Equation of a progressive wave is given by y = 0.2 cos π big(0.04 t + 0.02 x - (π/6) big). The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of (π/2) ?

Question

Equation of a progressive wave is given by y = 0.2 cos π big(0.04 t + 0.02 x - (π/6) big). The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of (π/2) ? (A) 4 cm (B) 8 cm (C) 25 cm (D) 12.5 cm

Tardigrade Admin · Accepted Answer

Comparing with y = a cos (ω t + kx - φ) We get, k = (2 π/λ) = 0.02 π ⇒ λ = 100 km Also, it is given that phase difference between particles Δ φ = (π/2). Hence, path difference between them Δ x = (λ/2 π) × Δ φ = (λ/2 π) × (π/2) = (λ/4) = (100/4) = 25 cm

Q. Equation of a progressive wave is given by $y = 0.2 cos π (0.04 t + 0.02 x - \frac{π}{6}) .$ The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of $\frac{π}{2}$ ?

4 cm

8 cm

25 cm

12.5 cm

None of these

Q. Equation of a progressive wave is given by y=0.2cosπ(0.04t+0.02x−6π​). The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of 2π​ ?