Answer:
0.2155 m
Step-by-step explanation:
To find the distance by which Speaker 1 needs to be moved until Ryan hears no sound, we can use the concept of constructive and destructive interference.
When two speakers emit sound waves with the same frequency and are in phase, constructive interference occurs, resulting in a stronger sound. However, if we move one of the speakers to a point where the path length difference (the distance one wave travels more than the other) between the two speakers is an odd multiple of half the wavelength (λ/2), destructive interference occurs, canceling out the sound.
The formula for wavelength (λ) in meters is given by:
λ = c / f
Where:
λ = Wavelength (in meters)
c = Speed of sound in air (approximately 343 m/s at room temperature)
f = Frequency of the sound (795 Hz)
λ = 343 m/s / 795 Hz ≈ 0.431 m
Now, for destructive interference to occur, the path length difference between the two speakers must be an odd multiple of half the wavelength (λ/2):
d = (2n + 1) * λ/2
Where:
d = Path length difference (in meters)
n = Any positive integer
We want to find the minimum distance (d) that Speaker 1 needs to be moved, so let's use n = 0 (the first odd multiple):
d = (2 * 0 + 1) * (0.431 m / 2) = 0.2155 m
So, Speaker 1 needs to be moved approximately 0.2155 meters to the left until Ryan hears no sound due to destructive interference.