Give some examples of everyday vibrating objects. Which exhibit SHM, at leastm ,)4x nb axpifjsi7,1 approximnjima4b1,s, 7)f xi xpately?

Is the acceleration of a simple harmonic oscillator ever zero?2ziru; lk o8a0 If so, where?

Explain why the motion of aw snw n3 7-nc).mufps3 piston in an automobile engine is approximately simple ha3pncnnsu-.37w)fw s m rmonic.

Real springs have mass. Will the truedeme t01u*ed, period and frequency be larger or smaller than given by the equations for a mass oscillating on the en ed0te,u *1mded of an idealized massless spring? Explain.

How could you double the maximum speed of a simple har;h -6e2anw1igp nf k/*li9txq monic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and th q*aaue;u 6+zgen is released. Describe the scale uzaeu*;g6 a q+reading as a function of time.

If a pendulum clock is acc 50uryxy df ;m;yg0y6of9g-kwurate at sea level, will it gain or lose time when taken tgumo 0f96yyw;;y k0 f-xd5r gyo high altitude? Why?

A tire swing hanging from a branch rev33fd 7 1)zybfqy z h+ fwvvabk5kw:59aches nearly to the ground (Fig. 11–48). How could you estimate5 )7 kf:3vdvzzfqwwyybba h3k+51 f9v the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a panvm0328uwwfr 0 kmrd3l fg t2c0 only if you shake the pan at a certain frg0dl0c 02 mvmw8uf3t3 rrf2kwequency?

Give several everyday ,ve0f bk.jy qm891aqy*cryz 2examples of resonance.

Is a rattle in a car ever a resonance phenomeno1j;0 fp lu;zxzn? Explain.

Is the frequency of a simple periodic wave equal to the frequency of itj-*n zfbnvz6,me *1rb s source? Why or why notf6vneb, nzb1*- mrz*j?

Explain the difference between the speed of0o8 ,km j btl zavm3u(qxy ee+1,34vne a transverse wave traveling down a cord and the speed of a tiny pie 3 4o 3mzxa8vjkvey0+t e 1,e(ubnql,mce of the cord.

Why do the strings used for the lowest-frequency notes on a piano n.5i(srk tyl01)4wans3j l no wormally have wire wraiw) r0ny (3.l1wota klsj5s 4npped around them?

What kind of waves do you think will travel down a horizont - lw7h,psolfoei 7qeu; e b4ylf2t491al metal rod if you strike its en4,w oiluqtfe9l-42f;eps 77le ohy1bd (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the bulm(u,ro ef 9,ytk modulus B,(9 ory,t femu is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as thkhi q+ tetj(wugrc-mm nz)0 m35::2uhey travel away from the n:2z tm0ec(r5k) w-u: mqm u ji3ghh+tsource.

Two linear waves hav)vw-p8 5jc wv+k0.n rzqh7bug5 upr*ee the same amplitude and speed, and otherwise are identical, except one has half the wav-uu7 8r hrzcnvwbj5)+q pw g k5*p0.evelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in F cg( .by-2//nywdduqg mg6jw /ig. 11–33, the frequency do2/6gn uy(dcbdw. mj//g yqg-wes not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segm sj+mm*:jgv 6gents, are there any places you could touch it with a knife6v:sgj* jg+m m blade without disturbing the motion?

When a standing wave exists 7kakl3j6f xny9 xnb.9+rh/ep on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this meanj/+axpr6 k h 9 n9l7y.e3xbkfn that energy was destroyed? Explain.

If we knew that energy was being transmitted from one placy nbv- 2bz+ iic-c;;dce to another, how mightbc zcv2 cdy- i;;nb+i- we determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amht . qh-a9zzl.plitude 0.18 m, what is the total distance it travels in one pel t-z.a z9.qhhriod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but i8sjjs9l:qj: b wa/hfh c,cd00s 85 cm long when a weijqf:hcds,a/8 shcj9 jw: b0l0ght 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 5.0 mm whec, qw6i;gey1kn its 68-kg driver gets into the driver’s sk ic;wg61,eyq eat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-k k)yp5 z5pqy*mg fish hangs from it. (a) What is the spring stiff5k 5*zmyppq )yness 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 vibra31 lzwdzgk8 n;tes with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kk g n8z3zd1;lwg hangs from it?    Hz

