Audible frequencies have a range 20 Hz to 20,000 Hz. Express this range in terms of
(i) Period T.
(ii) Wavelength `lambda` in air.
(iii) Angular frequency. Given velocity of sound in air is `330ms^(-1)`.

Explanation

Here, `v_(1=)=20Hz,v_(2)=20,000Hz,v=330ms^(-1)`
(i) Time period
`T_(1)=(1)/(v_(1))=(1)/(20)=5xx10^(-2)s`,
`T_(2)=(1)/(v_(2))=(1)/(20,000)=5xx10^(-5)s`
Thus the audible range in terms of period is from `5xx10^(-2)s" to "5xx10^(-5)s`.
(ii) Wave length
`lamda_(1)=(v)/(v_(1))=(330)/(20)=16.5m`
`lamda_(2)=(v)/(v_(2))=(330)/(20000)=16.5m`
Thus the audible range in terms of wavelength is from 16.5 to 0.0165 m.
(iii) Angular frequency
`omega_(1)=2piv_(1)=2pixx20`
`=40pi" rdas"^(-1)`
`omega_(2)=2piv_(2)=2pixx20,000`
`=40,000pi" rad "s^(-1)`
Thus the audible range in terms of angular frequency is from `40pi" rad"s^(-1)" to "40,000pi" rad "s^(-1)`.