A sound wave of frequency 20 Hz covers a distance AB of 300 m in 10s. What is the number of waves between A and B?

Options

A. 100
B. 150
C. 250
D. 200

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the Velocity of the Sound Wave
We are given the distance (AB) covered by the sound wave and the time taken.

- **Distance (AB)** = 300 m
- **Time** = 10 s

Using the formula for velocity:
\[ \text{Velocity} (v) = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values:
\[ v = \frac{300 \, \text{m}}{10 \, \text{s}} = 30 \, \text{m/s} \]

### Step 2: Use the Frequency to Find the Wavelength
We know the frequency of the sound wave is given as:
- **Frequency (f)** = 20 Hz

We can use the wave equation which relates velocity, frequency, and wavelength:
\[ v = f \cdot \lambda \]
Where:
- \( \lambda \) is the wavelength.

Rearranging the equation to solve for wavelength:
\[ \lambda = \frac{v}{f} \]
Substituting the values we have:
\[ \lambda = \frac{30 \, \text{m/s}}{20 \, \text{Hz}} = 1.5 \, \text{m} \]

### Step 3: Calculate the Number of Waves Between A and B
To find the number of waves between points A and B, we can use the formula:
\[ \text{Number of Waves} = \frac{\text{Distance}}{\text{Wavelength}} \]
Substituting the values:
\[ \text{Number of Waves} = \frac{300 \, \text{m}}{1.5 \, \text{m}} = 200 \]

### Final Answer
The number of waves between A and B is **200**.

---