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 the two waves with given wavelengths, we can follow these steps:

### Step 1: Identify the given data
- Wavelength of the first wave, \( \lambda_1 = 100 \, \text{cm} = 1.00 \, \text{m} \)
- Wavelength of the second wave, \( \lambda_2 = 101 \, \text{cm} = 1.01 \, \text{m} \)
- Velocity of both waves, \( v = 303 \, \text{m/s} \)

### Step 2: Calculate the frequency of each wave
Using the formula for frequency:
\[ \nu = \frac{v}{\lambda} \]

**For the first wave:**
\[ \nu_1 = \frac{v}{\lambda_1} = \frac{303 \, \text{m/s}}{1.00 \, \text{m}} = 303 \, \text{Hz} \]

**For the second wave:**
\[ \nu_2 = \frac{v}{\lambda_2} = \frac{303 \, \text{m/s}}{1.01 \, \text{m}} = \frac{303}{1.01} \, \text{Hz} \]

Calculating \( \nu_2 \):
\[ \nu_2 \approx 300 \, \text{Hz} \quad (\text{using a calculator, } \frac{303}{1.01} \approx 300) \]

### Step 3: Calculate the beat frequency
The beat frequency \( B \) is given by the absolute difference of the two frequencies:
\[ B = |\nu_1 - \nu_2| \]

Substituting the values:
\[ B = |303 - 300| = 3 \, \text{Hz} \]

### Conclusion
The beat frequency is \( 3 \, \text{Hz} \).

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