When two sound waves of the same frequency and amplitude meet, they interfere either constructively or destructively. In the case of constructive interference, the crest of one wave coincides with the crest of the other. The intensity of sound is maximum at a point where this type of interference takes place. In the case of destructive interference, the crest of one wave coincides with the trough of the other. The intensity of the sound at a point where this occurs will be minimum.
For example, a Stethoscope works on the principle of constructive interference. The sound waves, from the source, are divided and travel through different tubes before they reach the ear. Due to constructive interference, a loud sound of the heartbeats can be heard.
When the frequencies of the two interfering waves are not the same, the point of maximum and minimum intensities will not remain the same with time.
Periodic variations of the intensity of wave resulting from superposition of two sound waves of slightly different frequencies is known as the phenomena of beats.
One maximum and a following minima combined together is called one beat.
If f1 and f2 are the frequencies of the two waves that are meeting the number of beats per second 'N' is given by,
N = f1 - f2.
Graphical analysis of beats:
Wave 1 (f1)
S1
Wave 2( f2)
S2
Fig:
Analysis of Beats:
Let f1 and f2 be the two frequencies of sound waves, 1 and 2, emitted from two sources S1 and S2. At points A, C, D, E sound heard will be maximum, while at locations B1, B2, B3, minimum sound is heard.
Let the wave 1 and wave 2 are generated from sources S1 and S2 have frequencies of 13 and 15 Hz respectively. The two waves interfere and produce a resultant wave as shown in the figure.
In the resultant wave, the intensities are maximum where the crests of the two waves superimpose and minimum when the crests coincide with the troughs. Thus, the points A, C, D, etc represent the points of maximum amplitude or intensity resulting from constructive interference. The points B1, B2, etc, represent points where destructive interference takes place with minimum intensity as shown in the above figure.
In one second, the intensity of sound is increasing two times and decreasing two times. Therefore, the number of beats per second will be two, which is same as the difference in the two frequencies (15 - 13).