Question

Five sources of sound $S_1,S_2,S_3,S_4,\&S_5$of equal intensity I are placed in a straight line as shown. The point P is far away from sources. Let $\lambda$ be the wave length of waves emitted by the sources and initial phase of all waves be zero. Column-I shows distance of separation between sources and Column-II shows the resultant intensity of sound at point P due to all sources.

$\begin{array}{cccc}& ColumnI& & ColumnII\\ \left(a\right)& x_A=x_B=x_C=x_D=\frac{\lambda }{2}& \left(p\right)& Zero\\ \left(b\right)& x_A=x_B=x_C=x_D=\frac{\lambda }{6}& \left(q\right)& nonzero\\ \left(c\right)& x_A=x_B=x_C=x_D=\lambda & \left(r\right)& I\\ \left(d\right)& x_A=x_B=x_C=x_D=\frac{\lambda }{4}& \left(s\right)& 25I\end{array}$

• A. a $\to$ r; b $\to$ q; c $\to$ s; d $\to$ s
• B. a $\to$ q, s; b $\to$ q, r; c $\to$p, r; d $\to$ p
• C. a $\to$ q,r; b $\to$ q,r; c $\to$q, s; d $\to$ q, r
• D. a $\to$ p; b $\to$ q; c $\to$ r; d $\to$ s

Answer 1

The correct option is C a $\to$ q,r; b $\to$ q,r; c $\to$q, s; d $\to$ q, r

$\Delta {\varphi }_{12}={\varphi }_{13}=\frac{2\pi }{\lambda },\frac{\lambda }{2}=\pi {\varphi }_{14}={\varphi }_{13}=\frac{2\pi }{\lambda }.\lambda =2\pi A_R=3A-2A{A}_R=A$
$I_R=I$
For B
$A_R=A$
$I_R=I$
For C
$A_R=5A{I}_R=25I$
For D
$A_R=-A{I}_R=I$