The relationship between frequency, wavelength, and velocity depends on the nature of the wave and the medium through which it propagates.
For electromagnetic waves, such as light, the speed of light in a vacuum is a constant value (denoted by "c" in physics), approximately 3 x 10^8 meters per second. The speed of light is independent of the wavelength or frequency of the wave. However, the frequency and wavelength of light are inversely proportional to each other. As the frequency increases, the wavelength decreases, and vice versa. This relationship is governed by the equation:
c = λ * f
where c is the speed of light, λ (lambda) is the wavelength, and f is the frequency.
On the other hand, in the case of sound waves, the situation is different. Sound waves are mechanical waves that require a medium (such as air, water, or solids) to propagate. The speed of sound depends on the properties of the medium through which it travels, such as its density and elasticity. The frequency and wavelength of sound waves can be related through the equation:
v = λ * f
where v is the velocity of sound, λ (lambda) is the wavelength, and f is the frequency.
In this equation, the velocity of sound (v) is affected by the medium, not the frequency. Changing the frequency of a sound wave will not alter the velocity of sound in a given medium. However, altering the properties of the medium, such as temperature, humidity, or the composition of the material, can affect the speed of sound.