To understand how the speed and frequency of a wave change as it travels from one medium to another, we can use the relationship between wave speed (v), frequency (f), and wavelength (λ). This is given by the equation:
\[ v = f \cdot \lambda \]
When the wave moves from one medium to another, its wavelength changes. In this case, the problem states that the wavelength triples in the new medium. Let's denote the initial wavelength as \( \lambda_1 \) and the new wavelength as \( \lambda_2 = 3\lambda_1 \).
Since the wave is moving into a new medium, the speed of the wave in the new medium (let's call it \( v_2 \)) may change, and we need to analyze the frequency.
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Frequency remains constant: The frequency of a wave is determined by the source of the wave and does not change when the wave moves between different media. So, we have:
\[ f_1 = f_2 \]
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Speed of the wave changes: The speed of the wave in the new medium can be calculated using the new wavelength. If we denote the initial speed as \( v_1 \), we can express it as:
\[ v_1 = f_1 \cdot \lambda_1 \]
For the new medium, we have:
\[ v_2 = f_2 \cdot \lambda_2 = f_1 \cdot (3\lambda_1) = 3(f_1 \cdot \lambda_1) = 3v_1 \]
From this analysis, we can summarize:
- The frequency stays the same.
- The speed triples when moving into the new medium.
Thus, the correct statement based on the wave's behavior would be:
The speed will triple, and the frequency will stay the same.