Give some examples of everyday vibrating objetp sler4ya +k u080,kicts. Which exhibit SHM, at least approximatel,+ akl0tk8i4s 0upyrey?

Is the acceleration of a simple harmonic oscillator ever zero? If so, k)nbw/,mwde i. cvssh +8x 9 il:0gn1hwhere?

Explain why the motion of a piston in an automobile engine is approximate p yojv6d*5v1kq3ay:kly simpo1yavk 5 * 36q:yjdpkvle harmonic.

Real springs have mass. Wy r,-7ra:jyzk ill the true period and frequency be larger or smaller than given by the equatirkr : j-y7za,yons for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (j(dtw.s /: sk x3sh5kv e9+tpfSHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is rltn6srqm-jt 9 h4 v4,xelelq 4mh 9x4 nts6-vtj,rased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea levelxwfpt 5+mt/,v *cz r2f, will it gain or lose time when take pfx,c vt+*m5twzf2r /n to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48d 9f6bywzwt *+p 9awu n(f80xe:a/ty f). How could a 6:ybwf/(8n w+ e09wzpy fdxtuat*f9you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan onleu;l .2q10s pvvwh k m/*0xetfpc+2 ksy if you shake the pan at a certain 2t;u+ 1ecf.0p2lkkwsphv v q0xm es/*frequency?

Give several everyday exampyx g+v + 4;uanon4z+svles of resonance.

Is a rattle in a car ever a reson.byxhbxiw xinb41 ):- ance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of q/j4 x3jhb+f pj ),ipyits source? Why x+jp/j34pj hqif , )ybor why not?

Explain the difference between the speed of a:+ysu9b7hj v( po zuap0, ztxvpf;p7 : transverse wave traveling down a cord and the speed of a tiny 70 fp(jaovp;uuzz,vx: p+b9:h y p7ts piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano no vro- )2kk(hcormally have wire wrapped around thrhckv( k-2o) oem?

What kind of waves dol4)e mq3 myg6b you think will travel down a horizontal metal rod if you strike its end64g)mb3 qleym (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases u(a9zlh9 ti 5z*ksu*i with an increase in temperature, but the bulk modulus B is nearly independent of temperk u*t9si u5l9*(iahzzature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular watg mfy/v7my 4vu8s af b,g6v38-g yrp.her waves decrease in amplitude as they travel away from th7msv hvp mfg8.g6 yr 3uayg4yb8-v/,fe source.

Two linear waves have the same amplitude and speed, and otherwise are ideod*,lxqvp1. b ot, 7ckntical, except one has half the wavelength of the other. Which transmits more en 1 .*,ktxocvd7ob,ql pergy? By what factor?

When a sinusoidal wa,4s6erzeb1zu:*jb nd ve crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain wrzzbu6j:1 4se b* ,dnehy.

If a string is vibrating in three segments, are therg45at)p.ajq.xm+ kxke any places you could touch it with a knife blade without da k5.q. j4ak+m )xptgxisturbing the motion?

When a standing wave exists on a string, the vibrations of i;m m3(aw.(hlvx fzwd9 ncident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explaiwh(fzx(v93admlw; m. n.

If we knew that energy was being transmitted from one place t59 h2 5elgfunt3 ; tm7engokp7 :1jybho another, how might we determine whether tht gkge;oh9jl:fnm7 73p51bty e2 n h5ue energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the tot69b2wmh6;1 axoz jfxp kqz 0g9al distance it travels in one j ;z6k0 hfpg9zq bw1x am6x9o2period?    m

  An elastic cord is 65 cm long when a weight ofullbc ,8 nh,+h+4kty b 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this el l8+ knbuh+,h4ctbl,yastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm 3 z2 0nb-aogjxwhen its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be th0xz ojb-2 nga3e frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a -) . hvruv y,yg,(exjjsov6n12.7-kg fish hangs from it. (a) What is the so 1y( hue -v) ns,.jgvy,xrvj6pring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass ky/2o ras.rg+ of 0.60 kg is hung from it. What is its frequency if only 0.rgkr. y /os+2a38 kg hangs from it?    Hz

