Two identical loudspeakers L1 and L2 are placed 1.50 m apart and are driven by the same audio generator so that they emit sound waves of frequency 512 Hz in phase. An observer stands on the straight line joining the two speakers at a point P such that the distances are PL1 = 2.00 m and PL2 = 2.60 m. (Speed of sound in air = 320 m s−1.) Each speaker alone would produce a displacement amplitude of 1.5 mm at P.
a. (i) Calculate the path difference between the two waves reaching P and the corresponding phase difference.
b. (ii) Determine the resultant displacement amplitude at P when both speakers operate together.
c. (iii) Find the ratio of the intensity heard at P with both speakers operating to the intensity heard when only L1 operates. State whether P is a position of reinforcement or cancellation.