Question

A wave of frequency 500 Hz travels with a speed of 360 ms\(^{-1}\). The distance between two nearest points which are 60° out of phase is

• A. 12 cm
• B. 18 cm
• C. 50 cm
• D. 24 cm
• E. 6 cm

Hint:

Distance for phase difference = fraction of wavelength.

Answer 1

The Correct Option is A

Concept: Phase difference relation: \[ \Delta \phi = \frac{2\pi}{\lambda} \Delta x \]

Step 1: Find wavelength. \[ \lambda = \frac{v}{f} = \frac{360}{500} = 0.72\,\text{m} \]

Step 2: Convert phase. \[ 60^\circ = \frac{\pi}{3} \]

Step 3: Use formula. \[ \frac{\pi}{3} = \frac{2\pi}{\lambda} \Delta x \]

Step 4: Solve for \(\Delta x\). \[ \Delta x = \frac{\lambda}{6} = \frac{0.72}{6} = 0.12\,\text{m} \]

Step 5: Convert to cm. \[ 0.12\,\text{m} = 12\,\text{cm} \]

Step 6: Conclusion. \[ \boxed{12\,\text{cm}} \]