Construct a Table indicating the position x of henckc*n9j *1(b-szu the mass in Fig. 11–2 at times t = 0,t c*c*n zuh (j 9sn-k1be= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 cauf/i yov*-du qevv,+w -ght in a spider’s web. The web vibrates predominately with a fo-vyvife+,u d v*qw /-requency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When an)+h cno;d ffd9 addhfno +c ;d9)dfitional 680-g mass 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 times per .igmt r)e6g2o second with an amplitude oige omr t)6.g2f 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 bx4nityve ;t6zl d,ypu w;5vz 6 am(e70-x3he speed of a SHO half the maximum valu ; 3u6 vwnzx xet7iy4,5(-ebdm p; hvtyle06zae?$\approx$    A

A mass attached to the end of a spring is stretched a dista g26g 6 srf9uw92je+vvl1nkhx nce $x_0$ 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 mrfth6y 7gl*eee (gn.3,vdjn:g k5 qi9. If the spring is stretched an addt3jy*r(nven:qe7elg,.6fh9dg i5k gitional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3f fatc 3xv5s6s4*2gn y.0 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 moviny5 x*2fcf6 3tsg 4ansvg 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 80rmy)3*gr uh7 ,qzpk oi x.3qz5.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg b3 ,qh.5z mxoyq7u3* k)rpirz gall. With what speed will the ball leave the gun?    m/s

  A mass sitting on a hori3ae9 8zwb leh+zontal, frictionless surface is attached to one end of a sprin8 93ewb+hael zg; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring 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 = 0.45cos6.4t w0 *aw- i,nqgmu rvb .xb6d:dh(here x is in meters and t is in secgw:.di-( brn xubd6m0 a*,qh vonds. 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 equilib:q/bo4t5 f u.5ffsd jlrium is the energy of a SHO half KE and half PE? ±: fo/db5tf lqf s54u.j    A

  If one vibration has 7.0 ti99,rlo p,6tjscj*c vy bhkyc wyy k;bt.9 8h53mes the energy of a second, but their frequencies and.j, 9tjhctyo;srly* 35wyp6ch 9b vk 9k,c8yb masses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring oncef5j*y 3 lo ya) edcopu*rq6/7)*txg di every 0.6f/ddu jr *l7peqx6oy c3*5t ) g)io*ya5 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 iv1io vf/l nxe ( z4hk;lpe*:f:ubx5.ydentical parallel vertical springs, each with spring s (x5oiz:u.e4lk1bynhf e;lv :xp/v f*tiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t oz/b)c j0y6u nwhere x is in meters andnu/c0j) yz b6o t is in 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 B. For m/n9k-kvy oe u7+wvk(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 =r668f+bfl qopd5 -eawquq a 31 124 N/m) is struck by a hammer, which 18qqp-aabr 6q e6 u53dlf+owfgives 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 sprvt4/*jfpcgz mk1*n q; ing stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs frv*/n1ft zqjgcpk* 4;mom 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, w,mnr9i )cbs5eith 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 h )zwgwl pg6wc; wmlr*,a (*mj.orizontal spring whose spring stiffness copgam.z6 (g) wr,wj*wml *wl c;nstant 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 k rpp.bklg)o2-.7ug8 r4xfz qwg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the qxrkf4. w2ol7pr-8b) z gu pg.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. What is its (pavv0yl -z,j
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to makhnq/vtzu 80xge+c4 q,e exactly one swing per second? (That is, one complete vibration takes exac+ c 48zeghuq 0ntxqv/,tly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, w g8 -j5v4ky6,umrznuchere the acceleration of gravity is about,j 5mgr 8 uc4kn-uyzv6 0.37 that on Earth?    s

  What is the period of a st0) q cawik9b3r:f2cbjv hk9* imple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum /z*ab6j x+5jtrp m6hi bob has a mass of 365 gram+jjx6 5phti/maz b *6rs, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a lengt toue4errkg + 8o y6xz(d73yy,h of 0.9930 m. If the clock loses half a minutezro,yrt+3x4o ked8y u6(eyg 7 per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spee3vevqzfsg j 2p7 m:l h/1l:/byd $v_{max}$ 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 frequwmdciny*e;: . ency of 2.5 Hz. At it is released from rest starting at an angle ofw;n im.yd:c e* 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 1dqxe 610s clt8y6xmothat 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 fastm tel6x6s1qy8co0 xd1 are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz l:ua, arh)p(1 ,mflhnand travels with a speed of 343 m/s How far apart are the wavemp:),af,l ur1nhh(al crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kil(/tm v-lc8xaxy a u*4pm x),lrohertz) and travel with a spe/crultl,-x(xa m48maypv )x*ed 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 longitudinal waves7:h66/ vzlfze ka;em d in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus,w un4t+0p bs9k but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and 4 +0k wp9tbsunby what factor?   

