Q. Two identical sound A and B reach a point in the same phase. The resultant sound is C. The loudness of C is n dB higher the loudness of A.
A) 2
B) 3
C) 4
D) 6
Explanation
(d) If a amplitude of sound from A and $B$ each, then $I_{A} = I_{B}ka^{2}$,where k is constant.
Loudness due to $C(ie\ A + B)$
$I_{C} = k\left( 2a^{2} \right)4I_{A}$
$\therefore n = 10\log_{10}{\left( \frac{I_{C}}{I_{A}} \right) = 10\log_{10}4}$
$= 10 \times 0.6 = 6$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.