Chapter 14 1. A person’s heart rate is given in beats per minute. Is this a period or frequency? 2. Give three realworld examples of oscillatory motion. Swinging chandelier over roof of hall, pistons in thIf you want to learn more check out douglas gobeille
We also discuss several other topics like espm 50ac
If you want to learn more check out english 1000 mizzou
Don't forget about the age old question of ) YES HE DId, but could anyone give an example of how it could be used as an answer?
If you want to learn more check out withdrawing a desirable stimulus following an operant response is
If you want to learn more check out What edition of the Federal Register would hospital facilities be especially interested in?
e engine of a car, sound waves entering the ear cause oscillations of a membrane in the cochlea. 3. A child is on a swing, gently swinging back and forth with a maximum angle of 4.0 ∘. A friend gives her a small push so that she now swings with a maximum angle of 10 ∘By what factor does this increase her maximum speed? =sqrt(1cos10)/sqrt(1cos4) 4. A block oscillating on a spring has an amplitude of 20 cm. What will be the amplitude if the maximum kinetic energy is halved? (b)Doubled? Total energy directly proportional to amplitude squared E’=2E=mv^2=1/2m(v^2)= 20cm/sqrt(2)= 28.3cm/s (c)Quadrupled? E = 1/2*k*A^24 = [A'/A]^22 = A'/A A' = 2* 20 5. A block oscillating on a string has a period T=2.38sec. what is the period if the block mass is doubled? T=2pi x sqrt(m/k) T increases by a factor of sqrt (2) Tnew = 3.36 sec. What is the period if the oscillation amplitude is halved while m and k are unchanged? changing amplitde does not change the time period. Quadrupled? T decreases by a factor of sqrt (2). Tnew = 2.38 / 2 = 1.19 sec 6. A pendulum on Planet X, where the value of g is unknown oscillates with a period of 2sec. (a) period if mass is doubled? Period is independent of mass (b) length doubled? T=sqrt(l)T2=sqrt(T1) (c) time is independent of amplitude 7. Flies flap their wings at frequencies much too high for pure muscle action. A hypothesis: in mass spring systems, angular freq. w=sqrt(k/m) where w is directly proportional to 1/sqrt(m). Reduced mass=w increases=increase freq. of wingbeats 8. Rome is at higher elevation than London: the freefall acceleration is slightly less at this higher elevation. T is inversely proportional to squareroot of g.Time period of the pendulum at R is high than L. the clock run slow in Denver 9. If you want to play a tune on wine glasses, you’ll need to adjust the oscillation frequencies by adding water to the glasses. Adding h20 increases Period=decrease in freq. increase freq.=remove water. T=2pi x sqrt (m/k) 10. It is possible to identify promising locations for oil drilling by value means there is lowdensity material under the surface. gravity affects period. Time period of pendulum helps calculate the value of gravity with other known parameters 11. Sprinters push off the ball of their foot, then bend their knee to bring their foot up close to the body as they swing their leg forward Freq. of oscillation= 1/2pi x sqrt(mgd/I)à beinding knee decreases I. freq. increase=decrease I 12. Gibbons move through trees by swinging from successive handholds, as we have seen. To increase their speed. Bringing legs close to body=lower I. freq. increase = speed increase. 13. What is the difference between driving frequency and the natural frequency of an oscillator. Freq. with which the body is set into forced oscillations. Must be periodic. Independent of natural freq. freq. in which the body oscillates. At resonance, the driving freq. and natural freq. become equal 14. Humans have a range of hearing of approximately 20 Hz to 20 kHz. Mice have auditory systems similar to humans. Given this would you expect mice to have a higher or lower frequency range than humans? mass is less for mice= freq. will be more. Audible range for mice is greater. 15. A spring has an unstretched length f 20 cm. a 100g mass hanging from the spring stretches it to an equilibrium length of 30cm. (a) suppose the mass is pulled down to where the spring’s length is 40cm. when it is released, it begins to oscillate. What is the amplitude of this oscillation? (b) For the data given, what is the frequency of the oscillation? (c) Suppose this experiment were done on the moon. (a) 40cm30cm=10cm (b) k=mg/x(0.1kg)(9.8m/s^2)/0.1m=9.8kg/s^2 f=1/2(3.14)sqrt(9.8/0.1kg) (c) freq. is indep. On accel. Due to gravity. Freq stays the same if its done on the moon 16. A ball of mass m oscillates on a spring with spring constant k=200N/m. the balls position is x=(0.350m)cos(15t). with r measured in seconds. What is the amplitude of the ball’s motion? 