Final answer:
The power of a wave becomes 1/4 of the original value when the amplitude is decreased to half, based on the fact that power is proportional to the square of the wave's amplitude.
Step-by-step explanation:
When a sonographer decreases the amplitude of a wave to 1/2 of its original value, the power of the wave changes significantly. The power of a wave is proportional to the square of its amplitude. This means that if you decrease the amplitude of a wave to half of its original value, the power is reduced to (1/2)^2, which is 1/4 of the original power. Therefore, the correct answer to your question is B. It has become 1/4 of the original.