Q#1
The speed of sound in air is 332 m/s. Is it advisable to define the length 1 m as the distance traveled by sound in 1/332 s?Answer:
No. The speed of sound is not a universal constant like the speed of light in vacuum. The speed of sound in air depends on the pressure, temperature, humidity, and density of air. So the distance traveled by the sound in 1/332 s will not always give the same result.
Q#2
Consider Galileo's method of measuring the speed of light using two lanterns. To get an accuracy of about 10%, the time taken by the experimenter in closing or opening the shutter should be about one-tenth of the time taken by the light in going from one experimenter to the other. Assume that it takes 1/100 second for an experimenter to close or open the shutter. How far should the two experimenters be to get a 10% accuracy? What are the difficulties in having this separation?
Answer:
Let the distance between the experimenters = x. For the 10% accuracy, the time taken by the light in traveling from one experimenter to another, say = t.
So, t = x/c, where c is the speed of light.
From the given condition,
t/10 = 1/100
x/10c = 1/100
x = 10c/100 = c/10 = 3 x 10⁵/10 km = 30,000 km.
{c = 3x10⁵ km/s approx.}
The diameter of the earth is itself about 13,400 km and the surface is curved. So the required separation in a straight line on the surface of the earth is impossible to achieve.
Q#3
In Fizeau method of measuring the speed of light, the toothed wheel is placed in the focal plane of a converging lens. How would the experiment be affected if the wheel is slightly away from the focal plane?
Answer:
If the toothed wheel is placed slightly away from the focal plane, the light will not clearly pass through the gap. A part of the light cone near the tooth will be in the gap and another on the tooth. Thus clear blockage of the light will not happen even when the tooth is in front of the light and it will be always visible. Thus the experiment can not be done.
Q#4
In the original Fizeau method, the light traveled 8.6 km and then returned. What could be the difficulty if this distance is taken as 8.6 m?
Answer:
The speed of light in the Fizeau method is given as,
c = 4Dnν, n = number of teeth on the wheel, ν =number of revolutions of the wheel per unit time. D = distance between the wheel and the mirror = 8.6 m. If we assume n = 200, c = 3x10⁸ m/s approx.
Then,
ν = c/4Dn = 3 x 10⁸/(4 x 8.6 x 200) = 43,605 revolutions/second
It is a very high angular speed to achieve and not practical.
Q#5
What is the advantage of using a polygonal mirror with a larger number of faces in the Michelson method of measuring the speed of light?
Answer:
The velocity of light in the Michelson method is given as,
c = DνN
Where ν = number of revolutions per second, D = distance traveled by light and N = the number of faces in the polygonal mirror.
It is clear that if N is large, either ν or D can be reduced. Since ν is very large in this experiment which is very difficult to maintain, increasing the number of faces the number of revolutions can be reduced. Also, the distance D can be reduced.
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