Question

The diagram shows two isotropic point sources of sound. The sound waves are in phase with each other at the positions of the sources. What are the three lowest frequencies in the audible range at which fully destructive interference will occur at the position of the observer? Ignore the decrease in intensity that occurs with distance from the source. Use v = 343 m/s for the speed of the sound in the air

Answer 1

The three lowest frequencies at which fully destructive interference occurs are 171.5 Hz, 514.6 Hz, and 857.8 Hz.

The occurrence of fully destructive interference in the audible range is determined by the phase relationship between sound waves from two isotropic point sources. At positions where the waves are in phase, destructive interference leads to nodes, resulting in points of minimum amplitude. The condition for fully destructive interference involves a path difference equal to an integer multiple of the wavelength.

In this scenario, with a speed of sound in air (v) at 343 m/s, the three lowest frequencies (f) can be calculated using the formula f= v/2L, where L is the distance between the sources. The calculated frequencies are approximately 171.5 Hz, 514.6 Hz, and 857.8 Hz, representing the instances at which fully destructive interference occurs at the observer's position due to the specific wavelength relationships between the two sources.