Final answer:
The amplitude should be increased by a factor closest to the square root of the increase in intensity. For an intensity increase by a factor of 50, this would mean increasing amplitude approximately by a factor of 7.07, with the closest given answer being 10.
Step-by-step explanation:
To increase the intensity of a wave by a factor of 50, by what factor should the amplitude be increased? The intensity of a wave is proportional to the square of its amplitude. The amplitude should be increased by a factor closest to the square root of the increase in intensity. For an intensity increase by a factor of 50, this would mean increasing amplitude approximately by a factor of 7.07, with the closest given answer being 10.
Therefore, if the intensity is increased by a factor of 50, the amplitude should be increased by a factor of the square root of 50. The square root of 50 is approximately 7.07, but since that is not one of the multiple choice answers given, we can look for the closest answer which is (c) 10.