Two sound sources shown in the figure vibrate in phase. By moving `S_(1)` along `PS_(1)` consecutive minima are heard when `L_(1)-L_(2)` has values, `20cm`, `60cm` and `100cm`. What is the frequency of sound source if the speed of sound is `340 m//s`?

Options

A. `280 Hz`
B. `330 Hz`
C. `850 Hz`
D. `440 Hz`

Explanation

The minima will be heard at `P` when a crest from `S_(1)` and a trough from `S_(2)` reach there at the same time. This will happen if `L_(1)-L_(2)` is `lambda//2` or `lambda+(lambda//2)` or `2lambda+(lambda//2)` and so on. Hence the increase in `L_(1)` between consecutive minima is `lambda`, and from the data we see that `lambda=0.40m`. Then from `lambda=v//frArrf-340//0.40=850Hz`