Question

A siren creates a sound level of `60 H_(Z)` at a location `500 m` from the speaker. The siren is powered by a batter that delivers a total energy of `1.0 kJ`. Assuming that the efficiency of siren is `30%` , determine the total time the siren can sound.

Answer 1

Sound level (in `dB`)
`L = 10 log_(10) ((I)/(I_(0)))`
where, `I_(0) = 10^(-12) W//m^(2)`
`L = 60 dB`
Hence, `I = (10^(6)) I_(0) = 10^(-6) W//m^(2)`
Intensity, `I = (Power)/(Area) = (P)/(4 pi r^(2))`
rArr `P = I (4 pi r^(2))`
`P = (10^(-6))(4 pi)(500)^(2) = 3.14 W`
:. Time, `t = ((10 xx 10^(3))((30)/(100)))/(3.14)`
`t = 95.5s`