Question

Two loudspeakers A and B, 1.0 m apart, produce sound waves of the same wavelength and in the same phase. A sensitive sound detector, moving along PQ, parallel to line AB, 2.4 m away, detects maximum sound at P (on the perpendicular bisector of AB) and another maximum sound when it first reaches Q directly opposite to B, as shown in the figure. What is the wavelength of sound emitted by the speakers?

• A. 0.1 m
• B. 0.2 m
• C. 0.3 m
• D. 0.4 m

Answer 1

The correct option is B 0.2 m

We know that, path difference for two consecutive maxima $=\lambda$
$\Rightarrow AQ-BQ=\lambda$
$\Rightarrow \sqrt{B{Q}^2+A{B}^2}-BQ=\lambda$
$\Rightarrow \sqrt{(2.4{)}^2+1^2}-2.4=\lambda$
$\therefore \lambda =0.2m$
Hence, the correct choice is (b).