Give some examples of ever p-3)dhz:bvh:m g/ij ryday vibrating objects. Which exhibit SHM, at least approximately?-)gp:3 dzh/:v mrib jh

Is the acceleration of a simple harmonic oscillator ever zero? I- mn4qmtfh pn(f/pfj5 t:(s* nf so, where?

Explain why the motion of a piston in an automob0o 6twc ,enui vvma7,a*is j09ile engine is approximately simple harmon,6 t9v0 7vwaic0n oj* ,isaumeic.

Real springs have mass. Will the true period and frequency be larger or sm*7k n.x tn+sasaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explaikn+s*axnt 7s. n.

How could you double the maximum speed of a simple harmonic o8g-ged m5u-oj scillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and therq sis(2mnn rr 3;q.w 4v)g gg f53otury8q/6zn is released. Describe the scale readiny ;qfr s 8ung s5.oqrgt3q436g)2rrwz im(nv /g as a function of time.

If a pendulum clock is accurate at sea .:7 abrti0n bulevel, will it gain or lose time when taken au:rn7 0 tbib.to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (F4 yq 0k; rrp(8nc(sqkfcmn1r 1ig. 11–48). How could you estimate the height of the branch using onnn(k4mr qf rk8 r;10c(sy p1qcly a stopwatch?

Why can you make water slosh back and forth in a pr30cqv 3b8go n7ajwf/ug k -h(an only if you shake the pan atfug /n8b 7vqc0kwgj3oh 3-a(r a certain frequency?

Give several everyday examples of rq.h0k( oaljvh bfmt1id+1a2;esonance.

Is a rattle in a car ever a resonanu57jjd/ j5irnich4ibo p 02.sce phenomenon? Explain.

Is the frequency of a simple periodic wave equal to*x()jut1 t: :rq i2etfm4rr jm the frequency of its source? Why or4xt)r:i*u qt1 f(m:emrjt 2jr why not?

Explain the difference betwe57k0tlidfey g 8o;*dog,*o m tr4 t*tien the speed of a transverse wave traveling down a cord and the speed of a tiny rl od e8itft4** o*idy,7 tg05;gtokmpiece of the cord.

Why do the strings used for the lowest-frequency notes h eri87we.b13u csl c*on a piano normally have wireew37ih*s. 8rc1 c eulb wrapped around them?

What kind of waves do you think will travel down a horiw7wcbzrnj u(2ae2b;x st z7 8sw/h.y,zontal metal rod if you strike its ewnec;7 j.xuz ts wsy(a 7h8,b2r/z2bwnd (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but th(xu3grhfw 4 y)e bulk modulus B is nearly independent of temperature, how would you expewu(ry)4 hx f3gct the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amp 61sab d.; zzw65e4syuw )rofplitude as they travel away fr s ezzw4a d;opw5y6rb.fus16)om the source.

Two linear waves have the same amplitude and speed, and otherwise arf kk auq 0)1p9z)hw*hbe identical, except one has half the wavelength of the other. Which ahwp z9kku0q)h )1bf* transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as uom k e88hs9cy7ux/g(in Fig. 11–33, the frequency does not change (although the wavelength and velocit98u8ogsk(yec m /uh7 xy do change). Explain why.

If a string is vibrating in three segments, are rwv -h*d2 b,zoxt6 -dlthere any places you could touch it with a knife blade without disturbing the morz owtdvdhl- 2b*, 6-xtion?

When a standing wave exists on a string, the vibrations of incident aneu hqy1:: /vxtd reflected waves cancel at the nodes.u:qy1e v/xt :h Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted fr;tbd;d73 -o-qc xotym1s nu1j om one place to another, how might we d u1;dcsoy 1o; d- -jt3bmx7nqtetermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHMokl9g fwusigm((/)-s;m5o r w- rqs(l with amplitude 0.18 m, what is the total distance it travels in onerwgl-wm(/ krfu;im(sg- o)s(5sq9ol period?    m