Construct a Table indicating the pob(0ov/t awf 1fsition x of the mass in Fig. 11–2 at times t = 0,t = wov faf(1t/b0$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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. The web vibdx(*gu3(h,7dfl b dyyaqy/k ,rates predominately with a frequency of 4.0 q (l,d, /*dk ay db(hgfyyx7u3Hz.
(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 6dl5ypfuu1ho8c4 cc79nc) vispring vibrates with a frequency of 0.88 Hz. When an additional 680-g massvcpyl6ocu i 71nc94 cu85hd)f is added to 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 ,c- rhf+8uhv1j7juym times per second with an amplitude of 0.13hmj8 , fjuu-v1yr7h+c 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 s yosg/*xj1:ygp2ks7 dhdqc;ky bn(,, peed of a SHO half the maximum value yy*,q1js,k7g;kpc/h dsd ybog:x2n(?$\approx$    A

A mass attached to the end of a spring is stretc68zl) ca/oy6x nmp, if(+ qiknhed 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 f8z qg9eix53 jb3i zv4a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the eb xvqfz8394gj35 zii(new) equilibrium position again?    s

  An object with mass 3.0 kg is attachedpbblak7x 91h alxo1,n7 km o+ku),)o j to a spring with spring stiffness constant k = 280 N/mlk, o, bmpkl7u1)j9+ aoo7h k1axn) xb and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spr69jt*q ytrf+ wing of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what spt q6*+wjy9 ftreed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is bme37bc5c.si 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 fs3e cmb75bi. crom 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 t 4e i;e42ke)zxgnuq v hh75a3fo the equation x = 0.45cos6.4t where x is in meters and t is in seconds.ev4i732ah5ehuf)e kz;qxn 4g 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 frnp3 u vwm,v7w8ys3 *pcom equilibrium is the energy of a SHO half KE and half PE? 3pp c,us8mwy7vv *nw3±    A

  If one vibration has 7y3j4t)qk,q r s5mfb hu8 y/ ,fj;bew8h.0 times the energy of a second, but their frequencies and masses are the same, what is the rati8 ;s5, j4ufbqbqyf/j) 8e ykhtw 3,hmro of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a gc x;smv9- uxob q4g)(vertically hanging light spring once every 0.654xmg9)b-s (ucoq;gxv 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 springs, hx2j6+17 d;f52pf9riom7 n x y2oygkf,d xeen each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrationh fj2kd2 2,9pd77yxf 56n on;x xrfgme1eyio+?

  A 300-g mass vibrates according to the equation x 7td- cba8hr b(fwhs 2/9bsz j26fwwjo75v2o n= 0.38sin6.5t where x is in meters and t is in seconds. Detabb(f8w 2o2j sds62 9v77hn /jw5thb- rwco fzermine
(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 of6t3*aeaezul 5 SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at jal k( wq/ybt34tc *+hi2kd, hrest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial +wl3i* hbh djc/(a4ttky q2,kspeed 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(ggyga opwsy;52d,z 2z3m e9k with an amplitude of og, ps5g; 3 ym9(wgd2e 2kzzya28.0 cm when 0.260 kg hangs 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 stiffness constants .wpynz r.9q6nj1 )b 1vmhpir 8$k_1$ 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 firwlo;t j)x:w/z8 lqvp)xle8x.d fp()xed horizontal spring whose spring stiffnesrt(; jl p :odlwl) 8pv)8)wf xx/qe.xzs 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. After reaching hhumh;4 llnnv8 io2bhy yu, *,2is lowest point, h2l,,8; v hhlbu iyny2* hnum4oe 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 exactly 8 ntosej09/rs60 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 perfz-- cp1s9p5 hmw p6qu0qogx 9 second?p mzcf-99uh sq-o5 1pwgqpx 60 (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wherekpz i8nh c+ ,(e3e6aup the acceleration of gzei p p8c3kn a(e,+u6hravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulumqw7noyk r)0igsp *8t : 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a x8e bpg2l .(y ,izev(lmass of 365 grams, and it is released at an angyll,(p(i2.b 8e vxz gele 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. i3uzdzrr06wbr6(ji5 rufv 0 4 If the clock loses half a minute per day, how should you adjust the length of td (4urri5 6r3v6zz0 wirf 0jbuhe pendulum? shortened by    mm.

