The Mystery of Interference in Sound Waves

What happens when two speakers are 3.0 m apart and play identical tones of frequency 170 Hz, with Sam standing directly in front of one speaker at a distance of 4.0 m? Is this a loud spot or a quiet spot?

Answer: The phase difference is π in the destructive interference, making it a quiet spot.

When two speakers are 3.0 m apart and play identical tones of frequency 170 Hz, with Sam standing directly in front of one speaker at a distance of 4.0 m, a phenomenon known as sound interference occurs. In this case, the sound waves from the two speakers interfere with each other, resulting in either constructive or destructive interference.

In the given scenario, the phase difference between the sound waves produced by the two speakers is π, leading to destructive interference. Destructive interference occurs when the peaks of one wave align with the troughs of another wave, resulting in a cancellation of sound at certain points. This makes it a quiet spot where Sam is standing.

To calculate the phase difference, we can use the formula:

ΔФ = Δr * 2π / λ

Where:

Δr = path difference between the two sound waves

λ = wavelength of the sound waves

In this case, the path difference Δr is 1m and the wavelength λ is 2m. By substituting these values into the formula, we find that the phase difference ΔФ is equal to π, indicating destructive interference.

Therefore, the spot where Sam is standing is a quiet spot due to the destructive interference of the sound waves produced by the two speakers.