A progressive wave is represented as A progressive wave is represented as y=0.2 cos π(0.04 t+0.2 x-(π/6)) where 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

A progressive wave is represented as A progressive wave is represented as y=0.2 cos π(0.04 t+0.2 x-(π/6)) where 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

On comparing the given equation with y =a cos (ω t+k x-φ) we get, k =(2 π/λ)=0.02 and λ=100 cm It is given that phase difference between particles, Δ φ=(π/2) So, the path difference between them, Δ p=(λ/2 π) × Δ φ =(λ/2 π) × (π/2)=(λ/4) =(100/4)=25 cm

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

4 cm

8 cm

25 cm

12.5 cm

On comparing the given equation with y=acos(ωt+kx−ϕ) we get, k=λ2π​=0.02 and λ=100cm It is given that phase difference between particles, Δϕ=2π​ So, the path difference between them, Δp=2πλ​×Δϕ =2πλ​×2π​=4λ​ =4100​=25cm

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