To increase intensity of a wave by a factor of 50, by what factor should the amplitude be increased?
This is also coming from the homework based on topics the video didn't cover. I know that power is proportional to amplitude squared, but what does this have to do with intensity?
same reference as before. You need to totally understand the difference between amplitude and intensity. Intensity is energy, the square of amplitude.
This is the problem with video instruction, I am fairly confident it was there, but you missed it, and there was no teacher to slap you when your mind drifted, or restated it so you listened.
Aha! Thank you! I got them both right now!
To increase the intensity of a wave by a factor of 50, we need to increase the power of the wave by the same factor, as intensity is directly proportional to the power of the wave. Now let's relate the amplitude to power.
In a simple harmonic wave, the power (P) is given by the formula:
P ∝ A^2,
where A is the amplitude of the wave.
Since power is directly proportional to the square of the amplitude, if we want to increase the power of the wave by a factor of 50, we need to increase the amplitude by the square root of 50.
Let's do the math:
Factor by which power needs to be increased = 50.
Therefore, factor by which amplitude should be increased = √50.
Hence, to increase the intensity of the wave by a factor of 50, the amplitude should be increased by a factor of approximately 7.071 (approximately √50).