There are two waves having wavelength 100 cm and 101 cm and same velocity `303 ms^(-1)`. The beat frequency is

Options

A. 4 Hz
B. 1 Hz
C. 3 Hz
D. 2 Hz

Answer

To find the beat frequency of two waves with given wavelengths and the same velocity, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Wavelength of the first wave, \( \lambda_1 = 100 \) cm = \( 1.00 \) m (since \( 100 \) cm = \( 1.00 \) m)
- Wavelength of the second wave, \( \lambda_2 = 101 \) cm = \( 1.01 \) m (since \( 101 \) cm = \( 1.01 \) m)
- Velocity of both waves, \( v = 303 \) m/s.

2. **Calculate the Frequency of the First Wave**:
- The frequency \( f_1 \) can be calculated using the formula:
\[ f_1 = \frac{v}{\lambda_1} \]
- Substituting the values:
\[ f_1 = \frac{303 \, \text{m/s}}{1.00 \, \text{m}} = 303 \, \text{Hz} \]

3. **Calculate the Frequency of the Second Wave**:
- The frequency \( f_2 \) can be calculated similarly:
\[ f_2 = \frac{v}{\lambda_2} \]
- Substituting the values:
\[ f_2 = \frac{303 \, \text{m/s}}{1.01 \, \text{m}} \approx 300 \, \text{Hz} \]

4. **Calculate the Beat Frequency**:
- The beat frequency \( f_b \) is given by the absolute difference between the two frequencies:
\[ f_b = |f_1 - f_2| \]
- Substituting the values:
\[ f_b = |303 \, \text{Hz} - 300 \, \text{Hz}| = 3 \, \text{Hz} \]

### Final Answer:
The beat frequency is \( 3 \, \text{Hz} \).

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