Question

You want t0 find the frequency of two in-phase sound sources: You find that When you are equidistant from both sources, the sound you hear is at a maximum volume, and you find that when you are 3.4 m farther away from one source compared to the other; the sound minimum volume.

What is the lowest possible frequency of the sources? (You can use 343 m/s as the speed of sound in air:)

Answer 1

The lowest possible frequency of the two in-phase sound sources is 100 Hz.

Step-by-step explanation:

To find the lowest possible frequency of the two in-phase sound sources, we need to consider the interference pattern created by the sources. When two sound waves interfere constructively, they reinforce each other and create a maximum in volume. When they interfere destructively, they cancel each other out and create a minimum in volume.

In this case, when you are equidistant from both sources, you hear the sound at maximum volume, indicating constructive interference. When you are 3.4 m farther away from one source compared to the other, you hear the sound at minimum volume, indicating destructive interference. The difference in distance, 3.4 m, corresponds to half a wavelength (λ/2).

The lowest possible frequency occurs when the wavelength is the largest. Since we know the speed of sound in air is 343 m/s, we can use the formula v = fλ to solve for the frequency. Rearranging the formula, we have λ = v/f. Since the difference in distance corresponds to half a wavelength, we can write it as (λ/2) = 3.4 m. Substituting in the values, we get (343 m/s)/(f) = 3.4 m. Solving for f, we find that the lowest possible frequency is 100 Hz.