Which statement about wavelength and frequency in a single medium is true?

Which statement about wavelength and frequency in a single medium is true?

• A. They are inversely related
• B. They are directly related
• C. They are independent
• D. They are equal

Answer: (A)

In a single medium, the speed of a wave is fixed for that medium and type of wave. The relationship v = fλ links speed, frequency, and wavelength, so with v constant, frequency and wavelength must vary inversely: if you raise the frequency, the wavelength gets shorter, and if you lower the frequency, the wavelength gets longer. That’s why the statement that they are inversely related is the true description. The other ideas don’t fit because a direct relationship would imply wavelength grows with frequency, which would change the product fλ and contradict the fixed speed. If they were independent, there’d be no link between f and λ, which the equation shows isn’t the case. And they aren’t generally equal, since frequency and wavelength have different units and the product fλ gives the wave’s speed, not the same quantity.

In a single medium, the speed of a wave is fixed for that medium and type of wave. The relationship v = fλ links speed, frequency, and wavelength, so with v constant, frequency and wavelength must vary inversely: if you raise the frequency, the wavelength gets shorter, and if you lower the frequency, the wavelength gets longer. That’s why the statement that they are inversely related is the true description.

The other ideas don’t fit because a direct relationship would imply wavelength grows with frequency, which would change the product fλ and contradict the fixed speed. If they were independent, there’d be no link between f and λ, which the equation shows isn’t the case. And they aren’t generally equal, since frequency and wavelength have different units and the product fλ gives the wave’s speed, not the same quantity.