Question

A sound wave of frequency 500 Hz travels between two points X and Y separated by a distance of 600 m in a time of 2 s. The number of waves between the points X and Y are

• A. 1000
• B. 1500
• C. 300
• D. 600

Hint:

Use the relation \( \text{Number of waves} = \frac{\text{Distance}}{\lambda} \), and find \( \lambda \) using \( \lambda = \frac{v}{f} \) where \( v = \frac{d}{t} \).

Answer 1

The Correct Option is A

Step 1: Given:
Frequency \( f = 500 \, \text{Hz} \), Distance \( d = 600 \, \text{m} \), Time \( t = 2 \, \text{s} \) Step 2: Find speed of sound: \[ v = \frac{d}{t} = \frac{600}{2} = 300 \, \text{m/s} \] Step 3: Use wave speed formula \( v = f\lambda \) to find wavelength: \[ \lambda = \frac{v}{f} = \frac{300}{500} = 0.6 \, \text{m} \] Step 4: Number of waves between X and Y: \[ \text{Number of waves} = \frac{\text{distance}}{\text{wavelength}} = \frac{600}{0.6} = \boxed{1000} \]