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
How DO I SOLVE THIS????
To solve this question, we need to understand the concept of interference and wavelength. Interference occurs when two or more waves meet, causing their amplitudes to either add up constructively (resulting in a louder sound) or cancel each other out (resulting in a softer or inaudible sound).
To determine the wavelength of a sound, we can use the formula for calculating wavelength: wavelength = speed of sound / frequency. Since the question does not provide the frequency, we can assume it remains constant.
In this scenario, the two speakers are producing the same sound, which means they have the same frequency. To find the wavelength of sound at your location, we need to calculate the difference in distance (path difference) between the two speakers.
The path difference can be calculated by finding the difference in distances from your location to each speaker. In this case, the path difference between the two speakers is 10 feet - 7 feet = 3 feet.
Now, for the combined sound to be barely audible, the path difference should either be zero (constructive interference) or an integer multiple of one full wavelength. Possible wavelengths could be any value that satisfies this condition.
To determine which of the given options could be the wavelength, we need to find the greatest common divisor (GCD) of the path difference (3 feet) with each option. If the GCD is equal to the option itself, it means that the wavelength could be the value in question.
Let's calculate the GCD for each option:
GCD(3 feet, 1 foot) = 1 foot (wavelength 1 foot does not satisfy the condition because GCD ≠ 1 foot).
GCD(3 feet, 2 feet) = 1 foot (wavelength 2 feet does not satisfy the condition).
GCD(3 feet, 3 feet) = 3 feet (wavelength 3 feet satisfies the condition).
GCD(3 feet, 4 feet) = 1 foot (wavelength 4 feet does not satisfy the condition).
GCD(3 feet, 5 feet) = 1 foot (wavelength 5 feet does not satisfy the condition).
GCD(3 feet, 6 feet) = 3 feet (wavelength 6 feet satisfies the condition).
GCD(3 feet, 7 feet) = 1 foot (wavelength 7 feet does not satisfy the condition).
GCD(3 feet, 8 feet) = 1 foot (wavelength 8 feet does not satisfy the condition).
GCD(3 feet, 9 feet) = 3 feet (wavelength 9 feet satisfies the condition).
GCD(3 feet, 10 feet) = 1 foot (wavelength 10 feet does not satisfy the condition).
GCD(3 feet, 12 feet) = 3 feet (wavelength 12 feet satisfies the condition).
GCD(3 feet, 18 feet) = 3 feet (wavelength 18 feet satisfies the condition).
Based on the GCD calculations, the possible wavelengths that could result in the combined sound being barely audible are 3 feet, 6 feet, 9 feet, 12 feet, and 18 feet.