Question

Beats is an interesting phenomenon arising from interference of waves. When two harmonic Sound waves of slightly different frequencies and comparable amplitude are heard at the same time, we hear a sound of similar frequency (the average of two close frequencies), but we hear something else also. We hear audibly distinct waxing and waning of the intensity of the sound, with a frequency equal to the difference in the two close frequencies. Artists use this phenomenon often while tuning their instruments with each other. They go on tuning until their sensitive ears do not detect any beats.

Giving reasons for your selection, select pairs out of the following four waves in a medium which will give rise to (i) beats (ii) destructive interference (iii) stationary waves: a) y₁ = A cos 2π(v₁t + x/λ₁) b) y₂ = A cos[2π(v₁t + x/λ₁) + π] c) y₃ = A cos 2π(v₂t + x/λ₂) d) y₄ = A cos 2π(v₂t − x/λ₂) Given v₁ − v₂ is small.