Figure shows a tube structure in which a sund 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 ohet sound source can be varied elertronically between 1000 and 4000 Hz. Find the frequencies at which maxima of intensity are detected. The speed of sound in air =`3400ms^-1`.

Explanation

The sound wave reaches detector by two paths simultaneously be straight as well as semicircular track. The wave through the straight path travels a distance `l_1= 2 xx 20` cm and the wave through the curved part travels a distance `l_2= pi( 20 cm)= 62.8` cm before they meet a again and travel to the receiver. The path difference between the two waves received is, therefore,
`triangle l = l_2-l_1= 62.8 cm - 40 cm = 22.8 cm = 0.228 m`
The wavelength of either wave is `=(v)/(n)= (340)/(n)`. For constructive interference, `triangle l = N lambda`, where N is an integer.
or `0.228 = N((340)/(n))`
or, `n=N((340)/(0.228))= N(1491.2)Hz= N(1490)Hz`
Thus, the frequencies within the specific range which cause maxima of intensity are 1490 Hz and 2980 Hz.