If the wavelength of a wave is doubled while its speed remains constant, what happens to its frequency?

• A. The frequency is halved.
• B. The frequency is doubled.
• C. The frequency becomes zero.
• D. The frequency remains unchanged.

Answer: (A)

Verified step by step guidance

1. Recall the fundamental relationship between the speed (v), frequency (f), and wavelength (λ) of a wave, which is given by the equation: \(v = f \times \lambda\).
2. Since the problem states that the speed of the wave remains constant, we can treat \(v\) as a constant value in the equation.
3. If the wavelength \(\lambda\) is doubled, we can represent the new wavelength as \(\lambda_{new} = 2 \times \lambda\).
4. Substitute the new wavelength into the wave equation while keeping the speed constant: \(v = f_{new} \times \lambda_{new} = f_{new} \times (2 \times \lambda)\).
5. Because \(v\) is constant, set the original and new expressions equal: \(f \times \lambda = f_{new} \times 2 \times \lambda\). Cancel \(\lambda\) from both sides to find the new frequency: \(f = 2 \times f_{new}\), which implies \(f_{new} = \frac{f}{2}\). This means the frequency is halved when the wavelength is doubled.