Final answer:
To increase the wave intensity by a factor of 50, the amplitude must be increased by the square root of 50. When a longitudinal wave's speed increases in a new medium, its period stays the same, and its wavelength increases.
Step-by-step explanation:
Increasing Wave Strength
The strength or intensity of a wave is directly related to its amplitude. To increase the intensity of a wave by a factor, the amplitude must be increased proportionally. The energy of a wave is determined by its amplitude; thus, a higher amplitude means a more energetic wave. Specifically, to increase the intensity of a wave by a factor of 50, the amplitude must be increased by the square root of 50, because intensity is proportional to the square of the amplitude.
Wave Behavior in Different Mediums
When a longitudinal wave travels into a medium where its speed increases, two characteristics of the wave are affected: the period and the wavelength. The period of the wave stays the same because it is determined by the source of the wave and is independent of the medium. However, the wavelength increases because wavelength is the product of wave speed and period (given the period stays the same).