Reflection on Sound Waves Interference

Is Susan standing at a quiet spot or a loud spot?

If Susan stands 17.25 m from one speaker, is she standing at a quiet spot or a loud spot?

Answer:

Susan is standing at a quiet spot. When Susan stands 17.25 m from one speaker, the phase difference between the sound waves from the two speakers is 88.8 radians, which indicates that the waves are not in phase at Susan's location.

Interference of sound waves can lead to the creation of loud and quiet spots in a room, depending on the phase relationship between the waves. In this scenario, where two loudspeakers emit identical 115 Hz sound waves and Susan is walking between them, the distance she stands from one speaker determines whether she experiences a loud or quiet spot.

The wavelength of a sound wave can be calculated using the formula λ = v/f, where v is the speed of sound and f is the frequency. In this case, the wavelength is 3.00 m. When Susan stands at 17.25 m from one speaker, which is less than half a wavelength away, the phase difference between the waves becomes crucial.

The phase difference is calculated as Δφ = 2π(d/λ), where d is the path difference between the two waves traveling from the speakers to Susan. In this scenario, the phase difference is 88.8 radians, indicating that the waves are out of phase at Susan's location. As a result, she is standing at a quiet spot where the waves interfere destructively.