s. He myu ,rz2fufh f1f/par,gy, +q7easures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a fre0l fwt7c 2q kll1d 3,xrrf a(b..w9docquency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressionx10odr 7 alk2 qtc,lcw.d(lrfb9f. w3s)?    m

  (a) AM radio signals have frequencies between 550 kq834w scqgb7pHz and 1600 kHz (kilohertz) and tr3b 4gs8wp7cqqavel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudi+d5rgw ih x0a,nal 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 m,w d t4pwup0u epn7,1ykxc/ 8dense as the other. In which rod will the spee7m,w8p 4y0nut ,pexcw1 /dpk ud of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. Iwoku *hrtwkf7*-c+3 x0a- ulgf the tensi*f3 w* w+tk0xuglc -kao-u7hr on in the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 6201o2ybrpe 7saz g6svze 2x7*d - m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to 6bssrpd7z21 zgxe 7v-ay * e2oreturn.
(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 ship14fegm;- svwawn z;xd 1wk-*l just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is thewg*wwz 1 daf 4m1nv;e-xks;l- ocean at this point?    m

  P and S waves from an earthquake travel at different)loawfx 2(ebs,- ;c gl speeds, and this difference helps in locating the earthquake “epicenter2 )ca-,bsoef lxlg (w;” (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 approxi b k ; )zjeis+;.5dzm kktm,jqvob7o-/mated by a sinusoidal transverse wave.k,+5oqb;kei.ktv zzs7momj /- d)jb ; 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 contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earthquahi4 jhvurn,czo)ug,;,,1dfeke P wave passing through the Earth and detected at two points 10 km and d, nuhi1czregh, f, o)4u,v ;j20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through thes l/7b*b ;xftolrs, s6 Earth is measured to be ;o,*btl6 srl sxs7 bf/$ 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 frequenczh9j,za5 * 86irbmcd g4 /eph1wwtu5yy travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio 5b/ haj8d wec4uz1mzgy9pri6w h, 5*tof the amplitudes of the two waves?   

  Two waves traveling alon6 -zf6l3 mj h4d /d;pujn+ourvm**mdlg a stretched string have the same frequency, but one transports three times the power udj 3 lu6 vr/4nz*; +pmmjmodl*fh6-dof the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed a+k))lj8 lohv to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples dec+ johval)8k) lrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) hs48u yp7 idjsth4x 27Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of theuyh st7s j p2d8hi7x44 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 fundamental frequv qltm f( 9wftw6*+-ipency, what are the frequencies of the first four harmonics +9tv6t(wffp- mwi*ql?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingeretf tr 06/gpnd6d. At what frequency will it vibrate if it is fingered one-third of thrdt60n p6/g tfe way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four lj; 0jd3z yr4rao9cmnk m 51c:doops at a frequency of 280 Hz. Name at least three onzc5rm 9rj4;1moy c jk03 add:ther 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 the frequency of standing waves b6d tonz/rt ;,is 475 Hz/n;,ztob6 tdr , how far apart are two adjacent nodes?   m

  If two successive overtones of a vibra31 d w3q zducx;rzbw27;d(oduz*t oe-ting string are 280 Hz and 350 Hz, what is the frequency of the fundamental(1dwczo3z x-;7utd*z;ro3u q2 ewdbd?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the bt t3h9gmud* zv)b08ng ridge d)mgnu3t 9 v0gtzh*8bto 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 overtones?    Hz

  A particular guitar string is supposedu0u3yaq ik/a* to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension*q/uaa0 iy 3ku 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 vibrate at 200 Hz cn-s +7dt4afr, but it is measured to vibrate at 205 Hz. By what percent sho4-adfc7r s+ tnuld the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal strj ga8dkizy np6yj.,shj5-u7(vb*ehbl :y2 ( ying is attached to a small-amplitude mechanical 60-Hz vibrator. Thj-y62 hj *bykdy ujg ia hnzel(,(5v7s8:.b ype 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 p4 .uc sbnky,6of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kb6kpsn4yc u. ,g, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and fc+t;j ,xqa1. / *xx pc*x/tdag(vjmmnorth 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 1/mc +tjdtm(*a xv*xqnjc.;/xap,g xspeed of the water wave?    m/s

