Question

If the amplitude of a sound wave is quadrupled, by what factor will the intensity increase?

Answer 1

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)