If two transverse waves have the same wavelength, the wave with the greatest frequency will have the greatest speed.

Here's why:

* Wave Speed, Wavelength, and Frequency: The relationship between wave speed (v), wavelength (λ), and frequency (f) is given by the equation:

v = fλ

* Constant Wavelength: If the wavelength (λ) is the same for both waves, the wave with the higher frequency (f) will have a higher wave speed (v).

Example:

Imagine two waves on a string:

* Wave A: Wavelength = 1 meter, Frequency = 10 Hz

* Wave B: Wavelength = 1 meter, Frequency = 20 Hz

Using the equation above:

* Wave A Speed: v = (10 Hz) * (1 meter) = 10 meters/second

* Wave B Speed: v = (20 Hz) * (1 meter) = 20 meters/second

Wave B, with the higher frequency, travels at a faster speed.