If the amplitude of a sound wave is quadrupled, by what factor will the intensity increase?
Intensity= 10log amplitude, right?
so the question is what do you mean by amplitude. I assume by amplitude you mean the distance a matter particle vibrates. But energy is proportional then to amplitude squared, so
and then intensity =10 log amplitude^2
=10 log energy
so if amplitude is quadrupled, energy then is squared, so intentity must be doubled (log a^2=2loga)
To determine the factor by which the intensity increases when the amplitude of a sound wave is quadrupled, let's first understand the relationship between amplitude and intensity in sound waves.
The intensity of a sound wave is directly proportional to the square of its amplitude. Mathematically, it can be expressed as:
Intensity ∝ Amplitude^2
Now, when the amplitude is quadrupled (increased by a factor of 4), we can calculate the factor by which the intensity increases.
Let's assume the original amplitude is "A," and the new amplitude (quadrupled) is "4A." Using the relationship between intensity and amplitude, we substitute these values:
Original Intensity ∝ A^2
New Intensity ∝ (4A)^2
To compare the intensities, we divide the new intensity by the original intensity:
New Intensity / Original Intensity = (4A)^2 / A^2
= 16A^2 / A^2
= 16
Therefore, the intensity increases by a factor of 16 when the amplitude of a sound wave is quadrupled.