  A cord of mass 0.65 kg is stretched betweeni0ug s 4y1v1gl two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to v0i 4 glus11ygtravel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cab gbhthy7k-9gup ; 9+tile of length 620 m and diameter 1.5 cm. As the gondola comes to the gb+9gk9htp-y7ut;ih end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. a; )agfx3io-rHe hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the -)ri gx3fao; aocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this differenclt;01 tns/z ider2e(x+ 5 +ouy nc5khie helps in locating the earthquake “epicenter” (where the disturbance to+5tyzn d/ 0cois+5ih ;nue (e2ktl1 xrok 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 trans ()c* fqtxs2:pif*lhn verse 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 the ground? [Hint: Sh*f*it:f( lpsx n)2cqet the acceleration a>g]    m

  What is the ratio of (a) the intensities, andt+o;05p 9+nejmjx5yw yuz 89j3q v him (b) the amplitudes, of an earthquake P wave passing throu + jjw0hqy+3vt9ym9op8ni xm;ez 5u5jgh the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth *hlin,,+p* v6mzv6hyigj c0 q toq q2+is measured to be ht*g2 o0zh nq6v jy+v l*p+iqq6c,,m i$ 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 the same portion of th 4t 7xgghqg b7pkx 3e)+uv.1ql70qthge Earth, but one is carrying twice the energy. What is qubg7t t 4g +k.7qpx)7gxe3q h0g1hvlthe ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have twia2ir2 u ,z vuz9n;c5he same frequency, but one transpo5 i zunawir2v 2z9;uc,rts three times 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 observe w5j7n6qgu h*l*o 7gowd to move up and down a total vertical distance of 6.0 cm, from the lowest wn76hgl*o wj u5o*7g qto 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 Fig. 11–5 htr6)mtb4xb(2 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 latert (t )4rbhmb6x. (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 2d47m wy )a/st(xta tjz:t;fz7 rah 9gHz as its fundamental frequency, what are the frequencies of the first)rw dttt;j4xfh(7tm 7a /za9:syag2 z four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates larsnjo()d+qz,il7; i 5 r( cg(y5rkwat 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 the string vibrates iqr 5ka zcrswl n(7 y)5i+ lj(og,r(;das a standing wave.)    Hz

  A particular string resonates in four loops at a frendy)az)u 8e52 xdk:ug quency of 280 Hz. Name at leaszygn58 d2kux) da:u )et three other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing waves si)8- q evmkqvh; te58is 475 Hz, how far apart are two adjacen-mt e8e5;k h svq8i)qvt nodes?   m

  If two successive overtones of a vibrating )gf f- lihfyea5ff1hur1 0,- estring are 280 Hz and 350 Hz, what is ifulefhr1 150fyhaf)fe--,g the frequency of the fundamental?    Hz

  A guitar string is 90 cm long and 1lzi3mm1qdo2t0us mjmx88 l0has a mass of 3.6 g. The distance from the bridge to the support post is Lq ljmtz0l1i1m80sum2m do38x = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed toj)*r jn)ppb y4l jy7q6 vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent y bpj)ly6)74*rjnqp jshould 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 s ;gbu:it;c 1,n0h6 qcae1 owghupposed 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 frequency?1h6h;0 1qtgb a,wu ig: ecnoc; decreased by    %

