The sources of sound A and B produce a wave of 350   Hz in same phase. A particle P is vibrating under an influence of these two waves. If the amplitudes at P produced by the two waves is 0 . 3   mm and 0 . 4   mm , the resultant amplitude of the point P will be, when A P - B P = 25   cm and the velocity of sound is 350   m   s - 1 .

Step-by-step solution

The resultant amplitude of waves at the point P   is, A = A 1 2 + A 2 2 + 2 A 1 A 2 cos ϕ   Here, ϕ   is the phase difference and A 1   and   A 2   are amplitude of sound waves. For phase difference, ϕ = 2 π λ ∆ x   Here, ∆ x   is the path difference and λ   is the wavelength of sound wave. ⇒ λ = v f = 350   m   s - 1 350   Hz = 100   cm Path difference, ∆ x = A P - B P = 25   cm Therefor