Figure 7.75 shows a tube structure in which a sound signal is bent from one end and is received at the other end . The semicircular part has a radius of `20.0 cm`. The frequency of the sound source can be varied electronically between `1000 and 4000 Hz`. Find the frequencies at which maxima of intensity are detected. The speed of sound in air ` = 340 m//s`.

Explanation

The sound wave reaches detector bytwo paths simultaneously bystraight as well as semicircular track. 1he wave through the straight part travels a distance `l_(1) = 2xx20 cm` and the wave through thecurved parttravels a distance `l_(2) = pi (20 cm)=62.8 cm` before they meet again and travel to the receiver. The path difference between the two waves received is, therefore,
`Deltal = l_(2) - l_(1) = 62.8 cm - 40 cm`
= 22.8 cm = 0.228 m
The wavelength ofeither wave is `(v)/(n) = (340)/(n)` . For constructive interference, `DeltaI = Nlambda` , where N is an integer.
`0.228 = N(340/(n))`
`n = N(340/(0.228)) = N(1491.2) Hz`
= `n(1490)Hz`
Thus, the frequencies within the specified range which cause maxima of intensityare 1490 Hz and 2980 Hz.