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 P Q 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 . The wvelength of sound emitted by the speakers is

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 P Q 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 . The  wvelength of sound emitted by the speakers is

Infinity Learn · Accepted Answer

We know that the path difference between two consecutive maxima $$=$$λ,i.e. AQ−$$BQ=$$λ From figure $$AQ=$$ $$(BQ)2+(AB)2$$ $$=(2$$⋅$$4)2+(1)2=2$$⋅$$6m$$ $$2$$⋅$$6$$−$$2$$⋅$$4=$$λ  or  λ$$=0$$⋅$$2m$$

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