Two sound wave trains from two separate coherent sources propagate in the same direction and allowed

Question

Two sound wave trains from two separate coherent sources propagate in the same direction and allowed to interfere. If each source produces an intensity at certain point having a path difference (25 $\lambda / 2$ ) from the two sources the resultant intensity at that point is\

Professor PC Thomas Classes · Answer

Resulting intensity is given by $\mathrm{l}_{0}=\mathrm{a}_{1}{ }^{2}+\mathrm{a}_{2}{ }^{2}+2 \mathrm{a}_{1} \mathrm{a}_{2} \cos \delta$ where $\mathrm{a}_{1}$ and $\mathrm{a}_{2}$ are the amplitudes and $\delta$ is the phase difference Here a ${ }_{1} =\sqrt{I} \quad \mathrm{a}_{2}=\sqrt{I} \quad \delta=25 \pi$ because $\phi=\frac{2 \pi}{\lambda} \mathrm{x}=\frac{2 \pi}{\lambda} 	imes \frac{25 \lambda}{2}=25 \pi$\ $\cos 25 \pi=-1$\ $	herefore I_{0}=(\sqrt{I})^{2}+(\sqrt{I})^{2}+2(\sqrt{I})(\sqrt{I}) \cos (25 \pi)$\