Question

A source of sound $S$ and a detector D are placed at some distance from one another. A big cardboard is placed near the detector and perpendicular to the line SD as shown in figure (below). It is gradually moved away and it is found that the intensity changes from a maximum to a minimum as the board is moved through a distance of $20cm$. Find the frequency of the sound emitted. Velocity of sound in air is $336m/s$.

Answer 1

Step 1: Given data and drawing the diagram

Velocity of sound in air $v=336m/s$

Distance$=20cm$

Let frequency of the sound emitted $=f$

Let wavelength of wave $=\lambda$

Step 2: Find the frequency of the sound emitted

Distance between maximum and minimum intensity of wave is $\lambda /4$.

Since distance between maximum and minimum intensity is given as $20cm$. We can write,

$$\begin{gathered} \lambda /4=20cm \\ \lambda =80cm \\ \lambda =80x{10}^{-2}m \end{gathered}$$

Frequency in a sound wave refers to the rate of the vibration of the sound travelling through the air. It is given by

$$\begin{gathered} f=\frac{v}{\lambda } \\ f=\frac{336}{80\times {10}^{-2}} \\ f=420Hz \end{gathered}$$

Hence, the frequency of the sound emitted is $420Hz$