Question

Two small speakers are separated by a distance of 4 cm, as shown. The speakers are driven in phase with a sine wave signal of frequency 10 kHz. A small microphone is placed a distance 1.1 m away from the speakers on the axis running through the middle of the two speakers, and the microphone is then moved perpendicular to the axis. Where does the microphone record the first minimum of the interference pattern from the speakers as measured from the axis? The speed of sound in air is 343 m/s. Do not use the small angle approximation for this problem.

Answer 1

V = speed of sound in air = 343 m/s

f = frequency = 10,000 Hz

wavelength is given as

= V/f = 343 / 10x 10³ = 0.0343m

d = distance between speakers = 4 cm = 0.04 m

condition for minima is given as

dSin = (2n + 1) /2

(0.04) Sin = (2 x 0 + 1) (0.0343) /2

= 25.3

distance of minima is given as

distance = L tan = 1.1 tan25.3 = 0.5199m

condition for maxima is given as

dSin = n

(0.04) Sin = 1.(0.0343)

= 59.03

distance of minima is given as

distance = L tan = 1.1 tan59.03 = 1.832 m