Velocity of sound in a medium is 490m/s. two waves of wavelength 98 cm and 100 cm are superposed. Calculate the beat frequency.

Explanation

To calculate the beat frequency of two superposed waves, we can follow these steps:

### Step 1: Understand the relationship between velocity, frequency, and wavelength.
The frequency \( f \) of a wave can be calculated using the formula:
\[ f = \frac{v}{\lambda} \]
where:
- \( v \) is the velocity of sound in the medium,
- \( \lambda \) is the wavelength of the wave.

### Step 2: Convert the wavelengths from centimeters to meters.
Given wavelengths:
- \( \lambda_1 = 98 \, \text{cm} = 0.98 \, \text{m} \)
- \( \lambda_2 = 100 \, \text{cm} = 1.00 \, \text{m} \)

### Step 3: Calculate the frequency of the first wave.
Using the formula for frequency:
\[ f_1 = \frac{v}{\lambda_1} = \frac{490 \, \text{m/s}}{0.98 \, \text{m}} \]
Calculating this gives:
\[ f_1 = 500 \, \text{Hz} \]

### Step 4: Calculate the frequency of the second wave.
Using the same formula for frequency:
\[ f_2 = \frac{v}{\lambda_2} = \frac{490 \, \text{m/s}}{1.00 \, \text{m}} \]
Calculating this gives:
\[ f_2 = 490 \, \text{Hz} \]

### Step 5: Calculate the beat frequency.
The beat frequency \( f_{\text{beat}} \) is given by the absolute difference between the two frequencies:
\[ f_{\text{beat}} = |f_1 - f_2| = |500 \, \text{Hz} - 490 \, \text{Hz}| \]
Calculating this gives:
\[ f_{\text{beat}} = 10 \, \text{Hz} \]

### Final Answer:
The beat frequency is \( 10 \, \text{Hz} \).

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