Calculate the frequency of beats produced in air when two sources of sound are activated, one emitting a wavelength of 32 cm and the other of 32.2 cm. The speed of sound in air is `350 ms^-1`.

Explanation

To calculate the frequency of beats produced in air when two sources of sound are activated, we will follow these steps:

### Step 1: Identify the given values
- Wavelength of the first source, \( \lambda_1 = 32 \, \text{cm} \)
- Wavelength of the second source, \( \lambda_2 = 32.2 \, \text{cm} \)
- Speed of sound in air, \( v = 350 \, \text{m/s} \)

### Step 2: Convert wavelengths from centimeters to meters
Since the speed of sound is given in meters per second, we need to convert the wavelengths from centimeters to meters:
- \( \lambda_1 = 32 \, \text{cm} = 32 \times 10^{-2} \, \text{m} = 0.32 \, \text{m} \)
- \( \lambda_2 = 32.2 \, \text{cm} = 32.2 \times 10^{-2} \, \text{m} = 0.322 \, \text{m} \)

### Step 3: Calculate the frequencies of both sources
Using the formula for frequency:
\[ \nu = \frac{v}{\lambda} \]
Calculate the frequencies \( \nu_1 \) and \( \nu_2 \):
- For \( \nu_1 \):
\[ \nu_1 = \frac{350 \, \text{m/s}}{0.32 \, \text{m}} = 1093.75 \, \text{Hz} \]
- For \( \nu_2 \):
\[ \nu_2 = \frac{350 \, \text{m/s}}{0.322 \, \text{m}} = 1087.89 \, \text{Hz} \]

### Step 4: Calculate the frequency of beats
The frequency of beats \( n \) is given by the absolute difference between the two frequencies:
\[ n = |\nu_1 - \nu_2| \]
Substituting the values:
\[ n = |1093.75 \, \text{Hz} - 1087.89 \, \text{Hz}| = 5.86 \, \text{Hz} \]

### Step 5: Round the result
Since the number of beats is typically expressed as a whole number, we round \( 5.86 \) to \( 6 \).

### Final Answer
The frequency of beats produced is approximately \( 6 \, \text{beats per second} \).

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