The wavelength of two sound waves are `49 cm` and `50 cm` , respectively . If the room temperature is `30^(@) C` , then the number of beats produced by them is approximately
(velocity of sound in air at `30 ^(@) C = 332 m//s`)

Options

A. `(a)6`
B. `(b)10`
C. `(c)13`
D. `(d)18`

Explanation

To solve the problem of finding the number of beats produced by two sound waves with wavelengths of 49 cm and 50 cm, we can follow these steps:

### Step 1: Convert Wavelengths to Meters
The wavelengths are given in centimeters, so we need to convert them to meters for consistency with the velocity of sound.
- Wavelength 1 (λ₁) = 49 cm = 0.49 m
- Wavelength 2 (λ₂) = 50 cm = 0.50 m

### Step 2: Use the Formula for Frequency
The frequency (f) of a wave can be calculated using the formula:
\[ f = \frac{v}{\lambda} \]
where:
- \( v \) = velocity of sound in air (332 m/s)
- \( \lambda \) = wavelength

### Step 3: Calculate Frequencies
Now we can calculate the frequencies for both wavelengths:
- For the first wave (λ₁):
\[ f₁ = \frac{332 \, \text{m/s}}{0.49 \, \text{m}} \]
\[ f₁ \approx 677.55 \, \text{Hz} \]

- For the second wave (λ₂):
\[ f₂ = \frac{332 \, \text{m/s}}{0.50 \, \text{m}} \]
\[ f₂ = 664 \, \text{Hz} \]

### Step 4: Calculate the Beat Frequency
The beat frequency (f_b) is given by the absolute difference between the two frequencies:
\[ f_b = |f₁ - f₂| \]
Substituting the values we calculated:
\[ f_b = |677.55 \, \text{Hz} - 664 \, \text{Hz}| \]
\[ f_b \approx 13.55 \, \text{Hz} \]

### Step 5: Round the Result
Since the problem asks for the approximate number of beats, we can round 13.55 Hz to 13 Hz.

### Final Answer
The number of beats produced by the two sound waves is approximately **13 Hz**.

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