Two sound waves of wavelengths 98cm and 100cm arrive at the same point,from two different source.The number of beats heard (per second) is (speed of sound is 392m/s)

Options

A. 8 Hz
B. 4 Hz
C. 6 Hz
D. 12 Hz

Answer

To solve the problem of finding the number of beats heard per second from two sound waves with different wavelengths, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Wavelength of wave 1, \( \lambda_1 = 98 \, \text{cm} = 0.98 \, \text{m} \)
- Wavelength of wave 2, \( \lambda_2 = 100 \, \text{cm} = 1.00 \, \text{m} \)
- Speed of sound, \( v = 392 \, \text{m/s} \)

2. **Use the Formula for Frequency**:
The frequency \( f \) of a wave can be calculated using the formula:
\[ f = \frac{v}{\lambda} \]
where \( v \) is the speed of sound and \( \lambda \) is the wavelength.

3. **Calculate the Frequencies**:
- For wave 1:
\[ f_1 = \frac{v}{\lambda_1} = \frac{392 \, \text{m/s}}{0.98 \, \text{m}} = 400 \, \text{Hz} \]
- For wave 2:
\[ f_2 = \frac{v}{\lambda_2} = \frac{392 \, \text{m/s}}{1.00 \, \text{m}} = 392 \, \text{Hz} \]

4. **Calculate the Number of Beats**:
The number of beats per second is given by the absolute difference between the two frequencies:
\[ \text{Number of beats} = |f_1 - f_2| \]
Since \( f_1 > f_2 \):
\[ \text{Number of beats} = f_1 - f_2 = 400 \, \text{Hz} - 392 \, \text{Hz} = 8 \, \text{beats per second} \]

5. **Final Answer**:
The number of beats heard per second is \( 8 \).