  An elastic cord is 65 cm long when a weight of 75 tr0 tsxd3l78vN hangs from it but is 85 cm long when a weight of 180 N hangs ftvxsrl8t0 73d rom it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compres( )c8 wz0y,1o0jr2her vqukfc s 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will o 2r1 0vccuwyhkjrzqfe8()0 ,be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs fro kh;m : zq57( xp7nlsyrhk4nr:0a;tehm it. (a) What is the spring stiffness cm; 4zl7ykq0h ( narpx7 hn:k h5:rs;etonstant $\approx$    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 9vbb+t6z9r ms5c5o1e .l j cmj3.0 Hz when a mass of 0.60 kg is hung from it. W 5socbzv959r+ mj.mtcel6 1j bhat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position 6e8nt(:w: jxye7qsuikits 4. x of the mass in Fig. 11–2 at times t = 0,t =i:sw6 7tyx .ti8kqs4eu(j:ne $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 web. vy+ :q01kzcoc1yz1 rkThe web vibrates predominatelykzr z +:01y1oc1 qkcvy with a frequency 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 m/hm2+8(g qifsh : oorHz. When an additional 680-g mass is added to m, thrqf 2mgoh+so(/i m:h8e frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an rc5 zep.+u.h( qig.df amplitud d.i+.pqzhc .ug5 e(rfe 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 spee wxjh6mnl )z03bv0w3 ad of a SHO half the maximum value?wbw3jz m h)al03xv06n$\approx$    A

A mass attached to the end of a spr78 dhlkrsyov(+j9fab/i 1 ,vzing 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 vertical sp;yj.7b)yagqdkac /az0ue 15p ring 0.315 m. If the spring is stretched an additional 0.130 m and released, how ;yda05 agqaeczjb 1k./)p yu7 long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a sprin2v3ug4a5ni 9e4mtx p zg with spring stiffness constant k = 280 N/m an t eugm3pa iv54xn942zd 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 pe f0v le3t;gu,r:60w(as eguN to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the e0v0p6:3tg (,usg eaf;wreul gun?    m/s

  A mass sitting on a horizontal, frictimsec,r 1.5vo/i2fip gonless surface 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 isrecim fso,5gp1 2.v/ i released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4tzm 0g2b7q:pvgtzmq96-nyp- r where x is in meters and t is in seconds. n0-76 yzq2m qz rtgbpm:9p-vg 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 equilibriuftf sb )3fl)mp4,y ln7m is the energy of a SHO half KE and half PE? ptbfl mf)f)ns,yl4 73 ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencies aneg u9:ps h7n q:0z4cfk0hpvn5d mv p5h: sguc9qh 4npnf:k0ez 07asses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging :6dlr6.kvx63pwvci m ( v /b 5exi 1f7jkpv(pjlight spring once every 0.(ixmv 6 :rv5 kk(pcj6.j p1pf ed w3v/l6vxbi765 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/;tusfrdb5*8 b pjd i* two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibjp isu;f /85tdb** dbrration?

  A 300-g mass vibrates according to the equation x = 0..iaozf.w6vmu/1 mscyh 90ob . p8t nw.38sin6.5t where x is in meters and t is inuzs.p ynwvf6.o1 .0om.9 tbc8m/wahi seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and . qhdy:z8s.rza2vfe ;js jg/3B. 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 awgkew1x pjs 69c89m1a7kl z o4 horizontal spring (k = 124 N/m) is struck by a hammer, which gikw 6cwaplxjzg94ms8 e191 k7o ves 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 spring stiffness constant 305 N/m vibrates with ah--),z-o yx7 m+s8gwnqlo pne n amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity+wqym78eozl-- o s -)x,gnn ph 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,v 6c9l*ehl( r(mpmplf)x;8f ivk,fr: with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal springfo +vr7.pz7ip whose spring stiffness+v.7f zroip7 p constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. Aftthy5w9y7w 3kler reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest7 ywytkhl59 w3 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. fu32n3kka5/)nhcrq8fveu v ah* 67ozWhat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it ismtf4n:mm6po;ic.+fd mik8k 0 to make exactly one swing per second? (That is, one comple tdmm cpmm fk+46kfo0n.:8 ii;te vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on E+st8lgewx.d(m .9y6kyy3 y moarth. What is its period on Mars, where the acceleration of gravity is about 0.37 ty yxt g+96 lym.kdsw(e .mo3y8hat on Earth?    s

  What is the period of a simple pendugqz :z3-vjtzy;s/3 uilum 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 m5f.leelto :w+:x sjz;, the pendulum bob has a mass of 365 grams, andz:.:5 l+w o see;xtfjl 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 hb 4j676d/yqa+ppoo5rpi ) ctbnd6 lt:as a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length j 54py6rpqbp+n)o6i6 :td7c /bdotla of the pendulum? shortened by    mm.

