Give some examples of everydase xmc-(mpmw: y*z ks3,c9ktsl,h: j1y vibrating objects. Which exhibit SHM, at least approximatel:9tyxs1z: (sm 3kjp*,cm,wlsk -chmey?

Is the acceleration of a simpler1vmr )y :s: g8 o)3zl*sbrxyq harmonic oscillator ever zero? If so, where?

Explain why the motion of a pists 38sa s,y(ggkt(og,gon in an automobile engine is approximately simp , gsoty(ag,8s(s 3ggkle harmonic.

Real springs have mass. Will the true period and frequency be larger or sr k (u:ls:8dr,qmo8 mimaller than given by the equations for a mass oscillating on thmr8ols d, k:mir q8:(ue end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmoco g2,pvw6qkg. f11mtnic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of *ay0dx p0 6c7z;wwywbe.mn: ea vertical spring scale, and then is released. Dweny 0.xewawdm0; *b67: zypc escribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, w),30o 9pblgvngvwlq 6 ill it gain or lose time when taken to high altitude? vwqpov609,gglb l3 n) Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 3i6b ug st68h/k(xjwm11–48). How could you estimate the height of the branch using only /68w3 smj6bg hkiuxt(a stopwatch?

Why can you make water slosh back and forth in a pan only if you shvep9ev*qo7: ;uiwv m7 ake the pan at a certain f*wmo7i:;p9 vve ue7 qvrequency?

Give several everyday examples of resonanan7bk 7 0bil+jce.

Is a rattle in a car ever a re)lxe fd5.f uov )v1la(sonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frek8u rpfxo56tqkhd ;x7 e0( ly1quency of its source? Why or wx07kpdy(x qo8f16et;5lru khhy not?

Explain the difference between the speed of a transverse wave traveling do7o7,*llsh/ n(z zdsv jiaon:1 wn a cord and the speed of a tinnz :hoi1/z7al,*sjv l ns d7o(y piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally l /of7i iq9.h ooa/q8ghave wire wrapped aroun. 8ql7o/ogo /i i9afqhd them?

What kind of waves do you think will travel down a horizontal metal rod if you wrai9wep;: j*wnmyiy7;y g-*strike its end (a) vertically from above and (b) horizontally parallel to its l9;7*m yiwjaw ;ye y-pn:i*wgrength?

Since the density of air decreases with an increase in temperature, buq jj-9v j /;2vsytdowd 62*jfnt the bulk modulus B is nearly independent of temperature, how would you ex* j9n q-vvw2ddofs/jt jj 6;y2pect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease inaq gklzx9by5 *eszt1c(f)z t /pk-b10 amplitude as they travel away from the source.z qa ct -xseb(kpk0g5y*1 lfb19)zz/t

Two linear waves have the same amplitude and speed, and otherwise are identi zvipnm* 7+:ubtcl1t *+wd zchj-+n3w cal, except one has half the wavelength oh cv3*+ 7bj1m+p i: wtz lzn*udc-+nwtf the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between tfsa , k: l,6/vsh j7mmpms.a7qo.3gvtwo sections of cord as in Fig. 11–33, the frequency does not change (although thea.jmf :s7s .t,,mo/lk3 pq g v6mh7avs wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are t k8rwihe1d1+/mhki l 3here any places you could touch it with a knife ilr3 11 me8k+w kid/hhblade without disturbing the motion?

When a standing wave exists on a :.n t r9r( vy*p.z)nocco-tm bstring, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was d.np9nrt.mr -o):c*o(z ytv cbestroyed? Explain.

If we knew that energy was being transmitted fromgam+):q1,c4htkazuv :3esv 86pbl ix27zt aw one place to another, how might we determine whether the energy ge, pqv: :zh7ztw u x326t+c aksaim)8lavb14was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m3cgg 2bhjjyn*6:o - hb, what is the total distance it tra26nh3gyjg-b h:cjb o* vels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from 96equrqnhh8j. **2l d2 oqgufit but is 85 cm long when a weqgn 6fd 8j9*r 2u *e.hol2qquhight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5wlu(r 8ald aq:hf.4 /v.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 vibration8.wu( dlr fah/a:q4v ls?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hang5v:rcy rk 8k9qs from it. (a) What is the spring stiffness q krcvk: 9ry58constant $\approx$    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 ofaq5;likpy icn* 444agr6(qb i 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if onln44ai*6iq bgi a ;4kql5yp (cry 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of theu;: h8td7t 7bf; thlge mass in Fig. 11–2 at times t = 0,tut dl h:t7;;7fghte8b = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 z)r8qw qet8j; web. The web vibrates predominately with a frequency of 4.0 Hzwq)qrj8t8 ; ez.
(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 wxkso u7+2 fgc8qgw0g8ith a frequency of 0.88 Hz. When an additional 680-g mass igog q8sx uk fcw8+7g02s added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end2t 3a4do-r(p3tk7gua xxje;w of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Dex-w;ue g(paax tort 3d2 k43j7termine
(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 s,uc7:+g jsqkxj2wsk : peed of a SHO half the maximum val7s ,ckjx:jw:u2gsq k+ue?$\approx$    A

