The velocity of a wave depends on its medium and the type of wave. For mechanical waves traveling through a medium such as sound waves or waves on a string, the velocity is not directly dependent on the amplitude, frequency, or wavelength.
In the case of a mechanical wave on a string, the velocity is determined by the tension in the string and the mass per unit length. The wave speed on a string can be calculated using the formula:
v = √(T/μ),
where v is the wave velocity, T is the tension in the string, and μ is the linear mass density of the string. As you can see, the velocity is not influenced by the amplitude, frequency, or wavelength of the wave.
However, for electromagnetic waves (such as light or radio waves) traveling through a vacuum or air, the velocity is constant and is equal to the speed of light in a vacuum, denoted by 'c,' which is approximately 3 x 10^8 meters per second. In this case, the amplitude, frequency, and wavelength are related by the following equation:
c = λf,
where c is the velocity of light, λ (lambda) is the wavelength, and f is the frequency. From this equation, you can see that the velocity of an electromagnetic wave remains constant, and any changes in the amplitude, frequency, or wavelength are interrelated.
To summarize, for mechanical waves in a medium, the velocity depends on the properties of the medium, whereas for electromagnetic waves, the velocity is constant and the amplitude, frequency, and wavelength are interrelated.