Audible frequencies have a range of 20 Hz to 20 xx 10^(3) Hz. Express 't' is range in tems of (i) period T, (ii) wavelength air at, (iii) angular frequency w. (Given velocity of sound in 0^(@)C =331 m//s).

Audible frequencies have a range of 20 Hz to 20 xx 10^(3) Hz. Express

1.	Audible frequencies have a range of 20 Hz to 20 xx 10^(3) Hz. Express 't' is range in tems of (i) period T, (ii) wavelength air at, (iii) angular frequency w. (Given velocity of sound in 0^(@)C =331 m//s).
Answer» Solution :Velocity of sound in air at `0^(@)` C = 331 m/s. Audible frequencies, `lambda_(1) = 20 Hz`, `lambda_(2)= 20 xx 10^(3)` Hz (i) Period (T): Time period `T= 1/gamma`, we get, `THEREFORE T_(1) =1/gamma_(1) =1/20 = 0.05` s `T_(2) = 1/gamma_(2) = 1/(20 xx 10^(3)) = 0.055 xx 10^(-3)`s `therefore` Time period RANGE is `0.055 xx 10^(-3)` s. , (ii) Wavelength `lambda`: From the formula, `lambda = v/gamma` `therefore lambda_(1) =v/gamma_(1) = 331/20 = 16.55`m and `lambda_(2) =v/gamma_(2)= 331/(20 xx 10^(3)) = 0.0165`m `therefore` Wavelength ranges is 16.55 m to 0.0165 m. (III) Angular frequency `omega`: From the formula, `omega = 2pi gamma` `therefore omega = 2 PI gamma_(1)= 2pi xx 20 = 40 pi "rads"^(-1)` and `omega_(2) = 2pi gamma_(2) = 2pi xx 20 xx 10^(3)` `=40 pi xx 10^(3)` rad/s. `therefore` Angular frequency range is `40 pi` to `40 pi xx 10^(3)` rad/s.