The relationship between intensity and amplitude in a wave is not linear. Intensity is directly proportional to the square of the amplitude. Mathematically, the relationship can be expressed as:
Intensity = k * Amplitude^2
where "k" is a constant.
In this case, if the initial intensity is 300 (units not specified) and the initial amplitude is 200, we can write:
300 = k * 200^2
Solving for "k":
k = 300 / (200^2)
Now, if the amplitude is increased to 800, we can calculate the new intensity using the same equation:
New Intensity = k * (New Amplitude)^2
New Intensity = (300 / (200^2)) * (800^2)
Calculating the expression:
New Intensity ≈ 2400
Therefore, when the amplitude is increased from 200 to 800, the new intensity will be approximately 2400 (units depend on the original intensity units).