You are standing 7 feet from one speaker and 13 feet from another. Both speakers are producing the same sound. If the combined sound from both speakers is especially loud 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
And how do you find this out>?
A wavelength of 1, 2 or 3 feet will allow there to be constructive interference at the two locations. That corresponds to 6, 3 or 2 wavelengths difference between the two locations.
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To determine the possible wavelengths of the sound, we can use the formula:
Wavelength = Distance / Number of Antinodes
An antinode is a point of maximum displacement in a standing wave, where the amplitude is at its maximum. In this case, the distance between the two speakers is the distance of one full wavelength. So, we need to calculate the number of antinodes present between the two speakers at your location.
First, let's find the distance between the two speakers:
Distance between speakers = 13 feet - 7 feet = 6 feet
Next, we need to find the number of antinodes. A node is a point of minimum displacement, and between two nodes, there is one antinode. Since the distance between the two speakers is equivalent to one full wavelength, the number of antinodes is equal to half of the wavelength.
So, for example, if the wavelength is 2 feet, there would be 1 antinode between the speakers (half a wavelength). If the wavelength is 4 feet, there would be 2 antinodes between the speakers (1 full wavelength).
Now we can calculate the possible wavelengths by finding the factors of the distance between the speakers (6 feet) and selecting those that divide it evenly.
The factors of 6 are 1, 2, 3, and 6. So, the possible wavelengths are:
- 6 feet: This is possible as it is equivalent to a full wavelength between the speakers.
- 3 feet: This is possible as it is equivalent to half of the wavelength between the speakers.
Therefore, the possible wavelengths from the given options are 3 feet and 6 feet.
(Note: The options 1 foot, 2 feet, 4 feet, 5 feet, 7 feet, 8 feet, 9 feet, 10 feet, 12 feet, and 18 feet are not factors of the distance between the speakers, so they are not possible wavelengths for the given scenario.)