0.35m. frequency? (2pi*f=f=15/2pi=2.39Hz) value of mass m? m=k/m^2=200nN/m/15rad/s)^2=0.89kg total mechanical energy of the oscillator? E=1/2kA^2=1/2(200nm/0.35m)^2=12.25J and maximum speed? Vmax=Aw=(0.35m x 15rad/s)=5.25m/s 17. If you carry heavy weights in your hands, how will this affect the natural frequency at which your arms swing back and forth? Freq. of simple harmonic motion doesn’t depend on mass 18. A heavy brass ball is used to make a pendulum with a period of 5.5s. How long is the cable that connects the pendulum ball to the ceiling? L=T^2g/4pi^2=(5.5s^2)(9.8)/4pi^2=7.509m Chapter 15 1. In your own towards, define transverse wave. Give examples and observations? In a transverse wave the particle displacement is perpendicular to the direction of wave propagation. (s waves In an earthquake) 2. In your own towards, define longitudinal wave. Give examples and observations? In a longitudinal wave the particle displacement is parallel to the direction of wave propagation. (p waves in an earthquake) 3. The wave pulses shown in figure Q15.3 travel along the same string. Rank in order, from largest to smallest, their wave speed v1, v2, and v3. Explain? Vs=sqrt(T/mu) v depends on T. andlindear density(mu). Three wave pulses are traveling on the same string. So same mu=same T=same speed. 4. Is it ever possible for one sound wave in air to overtake and pass another? No the speed of sound in air at a certain temp. is constant. Ex:at 0deg. The Vs is 331m/s, so all the waves move w/ this velocity only and so on. No chance to overtake waves5. A wave pulse travels along a string at a speed of 200cm/s. What will be the speed if: (a) tension doubled (b) mass quadrupled, length unchanged. (c) Length quadrupled, mass unchanged? (d)mass and length quadrupled? Linear density=m/L vis directly poroprtional to sqrt of T, and L. Inversely proportional to m. (a) sqrt2(2m/s)=2.83m/s (b)1/2(2m/s)=1m/s (c) 2(2m/s)=4m/s (d) 6. A thermostat on the wall of your house keeps track of the air temperature. Explain how such system works? Speed of sound in air depends on temp. Speed of sound is higher at higher temp. varies w/ diff. temp.=Theres a time delay between emitted pulse and detection pulse. With this you can find the ave. temp. in air in a large volume system 7. Rank in order, rom largest to smallest wavelengths f1=100Hz, f2=1000Hz, f3=10000Hz, for sounds waves having frequency and explain? wavelength=v/f f1=343m/s/(100Hz)=3.43m, etc. f1>f2>f3 8. Bottlenose dolphins use echolocation pulses with a frequency of about 100kHz, higher than the frequencies used by most bats? Echolocation: using sound waves to locate distant objects. Speed of sound in water greater than in air. Freq. is directly proportional to the speed of sound.in water, they produce higher freq. 9. When you want to snap a towel, the best way to wrap the towel is so that the end you hold and shake is thick and the far end is thin. When you shake the thick end a wave travels down the towel. V=sqrt(Ts/mu). Towel in hand has greater linear mass density. So the speed of wave travels thru the towel slowly. Linear mass density is slowly decreased thru then end of the towel. Speed increases at end. 10. The volume control on a stereo is designed so that the three clicks of the dial increase the output by 10dB. How many clicks are required to increase the power output of the loudspeaker by a factor of 100? No, a click will increase the sound by a multiplicative factor in W/m^@ not a fixed amount 11. Denver, Colorado, has an oldies station that calls itself KOOL 105, THIS MEANS THEY BROADAST RADIO WAVES AT A FREQUENCY OF 105mhZ. wavelength=c/f(3x10^8m/s)/105x10^6Hz=2.85m 12. What is the frequency of blue light with a wavelength of 492nm? V=f x wavelength 3x10^8/400x10^9m=7.5x10^14Hz 13. Ultrasound can be used to deliver energy to tissues for therapy. It can penetrate tissue to depth approx. 200 times its wavelength. What is the approx. Depth of penetration of ultrasound at a frequency of 50MHz? D=200(1540/5x10^6)=6.16cm 14. A sinusoidal wave traveling on a string has a period of 0.2s, a wavelength of 32cm, and an amplitude of 3cm. v=wavelength/Tf=1/T32cm/.20s=160cm/s 15. Two strings of different linear density are joined together and pulled taut. What happens to the velocity? Speed of sound doesn’t depend on size or shape of wave, it depends on the medium property. From fig. The wavelength of string 2 is less than string 1. But freq. is unchanged. Lower wavelength=lower v16. You stand at x=0m, listening to a sound that is emitted at frequency Fs. Which of the following described the motion of the sound source? For first 2 sec. the apparent freq. is less than the actual. It moves away from you until t=2s. Then reverses direction and moves toward you. 17. A laser beam has intensity Io, What is the intensity, if a lens defocuses the laser beam to 1/10 its initial diameter? 