Derive a formula for the 6csj/kas94p vmaximum 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 28vahy 9hs1nf 2.5 Hz. At it is released from rest starting at an asf2yahv19h8n ngle 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 crests pass the bow of his anchored boat e 2x7*(sx+qgfp* xobc bejmf;,very 3.0 s. He measures the distance between two crebcx;* q 2pe+of,mjxx* s b7g(fsts to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequenxi :9,fp/h(7l enak od7t9enncy of 262 Hz and travels with a speed of 343 m/s How far 7lf p 9eno:axiteh,97/nk(ndapart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kil .j6pca1 a.7d j3-1fdiwiigqx ohertz) and travel aidai.qjj-f1gic7p x 1d36.w 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 longitudin ,p0lr*/dn fwbal 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 asb8ytf10az8s h the other. In which rod will the0818satfhy zb speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If q+ue4 e as*xkyxh*9 .ip3 .fkq.2drbpm+f-tqthe tension in the cord is 150 N,y3f + e.rekh+x*f2mp k* .b 49dsutq-qqxpi.a how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the too3* k:2cmoa 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 pulse along o2otkaoc3m:* 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 shl)qkn(v cp(t19koamesi 3a74 ip just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly7msal)cn oqv3i9ke(k(at 14p below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel atvioef/ pd n66gimr) 6kpf8 j/8 different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took p miif/ 6kd6ejv rpno)pfg8/86 lace).
(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 tradcxvninbv3c+mj;ys1q6 6; ah -oi 6- cnsverse 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 with then; a;iq-omd6hb- cx i+yc 66s13cvvjn ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplituddnjtw )7 c*fkkp4idf.5/t, ty es, of an earthquake P wave passing through the Earth and detected at4fi* ) tk,f7kjct .wn/yddp5t two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured tow1ozo61 tn 13u lurs,i;x cbj+ be tw;o3sjl6 zboc+uru1n 1xi 1, $ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the4 xltr8n- sg;00mm-rq 0fuspj same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wt0jgsxnu- p m8r-;qm40frsl 0 aves?   

  Two waves traveling along a stretched nov- qa (wy)j.ld +3;v2bhuflhl 1u0zstring have the same frequency, but one transports three t nb(l-1al3v20hjyqolh;+.uf )wdu zvimes the power 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 and down a total verticxll f8de 5 z)vnjuq7:+al ln8)lz5j+ux f 7qdv:edistance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in F2qw2 jciq2x/vt 9fajch1qk6br f8z: 2ig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each rj2tiq2 wb6cqfhjk 2 2 zf1x/:cvaq98other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequ* aium4kk tc rx,z9;+jency, what are the frequencies ofuc,+a k*t ;r kmi4zjx9 the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 2pg(m3-c-6r l-ub e;b vssxv5e94 Hz when unfingered. At what frequency will it vibrate if itm5-c-eg(;pvvbu - ls3 6xrse b is fingered one-third of the 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 loops at a frequency of 280 Hz. Namenhg.*en +k5+;xe zstm at least three other frequencies at 5exntgs +km h*z;+.enwhich 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 wa1e y4fy+ w;u)agiyh7gves is 475 Hz, how far apar iwy1gha)y+g;7fe4 yut are two adjacent nodes?   m

  If two successive overtones of a vibrating sg,ox69x4c.d . ubkpx1pk oj 8uqvnd+. tring are 280 Hz and 350 Hz, what is the frequency of the fundan.+px,u.ug opk c.q vd 9x 41b6xdokj8mental?    Hz