A mass attached to the end of a spring is stretched a dixmkw8e871; 5np; whsuygeb t;stance $x_0$ 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 stretcht s 9b0ft:s6ix 8q11naky 1ochj7-z fzed an additional 0.130 m and released, how long does it take to r9cjq nfb -otzs0 y7fi1 1tha zxs8k61:each the (new) equilibrium position again?    s

  An object with mass 3.q9mlrd0 cths s;x5;d1e3g n0 nxob,a ) 1oe2jj0 kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is mecn)x ; sxqe;blodhj931510g ,n j0or d2a tsmoving 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 compressq v)a. fjns72 ehm9df2.or (0nljcc4v the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. n0ac7 f( .qdmn.2e4 c)vj jv2h fs9lroWith what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface i87q, kx ua5 s/p9,ldrkou+qgz s 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 restozqs,ak p9 7x8+qkg/u dl5ru, 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 = 0.45cos6.47q tazxn72 i:jvu a.og4)e.s yt where x is in meters and t is in seconds. Determag..nj) 7uaev txy: iosq74z2ine
(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 ffg fd*u13w,os 76 kiehrom equilibrium is the energy of a SHO half KE and half PE? ±ed h is7f13uf,og*kw6    A

  If one vibration has 7.0 times the energy of a second, but their frh56d6 b fhuc:(cj--gv bfw9x pequencies and masses are the same, what is the rabhgd p- 6c6 (9chvjb:-5 uffxwtio of their amplitudes?   

  A 2.00-kg pumpkin osci d) 9(arpo5 wayt3w:9hokifu3llates from a vertically hanging light spring once every 0.a)a3woft 9dip h3(:w uoky95r65 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 vertical spsc65nacr. bnqx6 ;xh)/ aut/urings, each with spring stiffness constant k (Fig. 11–49). What will be thecbhx6n5 c6//a xn) r.uqtas;u frequency of vibration?

  A 300-g mass vibrate7.3a h4s 1,- kyoc iuon/fkp*enfwyz*s according to the equation x = 0.38sin6.5t where x is in meters and t is h3oao* w1k cp7n*zn y-i,f/. k ufes4yin 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 SH.-p 0*rpmktpw(bi. af2 f76aow7ps uyM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 12vw5( eow3tb)*5t z5g vtff gjc.:x :hq7jk8aq4 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determitc(w:gt .:hvoq3*z )afj bwjk 55 tfq v7x8ge5ne
(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 ampli*h u)-rhr; wiztude of 28.0 cm when 0.260 kg hangs from it. The mass passes *rzru );w h-hithrough 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,.xhv wkvlofunxw:)/9dms2/ . 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 fixeq j k/4av/v9n*paag3qd horizontal spring whose spring stiffness constang*3j/paa9 avqq4nkv/t 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 reaching his )8*3h1ykr uqdl:ramf lowest rq81d klu :3 *rahmyf)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 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.-lzgp hqbs r,j54 cw4 exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to makeb 9umin;s up+1 exactly one swing per second? (That is, one complete vibration takes exactly ;bp miuun9s+12.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its pn(g**uh pe.ffeob-9 7toom-ueriod on Mars, where the acceleration of gravityoefbo*hfg*e.n7mtu( -u -o9p is about 0.37 that on Earth?    s

  What is the period of * c/;(fs aavqw3kq-oia simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple p3llid*s a,p5 rendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is rell3ra5*, dlps ieased 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’i9 hlaxrt,c ;.g6lx)sgrv9 h;s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you ad9x ,rgs it9)a;xh;.rl6c hgvljust the length of the pendulum? shortened by    mm.

