What is the Difference Between Wave Velocity and Wave Frequency?

Wave velocity and wave frequency are two fundamental properties of a wave. Here are the key differences between them:

Definition: Wave velocity describes how fast the energy is propagating, while wave frequency describes how fast the wave is oscillating. In other words, frequency is a measure of the wave's "repetition," while velocity is a measure of its "speed".
Unit: Wave velocity is measured in meters per second (m/s), while wave frequency is measured in Hertz (Hz), which represents the number of cycles that occur in one second.
Relation: For any given wave, the product of wavelength and frequency gives the velocity. This relationship is mathematically expressed as: $$V = f \times \lambda$$, where V is the velocity of the wave, f is the frequency of the wave, and λ is the wavelength of the wave.
Dependence: Wave velocity is a property of the medium, and its speed can be described by the term impedance, which is the resistance of the medium to the propagation of the wave. Wave frequency, on the other hand, is a property determined by the source of the wave and remains constant regardless of the medium it travels through.

In summary, wave velocity refers to the speed at which a wave travels through a medium, while wave frequency refers to the number of oscillations a wave undergoes in a unit time. These two properties are related through the wavelength of the wave and are essential for understanding and describing wave behavior in various fields, such as classical quantum mechanics and acoustics.