  An earthquake P wave t(f l bup62xv9yraveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it apx(l 96yubvp2fproaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity chanwr0 ,pdf m-f5s a,fy4(3xy.plkqk 4e kges from 2.8 m/s to 2.1 m/s If the incident wave crests ma0ymkp e(dxfq r.-p4lyf,akw ,skf345 ke 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 laivqt r l0)*2 3gqdw9ltadb6t1yer of cold, dense air. If the sound wave hits the cold air interface at an angle9rg3qt0ld1dl i2t* b)w6ta vq 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 earthquakwf z1; z k;rfhoayf1./e wave strikes a boundary between two types of rock at a 38y hro;k.f1fz;a/ 1wf z $^{\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 diam +t w0 g:jujiv1wuon tiwavc.;7l 81:rgf:: jketer. According to the user’s manual, the dish has to be pointed :8vfgaj iw or0+wji1gl.; kju 7tu:w1tcv::n in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and veloc0lgcc :c69sed7 +o5hp hnj0gfity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Ap0cd9 7 o5j fhnpg0lccsheg:+6proximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness consgku.2r/i.g8 iyd7/ t 1hx tmiztant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of en/gt.z d 8.k/2mixuit7rgi1hyergy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which streu8q kd/4bdm*e tches the net 1.1 m. Assume that the net behaves u48be/ qdd*kmlike a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. T+ d (oouyty s-f+z5atzj d965,pvj/dx he mass then falls 33 cm before it stops and begins to rise. What5ds ,adxj+dpv( yzo z 95oj6tyut f/-+ is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed ornh-e7,we yzv51(16azbq v pwf 22 m/s (Fig. 11–54), compressing the v17p(nzb aeze ,61w vh5 -ywqrspring 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace of aw2ils4; .y*j.wiwg d about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 1ay ;2iwijd.lw*s. wg41–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the cenzpxc ;:i fy-a+ter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of tcxpy-a: z;i+f he sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.4u e-j mm(q4w7qlrt 1;p0t where x is in meters and t in seconds. Determine -7 t1(r ;m e4jmqpuqlw
(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 74l* dgyu)- aelsvl. rits frequency if it accelerates at 0.50g (a ea l7rv .4*duglys-l)) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a5st-7i f xt jkd kpr9q)f09t/poxpx ff0;6hq9 lake. When a 75-kg man stands on the raft, it sinks 4.0 cm xft0 rq5fhpf0/xtq;o9 96t-id xk)pf9 7kj psdeeper into the water. When he steps off, 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) and 4 )vl7lh7 i7cmq75uvw:hadeh 440 Hz (A). deic) vhl h5 ula7w7hvq47m7:
(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 cordri p1u5c/ e8v g6wvrp, 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 wavelengve,w irp8gpr u/51v6 cth greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency om8idv xty(r7-jgy+u66k /chof 264 Hz, and the tip of each prong moves 1.8 m8 y/ckxruvh+(j6- od7tigmy6 m to 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 x8 tea,nbj47p ij64uifrequency 1.5 cycles per sepu x47i 6e4ab,n8ijtjcond. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” +won6c:qqwl8)zy1u e end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57)wzqy+new:1 o 6lq8c u). 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 2.000hrw*e. o+ ej3 po8h9rr xid7+p s — each one-way swing takes 1.000 s.ex7o 9p 83rh+j+wri d*po.rhe
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical directioep plt z5+0o8mubh7:nn or can swing as a pendulum of s05mh+nepz 7tbu8o:p lmall 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 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 hxt;) ton: s7karrxxah4d(6* 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will thk;):xhs a7to(hdtr a*xn 46rxe two pulses first meet?    m

A block of mass M is suspende fbk,o5rs d8xqpd-1i5d from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top f ,dds1qx8b- ko 5pi5rof 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 4:07 egcj wybka 1200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of jcy7 e:4bkg w06.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which alsocg7(cgykl),qu6x) fw gives the dim )(gkufg y) 7q6w,clxcensions 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 the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz