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 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
you want them inphase, which means a whole number of wavelengths.
1ft will work...
To determine which wavelengths could result in an especially loud combined sound at your location, we need to consider the interference patterns created by the two speakers.
The distance between the two speakers is 14 - 5 = 9 feet.
Interference occurs when two sound waves arrive at the same location with a phase difference that causes them to either reinforce or cancel each other out.
In this case, if the distance between the speakers is an integer multiple of the wavelength, constructive interference will occur, resulting in a louder sound at your location. So, we need to find all the wavelengths that evenly divide the distance between the speakers (9 feet).
Let's check each option:
1 foot: Does not evenly divide 9 (9 ÷ 1 = 9 remainder 0).
2 feet: Does not evenly divide 9 (9 ÷ 2 = 4 remainder 1).
3 feet: Does not evenly divide 9 (9 ÷ 3 = 3 remainder 0).
4 feet: Does not evenly divide 9 (9 ÷ 4 = 2 remainder 1).
5 feet: Does evenly divide 9 (9 ÷ 5 = 1 remainder 4).
6 feet: Does not evenly divide 9 (9 ÷ 6 = 1 remainder 3).
7 feet: Does not evenly divide 9 (9 ÷ 7 = 1 remainder 2).
8 feet: Does not evenly divide 9 (9 ÷ 8 = 1 remainder 1).
9 feet: Does evenly divide 9 (9 ÷ 9 = 1 remainder 0).
10 feet: Does not evenly divide 9 (9 ÷ 10 = 0 remainder 9).
12 feet: Does not evenly divide 9 (9 ÷ 12 = 0 remainder 9).
18 feet: Does not evenly divide 9 (9 ÷ 18 = 0 remainder 9).
Based on the calculations, the wavelengths that could result in an especially loud combined sound at your location are 5 feet and 9 feet. So, the options to choose would be:
- 5 feet
- 9 feet