to increse intensity o f a wave by a factor of 50, by what factor should the amplitude be increased?
Intensity of a wave is proportional to the square of amplitude, so if you increas amplitude by sqrt 50, ...
To increase the intensity of a wave by a factor of 50, the amplitude should be increased by a factor of √50 or approximately 7.071.
The intensity (I) of a wave is directly proportional to the square of the amplitude (A) according to the equation:
I ∝ A^2
If we want to increase the intensity by a factor of 50, we can set up the equation:
50I = (A × α)^2
Where α represents the factor by which we increase the amplitude.
Simplifying the equation, we have:
50I = A^2 × α^2
Since we want to find the factor by which the amplitude should be increased, we can divide both sides of the equation by I:
50 = α^2
√50 = α
Therefore, the amplitude should be increased by a factor of √50 or approximately 7.071 to increase the intensity of the wave by a factor of 50.
To increase the intensity of a wave by a factor of 50, we need to determine how the amplitude of the wave should be increased. Intensity is directly proportional to the square of the amplitude.
Mathematically, the relationship between intensity (I) and amplitude (A) is given by:
I ∝ A^2
Where ∝ represents proportionality.
If we want to increase the intensity by a factor of 50, we can write it as:
50I = A^2
Now, to find the factor by which amplitude should be increased, we need to solve for A.
Taking the square root of both sides:
√(50I) = A
Simplifying:
A = √50 * √I
So, the amplitude should be increased by a factor of √50 to increase the intensity of the wave by a factor of 50.