  A guitar string is 90 cm 4e:f cb3w+bc , / k9xwtionqz/kyx;-hlong and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is uy/w/k x9tnxocibkwf+e-:;4, cz h3qb nder a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to v-x0osq4 25dk7o5sfze9 pvoym0 ahvr+ ibrate 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 fp9q4 oy r0fvos+ 5e2 hm7o5ks0-zdaxv requency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but ic1u/ 1oln53hf:gy*gj/uv ,1 ksk zq nzt is measured to vibrate at 205uk,hk jyolv1nn1cz/ u:z/1sg fqg 53* Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal s f0ph)2 fo+ilotring is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per un flp0o+oi2 )hfit 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 strix2n,p zt nb4.fng may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave p2pt.4zn ,b fnxatterns 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 right freqvy;qis nt:c+4/ jd13vkn3rnv uency, the water alternately rises and falls at each end, remaining relatively calm at the center. Supposes3dnqk nviv3 ;1yc tnv/r+ 4:j the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s s f4-tzjn* pw5 5eaah/etrikes a boundary within the Earth between two kinds of material. If5t/*4ephaa5jw n -fe z 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 underwya+l2pj m(2: ;o 3ag3yvzgqrviq; z;uq*qx2w ater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests makel2(ar3;x q;v pujiya2mqy q:*vg q; 2 3w+ogzz a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when i qq fd+r ;zb(6ixum7i-t hits a layer of cold, dense air. If the b6 xfrz(q idiqum;-+7 sound wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between twj) 5 ey, y.+qmf -fnfmgt0ozv*o types of rock at a 38 )y*mz tfqfm ey0fovj ,+5.- gn$^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to th0yi2:yw) sv zhe user’s manual, the dish has to be pointed in the direction of the satellite, :zshy)w20v iy 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 velxf nw)76 zjt b7v9ud8uocity 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? jf9u zux77d8b tn)6wv(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 stiffnwngd; av5m6lt5:fu 9r; r6iciess 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 (approxima96l5n6ri f5g wt :u;dravmic; tely 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches thq9y 7zmizo5) ujz us+2e net 1.1 m. Assyi)j 7m2 zuo59u zs+zqume that the net behaves like 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. (o y*z1 y0me eux6+oqyThe mass then falls 33 cm befe+q01ye6y*uox yzo(m ore it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54) 1 1f*skhzw7zzs7l u0z, compressing the spring 5.0 m. (a) What k7wsf01lz z7szz *uh1is 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 jus +y-5.co r+d.kta;tqk prg)oct the right pace of about 1 step per second, the coffee sloshes more and more untcrt t-.) kkgqdy5; +r p+a.ocoil 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 certa(jpjuh /7c/ nwy fy8e:in groove 10.8 cm from the center of a 33-rpm phonograph record havp :/ /jh(yuf8jecwyn7e a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates achqe at,b,d k6 (.4uejqcording to the equation x=0.650cos7.40t where x is in mq,j4bu ,qe (t.ek had6eters and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with:tw g b,qc.k )e0*yurp frequency f. What is its frequency if it accelerates at 0.50g (a) upwq.ycwue) * ,tkg0bpr:ard,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands lvifs:c3jc6b;(f p:ldqj (zn- *tso- on the raft, it sinks 4.0 cm deeper into the water. When he steps off:t6;p --jnlics :obd3*zfvlsc( f(jq, 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) andrij u)zx8b7iaq ( j,i8 440 Hz (A). )j z8(u jaqb8iix ir,7
(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 cord bpuz*/nku obt.55e)(j / /wlsb m4wfb 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)n*l /bkw f 5 z/./uwu5ebbpojs4tm(b 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 lighter?

  A tuning fork vibrates at a frequency of 264 598pk yso z6dh+yv8gd, wdnr7Hz, and the tip of each prong moves 1.8 mm to either side of center. Calcu9 5 rkddzs +og87h8pwyv,dny6late
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simslsyx )/;9r usple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end9sry)ux l/ s;s 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” end ifnhfg,nyz( /g - that 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 stringyn g,/znhf(-g with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing t4;y2l k ti,ci5/yns kiakes sy4 ki tiy;/n25,k cli1.000 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 can swinsmgq,baps2 5 -xftm,-g as a pendulum of small amplitu qpmx -tg- mf2b,5a,ssde, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 ,+fpjybkq*9spnv8d 5 ycl: n/ N. A pulse is generated at one end, and 20.0 ms later a second pulse is gener *c y5sj vdk9/f:y8qp,pnbl+n ated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling wk :wazzbl *u(q1q nzp..sup 2,*fh/sby a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude zwq**puh(s uz nlf2s.1p/a: qz k.w,bof 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 craneo /zkt3(y ko;w 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(;oy k3k /wtoz 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 : p9r(;0gn w x9doubgpq/o( mpthe dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrat09gobp/mgopp u ((:;rd9x w nqe. 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