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).

Audible frequencies have a range 20 Hz to 20,000 Hz. Express this rang

1.	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).
Answer» SOLUTION :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)`.