A wave of frequency 500 HZ travels between X and Y, a distance of 600 m in 2 sec. How many wavelength are there in distance XY :-

Options

A. 1000
B. 300
C. 180
D. 2000

Explanation

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

### Step 1: Identify the given values
- Frequency (f) = 500 Hz
- Distance (d) = 600 m
- Time (t) = 2 s

### Step 2: Calculate the velocity of the wave
The formula for velocity (v) is given by:
\[ v = \frac{d}{t} \]
Substituting the known values:
\[ v = \frac{600 \, \text{m}}{2 \, \text{s}} = 300 \, \text{m/s} \]

### Step 3: Calculate the wavelength (λ)
The relationship between velocity (v), frequency (f), and wavelength (λ) is given by:
\[ v = f \cdot \lambda \]
Rearranging this formula to find the wavelength:
\[ \lambda = \frac{v}{f} \]
Substituting the values we have:
\[ \lambda = \frac{300 \, \text{m/s}}{500 \, \text{Hz}} = \frac{300}{500} \, \text{m} = \frac{3}{5} \, \text{m} \]

### Step 4: Calculate the number of wavelengths in the distance XY
To find the number of wavelengths (n) in the distance XY, we use the formula:
\[ n = \frac{d}{\lambda} \]
Substituting the values:
\[ n = \frac{600 \, \text{m}}{\frac{3}{5} \, \text{m}} \]
This can be simplified as:
\[ n = 600 \, \text{m} \times \frac{5}{3} \]
Calculating this gives:
\[ n = 600 \times \frac{5}{3} = 600 \times 1.6667 = 1000 \]

### Conclusion
The number of wavelengths in the distance XY is **1000**.

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