A sound wave of frequency 500 Hz covers a distance of 1000 m is 5 sec between the points X and Y. Then the number of waves between X and Y is

Options

A. `500`
B. `1000`
C. `2500`
D. `5000`

Explanation

To find the number of waves between points X and Y, we can follow these steps:

### Step 1: Determine the velocity of the sound wave
We know that the sound wave covers a distance of 1000 meters in 5 seconds. We can calculate the velocity (v) using the formula:

\[ v = \frac{\text{distance}}{\text{time}} = \frac{1000 \, \text{m}}{5 \, \text{s}} = 200 \, \text{m/s} \]

### Step 2: Calculate the wavelength (λ)
We can use the relationship between velocity (v), frequency (f), and wavelength (λ):

\[ v = f \cdot \lambda \]

Rearranging this formula to find the wavelength gives us:

\[ \lambda = \frac{v}{f} \]

Substituting the values we have:

\[ \lambda = \frac{200 \, \text{m/s}}{500 \, \text{Hz}} = 0.4 \, \text{m} \]

### Step 3: Calculate the number of waves
The number of waves (N) can be calculated using the total distance (d) and the wavelength (λ):

\[ N = \frac{d}{\lambda} \]

Substituting the values we have:

\[ N = \frac{1000 \, \text{m}}{0.4 \, \text{m}} = 2500 \]

### Conclusion
The number of waves between points X and Y is **2500**.

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