Figure shows a tube structure in which a sound signal is sent from one end and received at the other end.…
Figure shows a tube structure in which a sound signal is sent from one end and 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.
Solution
Sol. According to the question,
Path difference, $\Delta x = \pi r - 2r = (\pi - 2)r$
For maximum intensity,
$\Delta x = n\lambda$
$\Rightarrow (\pi - 2)r = n\lambda = \dfrac{nv}{f}$
$\Rightarrow f = \dfrac{nv}{(\pi - 2)r} = \dfrac{n\times 340}{(3.14 - 2)\times 0.2}$
$ = 1491n\ \mathrm{Hz}$
If $n = 1$, then $f = 1491\ \mathrm{Hz}$
Answer: $1491\ n\ \mathrm{Hz}$