Question

A sound wave of frequency 10 Hz travels in a medium at a speed of 320 m/s. If phase difference between any two particles is 45°, then the path difference is:
1. 4 m
2. 8 m
3. 12 m
4. 16 m

Answer 1

Correct Answer - Option 1 : 4 m

The correct answer is option 1) i.e. 4 m.

CONCEPT:

• A wave is defined as a form of disturbance that carries energy from one point to another.
• The velocity (v) of a wave related to its wavelength (λ) and frequency (f) as follows:

\(f =\frac{v}{\lambda}\)

The relation between phase difference (ΔΦ) and path difference (Δx) is given by:

\(Δ \phi = \frac{2\pi }{\lambda }Δ x\)

​CALCULATION:

Given that:

Frequency, f = 10 Hz

Velocity, v = 320 m/s

Wavelength, \(λ =\frac{v}{f} = \frac{320}{10} = 32 \:m\)

This wavelength is the wavelength associated with one complete cycle of displacement of particle i.e. 360∘.

If the phase difference is 45°, 

\(360∘ → 32 \:m\)

\(45° →\frac{32 \times 45^{\circ}}{360^{\circ}} = 4\:m\)

Therefore, the path difference will be 4 m if the phase difference is 45°.