10 times its initial diameter? I1(d0/10)I1=Io((Do^2x100)/ (do^2))=100Io=100times and I1=Io(Do^2/100Do^2)=I0/100=1/100th of the itial value Chapter 16 1. A light can pass easily through water and through air, but light will reflect from the surface of a lake. What does this tell you about the speed of light in water and air? Air has lower refractive index. Light waves travels from the rarer medium to denser medium. Speed of light decreases in denser medium 2. A string has an abrupt change in linear density at its midpoint so that the speed of a pulse on the left side is 2/3 of that on the right side? V=sqrt(T/mu). Speed of pulse on left side is low. Speed of wave in string is inversely proportional to linear density. Left side has greater linear density. If you start from left hand to right hand side it wouldn’t be inverted bs its moving from high to low density. 3. A guitarist finds that the pitch of one of her strings is slightly flat the frequency is a bit too low. Should she increase or decrease the tension of the string, explain? F1=1/2L(sqrt(Ts/mu). F1 is proportional to sqrt of T. freq. is too low by 14% means tension should decrease 4. Certain illnesses inflames your vocal cords, causing them to swell. How does this effect pinch of your voice? Explain? Freq. of mucosal wave determines pitch. Vocal cords are increased. Linear mass density increases=freq. decreases bc its generated by vocal cords. 5. A typical flute is 66cm long, a piccolo is very similar instrument, though it is smaller with a length of about 32cm. how does the pitch of a piccolo compare to that of a flute? F=v/2L343m/s / 2x0.66m=260Hz 6. Suppose you were to play a trumpet after breathing helium, in which the speed of sounds is much greater than air. Would the pitch of the instrument be higher or lower than normal, or could it be unaffected? Fm=m(v/4L).v and freq. in helium is higher than in air. Pitch of instrument is slightly higher with helium inside the tube than air. 7. If you pour liq. In tall narrow glass, you may hear sounds with a steadily rising pitch. What is the source of the sound and why does it rise as the glass fills? Pouring in narrow glass=air molec. Vibrate=produce sound=increase level of liq., decrease in L=increase in freq.=pitch will rise when liq. Increases. 8. When you speaker after breathing helium, in which the speed of sounds is much greater than air. Your voice sounds quite different. The frequencies emitted by your vocal cords do not change. Since they are determined by the mass and tension of your vocal cords. Freq. of voice stays the same w/ change in quality. Bc its determined by vocal cord vibrations and linear mass density9. Two sinusoidal waves with the same amplitude A and freq. f travels in opposite directions along a long string. You stand at one point and watch the string. The max. Displacement of the string at that point is? Y=A+(A)=AA=0 10. A student in her physics lab measures the standing wave modes of a tube. The lowest freq. that makes a resonance is 20Hz. As the freq. is increase, the next resonance is at 60Hz. What will the next 2 resonance be after this? F1=20Hz, F2=60Hzm F3=5(20Hz)=100Hz 11. An organ pipe is tuned when the temperature in the room is 20 degrees. Later, when the air has warmed up to 25 degrees, the resonant wavelengths will have? Speed of sound is proportional to temp. freq. increased, freq. greater than 384Hz 12. The frequency of the lowest standing waves mode on a 300cmlong string is 40Hz. What is the wave speed on the string? F=m(v/2L) 20s^1 x 2x1m=40m/s 13. Suppose you pluck a string on a guitar and it produced the note A at a freq. of 440Hz. Now you press your finger down on the string against one of the frets. F’/f=l/l’L/(4/5L)=5/4 f’=(5/4) (440Hz)=550Hz Chapter 17 1. The frequency of a light wave underwater is 5.3x10^14Hz. Is the freq. of this wave higher, lower or the same after the light enters the atmosphere, explain? The same, bc freq. of light waves doesn’t depend on the medium. 