Figure shows a tube structure in which a sound signal is sent from one end and is received at the other end. The semicircular part has a radius of 10.0 cm. The frequency of the sound source can be varied from 1 to 10 kHz. Find the frequencies at which the ear perceives maximum intensity. The speed of sound in air ` = 342 m//s`

Explanation

The sound wave bifurcates at the junction of the straight and the semicircular parts. The wave through the straight part travels a distance `s_(1) = 2 xx 10 cm ` and the wave through the curved part travels a distance `s_(2) = pi 10 cm = 31.4 ` cm before they meet again and travel to the receiver. The path difference between the two waves received is, therefore.
`Delta s = s_(2) - s_(1)= 31 . 4 cm - 20 cm = 11.4 cm `
The wavelength of either wave is `(v)/(f) = (330 m//s)/(f)` .
For constructive interference, `Delta p = nlambda ` , where n is an integer.
or , ` Delta p = n * (v)/(f) rArr f = (n.v)/(Deltap)`
`rArr (n. 342)/((0 . 114)) = 3000 n `
Thus, the frequencies within the specified range which cause maximum of intensity are
`3000 xx 1 3000 xx 2 and 3000 xx 3 Hz`