Question

Two loudspeakers sit next to each other on a line in a 10◦C room.They both emit a 660 Hz sound

1. If the speakers have the same phase constant, what is the smallest distance between the speakers for which the interference of thesound waves is perfectly constructive?

2. If the speakers have phase constant difference equal to π, what isthe smallest distance between the speakers for which the interference of the sound waves is perfectly constructive?

3. If the speakers have the same phase constant, what is the smallest distance between the speakers for which the interference of the sound waves is perfectly destructive?

Answer 1

v = λ × f        λ = v / f ..........(A)

Here, V= speed of sound at temperature 10 degree.

Temperature dependence of speed of sound is given by

T is in kelvin.

so, at 10 C, V = 337.51 m/s.

so, Using equation A.

λ(wavelength) = 51.138 cm.

1. If they have the same phase, they will interfere constructively if their high amplitute coincide with each other. this would happen if they are placed atleast half a wave length away.

so, the minimum Distance = 51.138/2 = 25.56 cm. Ans.

2. If they have a phase difference of pi. They need to have a distance of one wavelength between them.

so, Minimum distance = 51.138 cm.

3. Now they have same phase, their low and high would meet once they have a distance of one wavelength.

so, Minimum distance is again 51.138 cm.