2. Rank in order according to their speeds, from slowest to fastest. (a) 425nm wavelength light thru plain of glass (b)500nm thru air (c)670nm thru vacuum? (a) V=3x10^8/1.33=2.255x10^8 (b) =3x10^8/2.42=1.239x10^8 (c) = 3x10^8/1=3x10^8 3. The wavelengths of a light wave is 700nm in the air, this light appears red. If this wave enters a pool of water, its wavelength becomes 530nm. If you were swimming underwater, the light would still appear red. Given this, what property of a wave determines its color? Freq. doesn’t change as the wave moves from one medium to another. Swimming underwater= red light entering pool looks red bc of the property of wave freq. 4. A double slit interference experiment shows fringes on a screen. The entire experiment is them immersed in water, do the fringes on the screen get closer, further apart or remain the same or disappear entirely, explain? D(y/L)=m x wavelength y decreases as wavelength decreases. Fringes get closer, if its immersed in water 5. In a double slit interference experiment, interference fringes are observed on a distant screen. The width of both slits is then halved without changing the distance between their centers. (a) what happens to the spaces? (b) what happens to the intensity of the bright fringes? Delta y=wavelength xL/d—space remains the same bc spacing between fringe m and m+1 given in equation. If two slits aren’t narrow, the interference between waves from diff. parts of the same sources will take place and contrast will be poor. Intensity will decrease. 6. (a)What will happen to the fringe spacing if the wavelength of the light is decreased? (b) What will happen to the fringe spacing if the spacing between slits is decreased? (c) suppose to the wavelength of light is 500nm, how much further is it from the dot on the screen in the center of fringe E, to the left slit than it is to the dot to the right slit?7. Suppose the 2 slits were preplaced by 30 slits having the same spacing, d, between adjacent slits? (a) would the # of fringes increase, decrease or stay the same? (b) would the fringe spacing change? (c)would the width of each fringe change? (d) would the brightness of each fringe change? (a)Spacing decreases=wavelength decrease.(b)Slit spacing decrease=fringe spacing increases (deltay=deltaL/d).(c) L(distance to screen) decreased=delta y decreases. (d)If dot is on mth height fringe= it will be delta r length further from left slit than right slit. 8. What happens to the width f the central maximum if (a) wavelength increase? W=2.44*wavelength*L/D if wavelength of source increases, central max. increases (central max. proportional to wavelength) (b) Diameter decreases? If diameter increases, the width of central max. decreases. (c) Diameter less than light wavelength? If the size of the aperture is less than wavelength source, o diffraction pattern is observed. 9. Light with a wavelength of 600nm is incident on a diffraction grating that has 100 slits. The first order max. Is observed at a point P on a distant screen. How much farther does the light travel from the first slit to point P than the light from the 100th? D=sin(theta)/m x wavelength. Sintheta=1x60x10^9mtheta=sin^1=(0.6)=36.86 L=y.tantheta=23.2/tan(36.86)=30.94m 10. Light of wavelength 500nm in air enter a pool of water with the index of refraction n=1.33. when the light enters the pool, which of the following properties of the light will not change? Freq. doesn’t change a wave moves. Wavelength and speed change. 11. The freq. of a light wave in air is 4.6x10^14Hz. What is the wavelength of this wave after it enters a pool of water? Vwater=3x10^8/1.33=2.255x10^8m/s wavelength=2.255x10^8/4,6x106m=490nm 12. Light passes thru a diffraction grating with a slit spacing of 0.001mm. a viewing screen is 100cm behind the grating. If the light is blue, with a wavelength of 450nm, at about what distance from the center of the interference pattern will the first order max. Appear? Y=(L*m*wavelength/d)=1mx1x450x10^9/0.001x10^3=0.45m 13. Blue light of wavelength 450nm passes thru a diffraction grating with a slit spacing of 0.001mm and makes an interference pattern on a screen 80cm away. M=(0.001x10^3m)sin90)/450x10^ 9m=2 14. Light passes thru a 10 m wide slit and is viewed on a screen 50cm behind the slit. If the width of the slit is double the band of light on the screen will? If width of slit is narrowed, y increases which makes the band of light wider Chapter 18 1. When you look at your reflection in the bowl of a spoon, why is it upside down? Obj. is at a distance greater than focal length of concave mirror which always forms a real and inverted image. 2. A concave mirror brings the sun’s rays t the focus at a distance of 30cm from the mirror, if the mirror were submerged in a swimming pool, would the sun’s rays be focused nearer to, farther from or at the same distance from the mirror? Replacing air w/ water foesnt change the focal length until the mirror is at min. depth. If the mirror is submerged in a swimming pool, rays will focus at same distance from mirror (30cm)3. A lens can be used to start a fire by focusing an image of the sun onto a piece of flammable material. All other things being equal, would the lens with a short focal length to a long focal length be a better fire starter? Shorter focal length= all rays that fall on lens converge as point image and is focused better which makes it better to use shorter focal length. 