Two audio speakers are kept some distance apart and are driven by the same amplifier system. A person is sitting at a place 6.0 m from one of the speakers and 6.4 m from the other. If the sound signal is continuously varied from 500 Hz to 5000 Hz, what are the frequencies for which there is a destructive interference at the place of the listener? Speed of sound in air` = 320 ms^-1`

Answer

1200 Hz, 2000 Hz, 2800 Hz, 3600 Hz and 4400 Hz

Explanation

Path difference = 6.4 - 6 = 0.4 m
high wavelength = `(v)/(n_(L)) = (320)/(500) = 0.64)`
low wavelength = `(v)/(n_(H)) = (320)/(5000) = 0.064m`
Destructive interference occures when
`Delta = (2n + 1) (lambda)/(2)`
`0.4 = (2n + 1)(lambda)/(2)`
`lambda = (0.8)/(2n + 1)`
Thus coresponding frequencies are
`n = (320)/(lambda) = (320)/(0.8) xx (2n + 1)`
= 400(2n + 1)
= 400 Hz, 1200 Hz, 2000 Hz, 2800 Hz, 4400 Hz, 5200 Hz,....