Derive a formula for ther( r( toegx;ow1)hkplpr (op11(q r7q maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At mqs2 fnn s:thzfmjp8h t;qxz345; t(9 it is released from rest starting q:f 9qjns8m (s42xphz;tnf t thm5z; 3at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave cretsh6 r. 3w:erdt75 fypsts pass the bow of his anchored boat every 3.0 s. He measuret 7.6 5r3pye :thdrswfs 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 frequency of 262 Hz and travels with a speed of 3439pzbj(cbvm(b5rw o (; m/s How far apart are the wave crests (compressions)?z5(wbr; jpvo( (bc9mb    m

  (a) AM radio signals have frequencies between r,k4wqu.vo8j* :rm +zbcya7p 550 kHz and 1600 kHz (kilohertz) and travel with a spebw 74: c. vr,ku*rzjqa+o8 ymped 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 c 3im;5 bgjk1sof longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as the **uhx5 u u a7 mvjvze:c;6ro,sti1et7other. In which rod will the spuvctiej :o s1, thr*u*7e5va;xum76zeed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 koed 4vo8ol/ y:.u6 jwwg2rd;d, 8;wqb)r uhcxg is stretched between two supports 28 m apart. If the tension in the r xo y8ud)dhq o;.bwog6d:wr,u;vwc/2 8lj4ecord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connect6ts/yi1b) azj7i7ihv(t qcel - 6dl 7ned to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pul tnt- 6d )av7 iljeq/ l7y(izhbcs67i1se 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 belowc ,qo7evj+(czueo(: a5f) txj; fo3tu 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 the ocean at this poiuv qjx:)3ettj5c;f( ao,zue+ ( 7o cfont?    m

  P and S waves from an earthquake dh7 lyyt hpnqgr2o kev 7k9z 41pl1;8zry7x+ -travel at different speeds, and this difference helps in locattqz1 k rv2- ;nyxo 9 p8hl7+h77zlpd4y1erky ging 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 wave89h dfvn* *pai can be 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 begin to leave contact wi8v*ha ndif p*9th the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensitie;)vtqj7) zuklz 33byks, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from ttyv)b k)7 ;zku 3zj3qlhe source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measure 8eq7kmx8r/yu)eqtb ;d to be ux7 8eq/)rt ;mk b8qey$ 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 wavesvc;sd/n *9tme of the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amev /t9 ns;dc*mplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but on f.clb3/q0fjp7i p)4 m7aovtne transports three times the power of thpb f7a)j7mq0pn t/i3 lo4fcv .e other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond ijjk/ +wa30togs observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes jgjka0+/3w ot. 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 each other. (a) Sketch tk lpay.6c l1ed:b(b yk1cn-9u he 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 momenun:ck1ey (kbblp.9c d -a yl61t?

  If a violin string vibrates /eqm3 t 70w 4 nk7bzf3vvv0kemat 440 Hz as its fundamental frequency, what are the frequencies of the firstq/ v evfm0bv3 77nwek30 mz4tk four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrat2 fbzbu+cq 2 3gz*eov-lx5ty,es at 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, ob,x gqve z5obc2tu3f-y l z*+2nly two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at le7v pweh1ppo,i 5iegzj8(6us- ast three other fru iepps(zw v67h-jp1ie,5 go 8equencies 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 standing7e1 ;mf ,(zgg kjnra--6nk rpj waves is 475 Hz, how far apart are two adjacenk-r ga7p m n1jnjz(6ke-,; fgrt nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what is5 h2;iwn)c7upef sh-w the frequen fc5wh)wp 2u ;se-h7incy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from th n. :i)/d7 st) ocbbk23udvnern/;fcje 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 te sjc;v3nk//7:ucifo2 ). ndnb tbdr) wo overtones?    Hz

  A particular guitar string is supposed to, d0ay1 h /lss1g )g;rva-vnpxeun6i4 vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shosyldsa4/x6 )h,vp1n ne ;vrgug-1 ai0uld the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is 6(aqw9 wt;)kaef sy(iv edfp vg1)ecc/k/l-2supposed 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 the frcl)gas9(f6e/avi )q e pkvwyw1t/de2f k( c- ;equency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 6 q9j 5t2fw qikiug*oeg v8)ce,o 78oj00-Hzewig u0feo78 jv t5 goiqc)q9j8o k*2, vibrator. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the s8l)fota8sm 0to3pmz,hr cr . ,tring may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standinl mrst0h,)p, aoo tf.m8r3zc8g wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the righvp3flq: u-cspa69h m/t 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 speed of thh :63uqf s-l 9mca/vppe water wave?    m/s

