Wavelengths of two notes in air are `((90)/(175))` m and `((90)/(173))` m. Each note produces four beats per second with a third note of a fixed frequency. Calculate the velocity of sound in air.

Explanation

Given `lambda_(1) = (90)/(175) m and lambda_(2) = (90)/(173) m `
Let `f(1) and f_(2)` be the corresponding frequencies and v be the velocity of sound in air.
`v = lambda_(1) f_(1) and v = lambda_(2) f_(2)`
`:. F_(2) =(v)/(lambda_(1)) and f_(2) = (v)/(lambda_(2))`
Since `lambda_(2) gt lambda_(1) :. f_(2) gt f_(2)`
Let f be the frequency of the third note.
`:. f_(1) - f = 4 and f - f_(2) = 4 `
` :. f_(1) - f_(2) = 8 :. (v)/(lambda_(1)) - (v)/(lambda_(2)) = 8 `
`v [(175)/(90) - (173)/(90)] = 8 :. v [(2)/(90)] = 8 `