An observer is located directly between two speakers located 20 metres apart.Speakers are in phase and both are emitting a sound of 60Hz.How far away from the centre should the observer move to get the first destructive interference?
wavelength /8 gives wavelength /4 difference
To determine the distance at which the observer will experience the first destructive interference, we need to consider the conditions for destructive interference.
Destructive interference occurs when the waves from the two speakers are completely out of phase and cancel each other out. This happens when the path difference between the waves is a multiple of half wavelengths.
In this case, the observer is located equidistant from both speakers, which means that the path difference between the waves is 0 at the center. To find the distance where destructive interference occurs, we need to determine the path difference corresponding to a half-wavelength.
The formula for the path difference is:
Path difference = d * sin(θ)
Where:
- d is the distance between the speakers (20 meters in this case)
- θ is the angle between the line connecting the observer to the speakers and the line perpendicular to that line (in this case, θ is 0 because the observer is at the center)
The half-wavelength path difference occurs when the path difference is equal to half a wavelength, which can be expressed as:
0.5 * λ = d * sin(θ)
Since sin(0) = 0, the above equation simplifies to:
0.5 * λ = 0
This indicates that the path difference is already zero at the center, so destructive interference occurs there. The observer does not need to move away from the center to experience the first destructive interference.
Therefore, the observer does not need to move from the center to get the first destructive interference.