  One end of a horizontal string is attached to a smay2 wg;59hrt edxw msthajc13c85 3:olll-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length wyhj g2 5dlo;etmw5s 1t3rh a:9x3cc8 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 string may be adjusted by moving tho+bq/ylw: ti ow5 q+x,e pulley. If the hanging mass m is fixed at 0.080 kg, how many difyoiob,/xw tqw+ + :q5lferent standing 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 dw80;; msws yzz pxon 7k5gl86tub at just the right frequency, the water alternately rises and falls at each 7;k lszy gwm56z08p8od x;wnsend, 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 the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s*k-up)es2ludnf t1 2l strikes a boundary within the Earth between two kindssfd *n2leup)u l1t-k2 of material. 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 underwat wai02b)/-7j.ybn s bmfn cj+aer “shelf” where the velocity changes from 2.8 m/s to 2.1 mn0- w2i fba.+bj7 aymn bsc)j//s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense i6bss/tl 2m,m y8v c.nlj)4beair. If the sound wave hits the cold aiy8 )s .b,lnmcj6 mlbei2vst/4r 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 bet,f(;eb( hhhaa/ow,p k02 dl gaween two types of rock at a hkle,d, gab0o p(a2(afh /wh;38 $^{\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 the user’s7wfk w qud+o(6;pi-esf 8 +mo yh-ut(b manual, the dish has to be pointed in the direction- fw ow (h8+f-ste+iu7qobku ;py6m(d 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 velocity 750 km/h travels across the Pltg, y-jzkeh7wqki-3-c/4f1 iwfi. wacific Ocean. As it approaches Hawaii, people observe an unus47zfi.-3iy1cflh-q w,-egtwj i k/w k ual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper8 9f0blbbq 4vx has 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 (b0 bfqbvl94 x8approximately 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 th0fl vj;djj *5ee net l0ejj*vjdf 5 ;1.1 m. Assume 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. The man 6n7vq xh,wu/ss then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation? 7/6qwn,vhnx u    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), cob,gajxq h, 6-mmpressing the spring 5.0 m. (a) What is the spring stiffness constan 6h,mq bagx-,jt 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 cblf) m1ah c *c7 l57 /a+:am;cmisxpkpm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in cf:cmi )maa/ l pksc x*p+51 7l7hm;bathe coffee.    cm/s

  The ripples in a certain groo6aqoke3u: n8wve 10.8 cm from the center of a 33-rpm phonograph record have8we:qo6k nua 3 a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates aten; ab1nz:cu:kn / )57r4 pwuckjh9zccording to the equation x=0.650cos7.40t where x is in meters and t in seconds. Dete cbc 9jp5ze; nn wr/k )aknh174u:zut:rmine
(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 ip6zx 795lclr ;v*lqnats frequency if it acceleratesz l;x*lq9n7 lcapr65v at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on j+/s9h ylx /f be(anz)8oxu+ ha lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper iajb 8u/9x hyfxz+ ns)o/(hl +ento the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument ar9xocm (h,1,a3tzj iite tuned to play at 392 Hz (G) and 440 Hz (A).,i,h93 1xt(atc jimo z
(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 of Fig. 11–33. /.e *v.z;lbv qam0hk2mbsw(i 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 hebv/(qab.mv *.siw0m2 zk;ltwo 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 frequel6me y8v 01cvk 2uclckk7m;s+ncy of 264 Hz, and the tip of each prong moves 1.8 mm to either side of clskm;6 celkcmuv8 2y0+kc1 v7enter. 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 frequency xjxlxh6w32lxz +94ygmkk(* m1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in og * hxxmxj2kxy936mw4llz k (+rder 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 i bvj/5b5l nn0zf that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the res vb05 /nnzblj5onant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 sbpwomure b 8o r,2ptco*+c a1p54b(r+zeb,-e — each one-way swing takes pwz 8mbortpe5 u*bb2o+be o4+(, 1rr e pcc,-a1.000 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 diro o -4z hxh5m3f7rx2xhection or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the veozmf2x rohx7 xh3h-54 rtical 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 a qa *r/ m 89xm*jswdb53y6, (piwvep 08mrcldtension of 255 N. A pulse is generated at ond 9cwa y/e mxr0rs, 5pwm*l836(*p8mi d bvjaqe 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 q,bhk3(d; dh5sc4 tlphq3ocn*g 5hf3from a ceiling by a spring 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 c4hh3k,35 qhhfglqd(3c p*;bos tn 5dthe 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 stee gu(r*-g:cl 1i /pnlivl 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: Refgncu i *r/-iv(lgpl 1:er to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 7*:kji7eef36q osv w* h-cd gx(which also gives the dimenwh*7ksg ve7qj fo 6ce3 d:*x-isions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz