To analyze the relationships between wave speed (v), frequency (f), and wavelength (λ), we can use the fundamental equation of wave motion:
\[ v = f \times \lambda \]
From this equation, we can derive the following relationships:
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Wave speed (v) and wavelength (λ) can vary inversely to produce the same frequency (f): If frequency is constant and wavelength increases, wave speed must also increase, and vice versa.
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Frequency (f) and wave speed (v) can vary directly with the same wavelength (λ): If the wavelength is constant, any increase in wave speed results in a proportional increase in frequency.
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Wavelength (λ) and frequency (f) can vary inversely to produce the same wave speed (v): If wave speed is constant, an increase in frequency means the wavelength must decrease, and vice versa.
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Frequency (f) and wavelengths (λ) can vary directly to produce the same wave speed (v): This statement is incorrect because if wave speed is constant, an increase in frequency results in a decrease in wavelength.
Given these relationships, the correct conclusion based on the information in the table is:
Wavelengths and frequency can vary inversely to produce the same wave speed.
So, the statement that aligns with our derived relationships is: Wavelengths and frequency can vary inversely to produce the same wave speed.