You are standing 5 feet from one speaker and 14 feet from another. Both speakers are producing the same sound. If the combined sound from both speakers is barely audible at your location, which of the following could be the wavelength of the sound?
your distances from the speakers are different by a half wavelength (this is the reason for the sound "cancelling")
14 - 5 = 11
so the sound wavelength could be 22 ft
To determine which wavelength of sound could result in the combined sound being barely audible at your location, we need to consider the principle of interference.
Interference occurs when two sound waves combine either constructively (in phase) or destructively (out of phase). Constructive interference results in a stronger combined sound, while destructive interference results in a weaker or even no sound at all.
In this scenario, the two speakers are producing the same sound, meaning that the two sound waves arriving at your location are likely to be identical in frequency, amplitude, and phase.
Since the combined sound is barely audible, we can deduce that destructive interference is occurring. Destructive interference happens when the peaks of one sound wave align with the troughs of the other, causing them to cancel each other out.
For this to happen, the two sound waves need to be out of phase by exactly half a wavelength.
To find the wavelength, we can calculate the path difference between the two speakers to determine when the waves are out of phase by half a wavelength.
The path difference can be obtained by subtracting the distance from the first speaker to your location (5 feet) from the distance from the second speaker to your location (14 feet):
Path difference = 14 feet - 5 feet = 9 feet
Since the waves need to be out of phase by half a wavelength, the path difference should be equal to half the wavelength:
Path difference = (1/2) * wavelength
Therefore, the wavelength can be calculated as:
wavelength = 2 * path difference = 2 * 9 feet = 18 feet
Hence, the possible wavelength of the sound in this scenario could be 18 feet.
Note: This explanation assumes that the speakers are coherent sources, producing sound waves with the same frequency and consistent phase relationship.