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course Phy 202
3/16 1 pmProblem Number 2
What is the fundamental frequency of a longitudinal standing wave in an aluminum rod of length 4 meters, balanced at its midpoint, if a longitudinal disturbance travels at 5000 m/s?
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Wavelength is 2*4 m=8 meters since the node is in the center of the rod.
F=5000 m/s/ 8 meters= 625 cycles/s
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Problem Number 3
A string of length 8 meters is fixed at both ends. It oscillates in its second harmonic with a frequency of 27 Hz and amplitude .61 cm. What is the equation of motion of the point on the string which lies at 3.1 meters from the left end? What is the maximum velocity of this point?
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A sin ( (2 `pi f)(t-timeLag))
timeLag=distance/velocity
So .0061 m sin ((2`pi 27Hz)(t-timeLag))
How do I determine time and timeLag?
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@& From frequency and wavelength you can determine propagation velocity.
The second harmonic has NANAN along the length of the string. Since you know the length of the string you can find the wavelength.*@
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Problem Number 4
If the peaks of a traveling wave are separated by 3.4 meters, and if the wave propagates at 210 m/s, what is the frequency of the wave? What is the period of a cycle of the wave?
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f=210 m/s/3.4 m=62 Hz
T=1/f = 1/62Hz=.016
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@& .016 sec*@
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Problem Number 5
Two sources separated by 3.75 meters emit waves with wavelength .75 meters emit waves in phase. The waves travel at identical velocities to a distant observer. At any point along the perpendicular bisector of the line segment connecting the two points, the two waves will arrive in phase an hence reinforce. What are the first three nonzero angles with the perpendicular bisector at which the first interference maximum will be observed?
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Can you suggest a starting point?
@& The 'perpendicular bisector' is the line normal to the line AB, as we referred to it in class.
At angle theta to normal, the path difference will be AB sin(theta). Positive reinforcement occurs when the path difference is an integer number of wavelengths, etc..*@
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Problem Number 7
A candle flame 1.77 cm high is located 8 cm in front of a circular mirror. A real inverted image forms 5 cm from the mirror.
• What is the focal length of the mirror?
• How large is the image?
• Sketch a ray diagram explaining how the image is formed.
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Does “real inverted image” refer to the image of the mirror?
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Problem Number 8
Sound is created by the vibration of the air column in a pipe which is open at both ends. The pipe is 7 meters long, and the speed of sound is 348 m/s. How long should a second pipe, also open at both ends, be in order that its second harmonic match the frequency of the fundamental harmonic of the first?
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What are we assuming the wavelength to be? 14 meters?
@& @& The propagation velocity in the chain that's being pulled back will change, causing an effect on the phases that can't be determined without further information (i.e., effect of stretch on tension, and mass density).*@
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Problem Number 6
If the peaks of a transverse traveling wave in a string under a tension of 5 Newtons are separated by 3 meters, and if the wave propagates at 12 m/s, what is the mass of the string?
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12 m/s=sqrt (5N/ m/ 3m) square both sides
144 m^2/s^2=5N/ m/3m
144 m^2/s^2* m/3m=5N
144m^2/s^2 * m = 15 N m(multiple by 3 meters)
m=15 N m/ 144 m^2/s^2=.104 kg
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Problem Number 7
A string of length 9 meters is fixed at both ends. It oscillates in its fourth harmonic with a frequency of 37 Hz and amplitude .28 cm. If it is held under a tension of 8 Newtons, then what is its mass?
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9 m* 37 Hz=333 m/s
333 m/s=sqrt (8 N/ m/9meters)
110889 m^2/s^2=8N/m/9meters
110889m^2/s^2 * m/9Meters=8N
110889 m^2/s^2 *m= 72N m
m=.00065 kg
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@& The wavelength of the fourth harmonic is not 9 meters, it's 4.5 meters. Be sure you know how to reason this out.
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@& You're in pretty good shape, but be sure you know how to reason wavelengths of different harmonics using NANAN...*@