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

• A. The speed $v$ of a transverse wave does not depend on its wavelength $\lambda$ because for a given medium, $v$ is constant and any change in $\lambda$ is offset by an inverse change in $f$.
• B. The speed $v$ of a transverse wave is always equal to the wavelength $\lambda$.
• C. The speed $v$ of a transverse wave increases as the wavelength $\lambda$ increases, regardless of the frequency.
• D. The speed $v$ of a transverse wave decreases as the wavelength $\lambda$ increases, regardless of the frequency.

Answer: (A)

Verified step by step guidance

1. Recall the fundamental wave equation: \(v = \lambda f\), where \(v\) is the wave speed, \(\lambda\) is the wavelength, and \(f\) is the frequency.
2. Understand that for a wave traveling in a given medium, the speed \(v\) is determined by the properties of that medium (such as tension and mass density for a string) and remains constant.
3. Since \(v\) is constant in a given medium, any change in wavelength \(\lambda\) must be accompanied by an inverse change in frequency \(f\) to keep the product \(\lambda f\) equal to \(v\).
4. This means if the wavelength increases, the frequency decreases proportionally, and if the wavelength decreases, the frequency increases proportionally, so the speed does not change.
5. Therefore, the speed of a transverse wave does not depend on its wavelength alone; it depends on the medium, and wavelength and frequency adjust accordingly to maintain constant speed.