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: Calculate the velocity of the wave
The velocity (v) of the wave can be calculated using the formula:
\[ v = \frac{\text{distance}}{\text{time}} \]
Given that the distance between points X and Y is 600 m and the time taken is 2 seconds, we can substitute these values into the formula:
\[ v = \frac{600 \, \text{m}}{2 \, \text{s}} = 300 \, \text{m/s} \]

### Step 2: Calculate the wavelength of the wave
The wavelength (λ) can be calculated using the formula:
\[ \lambda = \frac{v}{f} \]
Where:
- \( v \) is the velocity of the wave (300 m/s),
- \( f \) is the frequency of the wave (500 Hz).

Substituting the values:
\[ \lambda = \frac{300 \, \text{m/s}}{500 \, \text{Hz}} = \frac{300}{500} = \frac{3}{5} \, \text{m} \]

### Step 3: Calculate the number of wavelengths in the distance XY
The number of wavelengths (N) can be calculated using the formula:
\[ N = \frac{\text{distance}}{\lambda} \]
Substituting the distance (600 m) and the wavelength (\( \frac{3}{5} \) m):
\[ N = \frac{600 \, \text{m}}{\frac{3}{5} \, \text{m}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ N = 600 \, \text{m} \times \frac{5}{3} = 600 \times \frac{5}{3} = 2000 \div 3 = 1000 \]

### Final Answer
There are **1000 wavelengths** between points X and Y.

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