Question
A wave enters a new medium and its wavelength drops by 50%. What likely happened?
A. The waves speed stayed constant
B. The waves speed increased slightly
C. The waves speed halved
D. The waves speed doubled
A. The waves speed stayed constant
B. The waves speed increased slightly
C. The waves speed halved
D. The waves speed doubled
Answers
GPT-4o mini
When a wave enters a new medium and its wavelength drops, this is typically accompanied by a change in the wave's speed. The relationship between wave speed (v), frequency (f), and wavelength (λ) is given by the equation:
\[ v = f \cdot \lambda \]
If the wavelength drops by 50%, it means that the new wavelength (λ') is half of the original wavelength (λ):
\[ \lambda' = \frac{1}{2} \lambda \]
If we assume that the frequency (f) of the wave stays constant (which is often the case when a wave transitions between mediums), the wave speed in the new medium would be:
\[ v' = f \cdot \lambda' = f \cdot \frac{1}{2} \lambda = \frac{1}{2} (f \cdot \lambda) = \frac{1}{2} v \]
This indicates that the wave speed has halved.
Therefore, the correct answer is:
C. The waves speed halved.
\[ v = f \cdot \lambda \]
If the wavelength drops by 50%, it means that the new wavelength (λ') is half of the original wavelength (λ):
\[ \lambda' = \frac{1}{2} \lambda \]
If we assume that the frequency (f) of the wave stays constant (which is often the case when a wave transitions between mediums), the wave speed in the new medium would be:
\[ v' = f \cdot \lambda' = f \cdot \frac{1}{2} \lambda = \frac{1}{2} (f \cdot \lambda) = \frac{1}{2} v \]
This indicates that the wave speed has halved.
Therefore, the correct answer is:
C. The waves speed halved.