Question

When beats are produced by two progressive waves of the same amplitude and of nearly the same frequency, the ratio of maximum loudness to the loudness of one of the waves will be $n$ . Where $n$ is:

• A. 3
• B. 1
• C. 4
• D. 2

Answer 1

Answer: (C)

4

Answer 2

We know that intensity $I\propto a^{2},$ where a is amplitude of the wave. The maximum amplitude is the sum of two anplitudes i.e., $(a +a=2a)$ Hence, maximum intensity $\propto 4a^{2}$ Therefore, the required ratio i.e., ratio of maximum intensity (loudness) and intensity (loudness) of one wave is given by $n,$ $n=\frac{4 a^{2}}{a^{2}}=4$