Wavelength of two notes in air is (90 //175) m and ( 90//173) m, respectively . Each pof these notes produces 4 beats//s with a third note of a fixed frequency . Calculate the velocity of sound in air .

Wavelength of two notes in air is (90 //175) m and ( 90//173) m, respe

1.	Wavelength of two notes in air is (90 //175) m and ( 90//173) m, respectively . Each pof these notes produces 4 beats//s with a third note of a fixed frequency . Calculate the velocity of sound in air .
Answer» Solution :Given : `lambda_(1) = 90//175 m and lambda_(2) = 90//173 m` If ` f_(1) and f_(2)` are the corresponding frequencies and ` v` is the velocity ofsound in air , we have ` v = f_(1) lambda_(1) and v = f_(2) lambda_(2)` `f_(1) = (v)/( lambda_(1)) and f_(2) = (v)/( lambda_(2))` SINCE , `lambda_(1) LT lambda_(2)` , we must have `f_(1) gt f_(2)`. If `F` is the frequency of the third note , then `f_(1) - f = 4 and f - f_(2) = 4` rArr`f_(1) - f_(2) = 8` `(v)/( lambda_(1)) - (v)/( lambda_(2)) = 8` `v [ (175)/( 90) - (173)/(90)] = 8` `v = 360 m//s`