Two sources of sound `A` and `B` produces the wave of `350 Hz`. They vibrate in the same phase. The particle `P` is vibrating under the influence of these two waves, if the amplitudes at the point P produced by the two waves is `0.3mm` and `0.4mm` then the resultant amplitude of the point `P` will be when `AP-BP=25cm` and the velocity of sound is `350m//sec`.

Options

A. `0.7mm`
B. `0.1mm`
C. `0.2mm`
D. `0.5mm`

Answer

D

Explanation

`lamda=(v)/(n)=(350)/(350)=1m=100cm`
Also path difference `(Delta x)` between the waves at the point of observation is `AP-BP=25cm`. Hence `Delta phi=(2pi)/(lamda)(Delta x)=(2pi)/(1)xx((25)/(100))=(pi)/(2)`
`impliesA=sqrt((a_1)^2+(a_2_^2))=sqrt((0.3)^2+(0.4)^2)=0.5mm`