You are standing 7 feet from one speaker and 10 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? Choose all that apply.
1 foot
2 feet
3 feet
4 feet
5 feet
6 feet
7 feet
8 feet
9 feet
10 feet
12 feet
18 feet
Can Damon please answer this
To determine the possible wavelengths of the sound, we need to consider the concept of constructive and destructive interference. When two sound waves from different sources combine, they can either reinforce each other (constructive interference) or cancel each other out (destructive interference).
In this scenario, the combined sound from both speakers is barely audible at your location, which suggests that destructive interference is occurring. Destructive interference happens when the peaks of one wave align with the troughs of the other wave, resulting in a canceling effect.
To find the conditions for destructive interference, we can use the formula for the path difference:
Path Difference = |Distance1 - Distance2|
In this case, Distance1 represents the distance from the first speaker to your location, and Distance2 represents the distance from the second speaker to your location.
Given: Distance1 = 7 feet and Distance2 = 10 feet
Calculating the path difference:
Path Difference = |7 feet - 10 feet| = 3 feet
For destructive interference to occur, the path difference should be an integer multiple of the wavelength of the sound. Therefore, we need to find the possible integers that can be multiplied by the path difference to obtain the potential wavelengths.
Possible wavelengths (in feet):
1 foot (not possible since it is smaller than the path difference)
2 feet (not possible since it is smaller than the path difference)
3 feet (possible since it is equal to the path difference)
4 feet (possible since it is 2 times the path difference)
5 feet (not possible since it is not an integer multiple of the path difference)
6 feet (not possible since it is not an integer multiple of the path difference)
7 feet (not possible since it is smaller than the path difference)
8 feet (possible since it is 2 times the path difference)
9 feet (not possible since it is not an integer multiple of the path difference)
10 feet (not possible since it is not an integer multiple of the path difference)
12 feet (possible since it is 4 times the path difference)
18 feet (not possible since it is not an integer multiple of the path difference)
Therefore, the possible wavelengths of the sound are 3 feet, 4 feet, and 12 feet.