4. Figure in which a beam of light in the air encounters a transparent block of index of refraction n=1.53. (angle given:50deg.) Some of the lights is reflected, some is refracted. (a)What is theta1? (b)Theta2? (c)Is there an angle of incidence between0 and 90 degrees such that all of the light will be reflected? (a) Theta1=90theta r=9050=40. (b)1sin(50)=(1.53)sintheta 1x0.766=1.53sintheta=sin^10.766/1.53=30 degrees=90theta r=9030=60. (c) sin^ 1=1/1.53=40.83NO 5. A 2m tall man is 5m from the converging lens of a camera. His image appears on a detector that is 50mm behind the lens. How tall is his image on the detector? H’h(s’/s)2=(0.05m/5m= 0.02m) 6. You are 2.4m from a plane mirror and you would like to take a picture of yourself in the mirror. You need to manually adjust the focus of the camera by dialing. Camera should be focused at a distance that’s equal to distance between image of person and the person. 4.8m 7. A concave mirror cannot produce a inverted, real image. s>2f 8. An object of 40cmfrom a converging lens with a focal length of 30cm. a real image is formed on the other side of the lens 120cm from the lens. What is the magnification? S+s’=120cms’=120cms 120cm40cm=80cmm=80cm/40cm=2x 9. The lens in figure, is used to product a real image of a candle flame. What is the focal length (12cm, 36cm) f=sxs’/s’+s=12x36/36+12=9cm 10. A converging lens of focal length 20cm is used to form a real image 0.1m away from the lens. How far from the lens is the object? S=fxs’/s’f=20cmx100cm/100cm20cm=25cm 11. You look at yourself in a convex mirror, your image is virtual and erect. Smaller than object. 12. An object is 50cm from the diverging lens with a focal length of 20cm. how far from the lens is the image, on which side of the lens is it? S’=fxs/sf=20cmx50cm/50cm+20cm=14.28cm Chapter 19 1. Suppose you have two pinhole cameras. The first has a small round hole in front of the camera the second is the same besides being square shaped. Slight variation in the pic. Will be observed t the edges of the pic. Due to diffraction of light while passing thru the edge of square and a circular aperture. 2. A photographer focuses his camera on his subject. The sub. Moves closer to the camera, to refocus? Lens should be moved further away b/c the sub movement caused the image distance to increase w/ no change to focal length 3. A nature photographer taking close up shot of an insect replaces the standard lens on his camera? (p=1/f) shorter focal length and positioned farther from the film b/c the lens is used for taking close up pics. So it must have high refractive power.4. The CCD detector in a certain camera has a width of 8mm. the photographer realizes. Shorter focal length, so the width of the aperture increases 5. Supposed you wanted special glasses designed to wear underwater, without a face mask should the glasses use converging or diverging lens? Converging b/c usually our eyes in water focus images on the retina, they will now focus then far behind the retina, resulting in a blurred image from hyperopia. 6. You have lenses with the following focal lengths f=25mm 50mm, 100mm, 200mm. which lens or pair of lenses would you use? (a) p=1/f f=25mm (b)microscope: focal length of objective is less than eyepiece, we arrange 2 lenses of focal lengths F0=25mm, fe=50mm) (c) telescope: focal length of obj. greater than eyepiece. (f0=50mm, fe=25mm 7. An 8yr old child and a 75 yr old man both use the same magnifier to observe a bug? M=NP/f focal length constant. As age increases, NP increases. Mag. Of old man will be higher than child. 8. A friend lends you the eyepiece of his microscope to use on your own microscope. NA=n(D/2f) focal length doubled, NA reduced in half. Doubled resolving power. Claim is valid. 9. A microscope has a tube length of 20cm. what combination of objective and eyepiece focal lengths will give an overall mag. Of 100x. M=Lx25cm/100=fofe=5 (possible combination=1cm,5cm) 10. The distant between the obj and eyepiece of a telescope is 55cm. the focal length of the eyepiece is 5cm. M=fo/fe=50cm/5cm=10x 11. A nearsighted person has a near point of 20cm and a far point of 40cm. when he is wearing glasses to correct his distant vision, what is near point? (a) 1/f=1/infinity+1/40cm=40cm. (b) p=1/f=1/0.4m=2.5D 12. A 60 yr old man has a near point of 100cm, making it impossible to read. Held at a comfortable distance of 40cm? 1/f=1m0.4m/0.4mx1m=1.5m^1=+1.5D 13. A person looking thru a 10D lens sees an image that appears 8cm from the lens. How far from the lens is the object? F= 1/10D=10cm s=fxs’/s’f=10cmx8cm/8cm(10cm)=40cm