Sound Wave

Beats and Time Interval Between Successive Maxima

When two sound waves of slightly different frequencies and are sounded together, we hear a phenomenon called "beats". The time interval between successive maxima (loudest sounds) is related to the beat frequency.

Step 1: Define Beat Frequency

The beat frequency, , is the absolute difference between the two frequencies. It represents how many times per second the sound gets louder and softer (the number of "beats" we hear).

Step 2: Relate Beat Frequency to the Time Interval

The period of the beat, , represents the time interval between successive maxima (loudest sounds). The period is the inverse of the frequency. In other words, it is the time it takes for one complete beat cycle to occur (loud -> soft -> loud).

Step 3: Substitute the Expression for Beat Frequency

Substituting the expression for the beat frequency into the period equation gives us the time interval between successive maxima.

Conclusion

The time interval between successive maxima is: .