Question

When the wavelength of sound changes from 1 m to 1.01 m, the number of beats heard are 4. The velocity of sound is

• A. 404 m/s
• B. 4.04 m/s
• C. 414 m/s
• D. 400 m/s

Hint:

When the wavelength of sound changes from 1 m to 1.01 m, the number of beats heard are 4. The velocity of sound is

Answer 1

The Correct Option is A

Step 1: Concept
Beats $b = n_1 - n_2$, where frequency $n = v/\lambda$.
Step 2: Equation
$4 = \frac{v}{1} - \frac{v}{1.01}$.
Step 3: Solving
$4 = v \left(1 - \frac{1}{1.01}\right) = v \left(\frac{0.01}{1.01}\right)$ $v = \frac{4 \times 1.01}{0.01} = 404 \text{ m/s}$.
Final Answer: (A)