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 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 =`340ms^-1`.

Explanation

The sound wave bifurcates at the junction of the straight and the semicircular parts. The wave thorough the straight part travels a distance `l_1=2xx20cm` and the wave through the curved part travels a distance `l_2=pi20 cm=32.8` cm before they meet again and travel to the receiver. The path difference between the two waves received is, therefore, `/_\l=l_2-l_1=62.8cm-40cm=22.8cm=0.028m`.
The wavelength of either wave is `v/v=(340ms^-1)/v`. For constructive interference `/_\l=nlamda` where n is an integer.
or `0.228m=n(340ms^-1)/v`
`or v=n(340ms^-1)/(0.228m)=n1491.2Hz~~n1490Hz.`
Thus the frequencies within the specified range whic cause maxima of intensity are 190 Hz and 2980 Hz.