Derive a formula for the maximumdrqflg25 f,jkl,(:s p speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. Awp64 +h p3la 0pyakht-t it is released from rest starting at ank p-hla 03+6py4w ahpt angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices thaau5. p6+ qyaumt wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wam ua+5.6u paqyves traveling?    m/s

  A sound wave in air has a frequency of 262isi7 q4c0iw:s)z,;yilt + sxa Hz and travels with a speed of 343 m/s How f:i, ztq+x)i lasy074 ;ws icsiar apart are the wave crests (compressions)?    m

  (a) AM radio signals have freq/ m-k ng8 )ozoyt )b)dme,kc6-,bftrouencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed of yo,8cm - knt)tgob)z6 r )oebk-fm ,/d$ 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 lor8pmz:r1 a oc4+9qxqlngitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one;wr xls(c 7ang+9z8hiubx ,0/mdy gc - is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by d/ w bigxaymcs(7l-g0uxn c;z+98rh , what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m (kb.gd+jo lcy:n gv+8 apart. If the tension in the cord is 150 N, how long will it take a pulse to travoj8gn+d g( .:clv+ybkel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a s sxzd 0w3r5bvs1(h ;*bg)uookteel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumpsw3 s;xvk)sbr uogh z(o*b015d 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 thzob:ajrkw 4wl6)// *9wlsspme surface of the sea. He hears the echo of the wave reflected from the ocean floor directly ww/9s :b)pmjar o/lksl 4w z6*below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquak y7*nnri u*p8 ckm87joe travel at different speeds, and this difference helps inmp 7r8k oiunnc*8*7j y locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal transver3if;* c vhjz)-zxqro0se wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually *0 ix -3h)fqz;cjvo rzinclude 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 -xer ;sz thbhfj9p/)*(a) the intensities, and (b) the amplitudes, of an earthquake P wave p)pe9h*;x/trfh z -sbjassing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an mn 9b*w76i9h rq0xziy0d)n gyearthquake wave passing through the Earth is measured to be 9*g 60wr7d9q)yimnn0xib yzh$ 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-d e fci+n qdh0826tsu of the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratiotud0hicdq 62e- n8+fs of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have thy;q1b;40j*j4nepy nhhjr r(se same frequency, but one transports three times the y(pjr40 * 4hyjbj;r1 q nsh;nepower of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up a: z/k ya2w4cdcnd down a total vertical distance of 6.0 cm, from the lowest to the /4 kawdc:z 2ychighest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward e l7 awqojn47 8i4c,rqs,hccp ,ach other. (a) Sketch the shape of the stringsa 7hc q4pnwi8,l,, ojrq7cc 4 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?

  If a violin string vibrates at 440 Hz ay68 n p62rcahi0zfw8p s its fundamental frequency, what are the frequencies of the first foaphic 0f8y6n2 8 pz6rwur harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at f:w3q jt+k4vkr3h8gw 294 Hz when unfingered. 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 tjgqhk+ : 3ktfw rw3v48he string vibrates as a standing wave.)    Hz

  A particular string resonates ind25g/lsmth*,+p t rg (v/p bgb four loops at a frequency of 280 Hz. Name at least three other fre, /r/+gmbpshtgbdv5 t( 2 lp*gquencies 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 q c( (ckc m-kz.pjjxh n(g*+;mIf the frequency of standing waves is 47cmcj((p(k .gcnq khx- z; *m+j5 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 37hjznwhb;.. y ff*pb8a 4zdug0.comc)c v. r .50 Hz, what is the frequency of the fu4mz8fh;cjw0. .b.z*)hdynga. vcuo r pfb.c 7 ndamental?    Hz

  A guitar string is 90 cm long bcnxvmp2+ s3s1 4iom1j5v7)tt (s enz and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is und v34n2 z1snp+(v eit1ms7xtobm )cs5jer a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suk. tz-kodd32 b4b0ez upposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct thu. -dkdtob0k b3 ez24ze frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate2t(ab /. o/x ihg:dagh at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be c.a i o/h:dg hgtab(/2xhanged to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitudebem rl: 6at3k; mechanical 60-Hz vibrator. Ther3ta6 b:;e kml 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 length4vdtr:6e,htr7m k4vj of the string may be adjusted by moving the pulley. If t4:k ethv 6dj,rvt4rm7 he 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 water back sfz :9a0met/kand 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 it /kfeam0s9z :s the speed of the water wave?    m/s

