A stroboscope is an arrangement which can make a rotating object appear at rest when it is viewed, and thus enables a spinning wheel, for example, to be studied at leisure. The stroboscope method can be used to determine the frequency of a tuning-fork, which is electrically maintained for the purpose.
Two light metal plates, A, B, each with a slit S in them, are attached to prongs of the tuning-fork F so that the slits overlap each other when the fork is not sounded, as can be seen in the diagram above. Behind the slit is a vertical circular white card C with black dots spaced at equal distances round the circumferences, and the dots on the card can be seen through S. the tuning fork is set into vibration, and the card is rotated by a motor about a horizontal axis through its center with increasing speed. At first an observer O, viewing the dots through S, sees them moving round in an opposite direction to that in which the card is rotated. This is because the intermittent glimpses of the card through S, sees them moving round in an opposite direction to that in which the card is rotated. This is because the intermittent glimpses of the card through S occur quicker than the time taken for one dot to reach the place of the dot in front of it, with the result that the dots appear to be moving slowly back. As the speed of the card is increased further, a stage is reached when the dots appear perfectly stationary.
Through the slit S, glimpses of the dots are seen twice in every cycle of vibration of the tuning-fork. When the dots first appear stationary, a particular dot such as X moves to a neighboring dot position Y at one glimpse of the wheel, then to the next dot position Z at the next glimpse, and so on. At the end of one second, 2f glimpses have occurred, where f is the frequency of the fork in HZ. If the wheel has m dots and is now rotating at n rev s-1, there have been m x dot successive movements in one second.
Thus, 2f = mn, or f = mn/2
At twice the speed of revolution, 2n rev s-1, the dots are again seen stationary. But this time only half their number is seen, as a particular dot moves through two dot places between successive glimpses. The dots may again be seen stationary at 3n, 4n, … rev s-1 of the wheel if the stress on the wheel at higher speeds is below a dangerous level.
As an illustration, suppose a wheel has 40 equally spaced dots and is viewed stroboscopically by a fork of 300 Hz. If the dots are seen stationary at the lowest angular speed, the number of revs per sec, n, is given by
600 = n x 40, or n = 15 rev s-1
A neon lamp, providing international flashes of light at a rate which can be varied by an electrical circuit, is used as a stroboscope in industry to adjust critically the speed of rotating wheels or machinery, which then appear stationary. The wear and tear with time of the moving parts of watches have been photographed with the aid of a stroboscope.
Relative Movement of Dots
It is sometimes impossible to keep the speed of rotation of the wheel in diagram above constant, so that the dots appear to move slowly forward or back. Suppose, the example, that 2 dots per second cross the line of view in a backward direction in the case of the fork and wheel just discussed. Instead of 40 x 15 or 600 successive dot movements at 15 revs per second, when the wheel appears stationary, there are now 600 – 2 or 598 successive dot movements. Since there are 40 dots round the wheel,
Therefore, New Rate of Revolution of wheel = 598/40 = 14.95 rev s-1.
Suppose that the 40 dots appear stationary again at a wheel rotation of 15 revs per sec when viewed stroboscopically with the fork of frequency 300 HZ, and the fork is now loaded with a small piece of plasticine. The fork frequency is then lowered to a value f’. In this case the time interval between successive glimpses is longer than before, so that the dots appear to move forward. Suppose the movement is 3 dots per 10 seconds across the field of view. The number of successive glimpses of the wheel is 10 x 2f’ in 10 seconds. In this time the number of successive dot movements is 10 x 40 x 15 -3, or 5997.
20f’ = 5997
f’ = 299.85.
Thus the frequency of the fork is lowered by 0.15 HZ.