Calculate the beat frequency heard when two sound sources of wavelength 35cm and 35.2 cm are sounded together. The speed of sound in air is 330 `ms^(-1)`

Answer

To calculate the beat frequency heard when two sound sources of different wavelengths are sounded together, we can follow these steps:

### Step 1: Convert Wavelengths to Meters
The given wavelengths are:
- \( \lambda_1 = 35 \, \text{cm} = 0.35 \, \text{m} \)
- \( \lambda_2 = 35.2 \, \text{cm} = 0.352 \, \text{m} \)

### Step 2: Calculate Frequencies
Using the formula for frequency \( f = \frac{v}{\lambda} \), where \( v \) is the speed of sound and \( \lambda \) is the wavelength, we can calculate the frequencies of both sound sources.

1. For the first wavelength \( \lambda_1 \):
\[ f_1 = \frac{v}{\lambda_1} = \frac{330 \, \text{m/s}}{0.35 \, \text{m}} \approx 943 \, \text{Hz} \]

2. For the second wavelength \( \lambda_2 \):
\[ f_2 = \frac{v}{\lambda_2} = \frac{330 \, \text{m/s}}{0.352 \, \text{m}} \approx 938 \, \text{Hz} \]

### Step 3: Calculate Beat Frequency
The beat frequency \( f_b \) is given by the absolute difference between the two frequencies:
\[ f_b = |f_1 - f_2| = |943 \, \text{Hz} - 938 \, \text{Hz}| = 5 \, \text{Hz} \]

### Final Answer
The beat frequency heard when the two sound sources are sounded together is **5 Hz**.

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