  An earthquake P wave trp9u+3 s9q alliaveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at a93aq9+ pu llisn 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” wl,oqfgbbr. 4 j0o yk59here the velocity changes from 2.8 m/s to 2.1 m/s If the inc4. 5bf o0qljbg oyk,9rident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of dzvz .ql7 sgn;2re65 tcold, dense air. If the sound wave hits the cold air interface at an tenl q;7sgz2dz.56rv angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types pvd,e2qci ,:oax2* sa wm5o 6hof rock at a v2: ,a a*sdoiw m2 xq,5e6pcho38 $^{\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. Ac4mp vjdmc/8u3. a5gr pcording to the user’s manual, the dish has to be4gpr/jm.3vmcd p8au 5 pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocite. 8mk 1 nrzv(:6zq( j5rah(4lk ad77dquv dzvy 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 kz:uv77a.kzd 8d4(vvh1 jr5azlqnqe( mr6 d( 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 nn7.oxy fxiq u+,hd 4)a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint:ufd nioxh,.x yn+)7q4 Use conservation of energy.]    m

  A 65-kg person jumps from a window tn0 aetrd5 gky3ef6 ciak 0d:4-o a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves likeag0 e-nte6 k0a53k cr:dy4dif a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass thenc31) e,k;mvrs2cbqv67 fwow g falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?bsvmce)co, 1v3fwg ;qw267rk    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fg*pwzvn 60 x)kig. 11–54), compressing the spring 5.0 m. (a) What is the szk 0wn*g6vp)x pring 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+7kc9,t -zn2f mjhuqsyt. mg5 pace of about 1 step per second, the coffee sloshes more and more unti,9 2h7-zc mu5tyjqgnk+.mftsl 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 10.8 cm from the center of a 33-rpm phon91) u rvlcvdky ,wxk-d(j 63lkt7k8*bxd uz j9ograph record have a wavelength of 1.70 mm. What will be the frequency of the w *c-98xk7dxdd )3lkk9vkvlub ,zy1jj u6(trsound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t) d g83abo fwg5) gwqal2o-(xw where x is in meters and t in seconds. Determinfw)(28waoad-g gqw )bxlgo35e
(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/5+ad q0cl keuo00lq l it accelerat0 au5qkc 0+0loeql d/les at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lap x:rq e4lwox17sv)) ory 1l(qke. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for)yq (l:pwx oelq11 )orx47svr 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 4je (unbj6ph0ajq( p,- skj2care tuned to play at 392 Hz (G) and 440 Hz (A).4,2q j j(jbje6k-(pspuh a c0n
(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 gdit;nbl8j0hl- ;4w ++gio rn traveling down the stretched two-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) foi;no8 4 iggbj;hl0r+tl nd+ w-r the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264gkp -t: kq3avntv b46- Hz, and the tip of each prong moves 1.8 mm to either side of center. Ca6-k:gqb-4k3an t pvvtlculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillatelh68 ns (3fjwws with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble place83fnwh(6sl jwd there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if th5+0q *sd kjdyz+1zj 2x6vszonat end 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 a string with one end fixed andnxd+2 sqdzy0 jkzo1v6+ *j5 sz the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takv-f vepl*9smw7r)in 8es 1.ewm*-vfi8 lp)snvr7 9000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the verti:9c;zndp r2lqafdz7wn *,1 pn8 *vgzg cal direction or can swing as a pendulum of small amplitude, rv1;n9 nd nzp ,flz 2zqg cp8a7dw:**gbut 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 mapsf rq g/4 gm13tsqz:2ss 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is gss 24qrfqzmg 3p:g/1 tenerated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sprid)w:t x mhi08nng with 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 allow the penny to just stay on t)txmdwh8n i:0op of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The ste ei:v6t7v;/c04z6c54uhh t ibvu a euwel 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 the period of the bouncing? [Hint: Refer to Table 9–1.]twc4bh 0 ;ieuuev6/hv7a 6czv uti54:    s

  A block of jello rests on a plac l6f5vyre d72te as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shlyr7c25fedv6 ear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz