Stroboscope

1. The stroboscope:

The stroboscope is used to measure speed; or example, to measure the period T_d of a rotation of a disk. To study the phenomenun, we should set some unique part on the rotating object as an index or reference ; like the point R in the figure.

Here is the principle:
Every T_d secondes, we have a flash that illuminates a disck rotating at T_r secondes. If k is an integer, and we assume that the disk rotates clockwise, we have the following cases:

1)- T_f = k x T_d: That is between two flashes, the disk has made exactly k revolutions. The disk seems stationary.

2)- T_f = T_d/ k: That is during the unique revolution of the disk ( between two flashes), the reference index is illuminated k times. We will see the hole k times. The point reference is illuminated at every 2π x r /k ( r is the radius of the disk).

3)- T_d = T_f + gap: Between two illuminations, the reference point is late of gap seconds. Between every two following flshes, the reference point becomes late of gap seconds. Forethermore, It seems then the disk rotates in the reverse direction (counterclockwise).

4)- T_f = T_d + gap: Between two illuminations, the reference point is ahead of gap secondes. Between every following flsh, the reference point becomes ahead of gap secones. Forethermore, It seems then the disk rotates in the real direction (clockwise).


In practice, the spectroscope is used to mesure frequencies of phenomena. in the device, we set, at first, the revolution T_d of the object greater the of the flash T_f; that is we start at the highest flash rate and adjust the flash rate down. Once the refrence point seems stationary, the two frequencies are equal.



2. Example:

If the object rotates at x RPM (Rotations Per Minutes), we start to set the flash rate; let's say at 2000 FPM (Flashes Per Minutes). If we see the reference point four times during a revolution, then x = T_d = 2000 / 4 = 500 RPM. If we slow the flash rate at 1000 FPM, we will see the point reference 2 times, foretheremore x = 1000 / 2 = 500 RPM ... till 500 FPM to see the reference point stationary.
We still continue to see the reference point stationary at the lower flash rates at T_f = T_d/k; with k = 5, 4, 3, 2, or 1.

Remark that at the very high flash rate (until the speed of light) we will see the reference point evrywhere in the disk.