  An earthquake P wave travelis e9aaq x,(dc8a(9larng at k.0 km/s strikes a boundary within the Earth between two kinds of mate9r aqlxaes8a(ad9(,crial. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “)ffuh.ac26i .igt1 psx n eut8n ,q65gshelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the f5t6h6iufngnxq)p.g ,2u e.a8 sc1 i tincident 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 ofvaf 48n(2c2g :6 lyo3znby xuklj-4ap cold, dense air. If the sound wave hits the cold air interface at ax4jya2-vf(g3k2ypluo nn64z 8lcb:a n 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 iq;t/tmqp- -8u st+yqbetween two types of rock at a 3 /q+u pytm;t-iqsqt8-8 $^{\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. Ackneejdx r+ag;ud 7+7 7cording to the user’s manual, the dish has to be pointed in the direction of the satellite, but an ;jx7duae d7 rke++7ngerror of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across7qv +vq 2q9absf3gqe5j3 mii 6 the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea leve37af5is v9jqgivm e+qqq32 6bl in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/mchu)c43e : -dbt) z1t( lrend /suwjh, Find the maximum compre3 :s/1ecbl4h-cwn z,)dueh)utd t(rjssion of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a sq* psnkb-305*mv5 fv5jyh ,i5tgvbh window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a v5st5 my-5 hfbq hiv kng p05*b3*jv,ssimple 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 then fpt, dnn.x6f:n uh+vr 6alls 33 cm before it stops and begins to rise. What is the freq,tnvn . d6n:p+fu xhr6uency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fikx5/ ivfa4vl 8g. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the sprilaxk 485 v/vfing?    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 coffio e 00q14r kjh4gaf/gvy,ya )ee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually i, eh0v4)g/ f 1ajog ar4k0qyyit 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 thp t3v-sldkbj v3q61g9e center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of thvvb l1-tk3d 9 6psg3jqe sound emitted?    Hz

  A 2.00-kg mass vibrates acc a jj8i32lbcjce*rfm2 /+st :yqpb8f ;ording to the equation x=0.650cos7.40t where x is in meters and t in seconds.ycb i82 f8+fa ;j3j 2pt*:b jqlrmc/se Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency cp ez/h f-e;v3f. What is its frequency if it accelerates at; -z ep/he3cfv 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg m /x5 ;gguygt:vw.bwi3 an stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the v5: wtigb w/.ug3 xy;graft 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 tunr+s5lhexl5ls/xr b80 ed to play at 392 Hz (G) and 440 Hz (r/r 8s5x lx+blhe5ls0A).
(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 stretched0+z7k to xga37wjm l0x 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) for 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 lightwz o0 +0mj xl73k7axgter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip t-0yi cp96l ysort04d bhcv;- of each prong moves 1.8 mt0 ls;vyc b4 69pch-tr- 0yoidm 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 freque3 k3lax )ma8t5t1/nq woav8prncy 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placedapn/3qa3x tmr)v 5ok8tlw81 a there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “fsyye f 1n( +; dxzdy444/zyd/qci1 zburee” end if that end is attached to a ring that can slide without friction on a f izy/4/xe (yu+ bqzzy41n y41;dcdsdvertical pole (Fig. 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 exactl) /ff: czef9hmy 2.000 s — each one-way swing takes 1zm)/hf9e f f:c.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or cank(w, taa/g:n03f yrv z+r5 xjp swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, (3n:rypkw5z,v0r taf g/ x+jaand 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 tensiodhv)bxve+2 m 8pb g)qkkg: 6m28oh ajti;ur03n of 255 N. A pulse is generatemx 6aqbp)rvub:;m 82 2hkigkg+t)j30v8ho edd at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceili 6o(cq: - 9f incmk;,hgbwm3;h3incf hng by a spring with spring stiffness constankhwm- , qfo6nchgc:i; ;mfh3n c 9bi3(t 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 top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable5xn, 0 2igm8lj8yvg3b9 yhndu is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the en,umhvg0jin988y2x ny 5lbdg3 d of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives x2zek67lh-m dujlh9+the dimensions of the block). You push it sideways as shown, and then yh7j eld2lu6-kx 9+mzh ou 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