Given the equation $v=\lambda f$, where $v$ is the speed of a transverse wave, $\lambda$ is the wavelength, and $f$ is the frequency, which of the following statements is correct about how the speed of a wave depends on its frequency?

• A. The speed $v$ of a wave always decreases as the frequency $f$ increases.
• B. The speed $v$ of a wave is independent of its frequency $f$; it is determined by the properties of the medium.
• C. The speed $v$ of a wave is equal to the frequency $f$ divided by the wavelength $\lambda$.
• D. The speed $v$ of a wave always increases as the frequency $f$ increases, regardless of the medium.

Answer: (B)

Verified step by step guidance

1. Recall the fundamental wave equation: \(v = \lambda \times f\), where \(v\) is the wave speed, \(\lambda\) is the wavelength, and \(f\) is the frequency.
2. Understand that for a given medium, the wave speed \(v\) is constant because it depends on the medium's physical properties, such as tension and mass density for a string, or elasticity and density for air.
3. Since \(v\) is constant in a given medium, if the frequency \(f\) increases, the wavelength \(\lambda\) must decrease proportionally to keep the product \(\lambda \times f\) equal to \(v\).
4. Therefore, the speed \(v\) does not depend on frequency \(f\) directly; instead, frequency and wavelength adjust inversely to maintain the same wave speed in that medium.
5. Conclude that the correct statement is: The speed \(v\) of a wave is independent of its frequency \(f\); it is determined by the properties of the medium.