As a wave travels from one medium to another, its wavelength triples. Which statement describes the speed and frequency in the new medium?(1 point)

Responses

The speed will triple, and the frequency will also triple.
The speed will triple, and the frequency will also triple.

The speed will triple, and the frequency will stay the same.
The speed will triple, and the frequency will stay the same.

The speed will stay the same, and the frequency will triple.
The speed will stay the same, and the frequency will triple.

The speed will stay the same, and the frequency will also stay the same.

1 answer

To analyze the situation, we can use the wave relationship given by the equation:

\[ v = f \lambda \]

where \( v \) is the wave speed, \( f \) is the frequency, and \( \lambda \) is the wavelength.

When a wave transitions from one medium to another and its wavelength changes, the following considerations apply:

  1. The frequency of a wave remains constant when it transitions between different media. This is because the frequency is determined by the source of the wave and not affected by the medium.
  2. Since the wavelength triples in the new medium, we can denote the initial wavelength as \( \lambda_1 \) and the wavelength in the new medium as \( \lambda_2 = 3\lambda_1 \).
  3. Assuming the frequency remains the same (\( f_1 = f_2 \)), we can see that the speed in the original medium is \( v_1 = f_1 \lambda_1 \) and in the new medium it will be \( v_2 = f_2 \lambda_2 = f_1 (3\lambda_1) = 3(f_1 \lambda_1) = 3v_1 \).

Thus, the speed increases by a factor of three while the frequency remains unchanged.

Based on this analysis, the correct answer is:

The speed will triple, and the frequency will stay the same.