there's a equation for wavespeed=wavelength*f
the wavespeed doesn't depend on the wavelength. Why not?
if you double the wavelength, won't the speed increase as well. In my book, it says that v is unchanged. I don't understand
Velocity = wavelength * frequency
The velocity changes with the wavelength. Your book probably refers to a situation in which both the wavelength and frequency change.
Generally, in physical mediums, the speed of propagation is a constant of the material, independent of the incoming wave. As a first approximation, treating velocity as a constant is good enough. But some material exhibit a very slightly changing wave speed that is related to the incoming wavelength, you see this as changing index of refraction as a function of wavelength. Remember Newtons rainbow in the prism? That works because the index of refraction is different (very slightly) for each color, and of course, the index of refraction is a measure of light velocity in the medium.
The equation you mentioned, wavespeed = wavelength * frequency (v = λ * f), is commonly used to calculate the speed of a wave when you know its wavelength and frequency. However, the equation itself doesn't explain why the wavespeed does not depend on the wavelength.
To understand why the wavespeed is independent of the wavelength, we need to look at the fundamental nature of waves. In a medium, such as air or water, waves propagate by transferring energy from one particle to another. The speed at which this energy is transferred is the wavespeed.
When waves travel through a medium, each individual particle of the medium vibrates back and forth. The wavelength represents the distance between two consecutive points of the same phase on the wave, while the frequency describes how many complete wave cycles pass through a given point in one second.
The key point to understand is that the particles of the medium do not move with the wave; instead, they oscillate about their equilibrium positions as the wave passes through them. The propagation of the wave itself is the result of this particle interaction, not the movement of particles along with the wave.
Because the speed of wave propagation depends on the interaction between particles in the medium, it is not influenced by the wavelength or frequency of the wave. The speed at which the particles of the medium pass the energy along remains constant, regardless of the wavelength.
So, when we double the wavelength while keeping the frequency constant, the waves still propagate at the same speed. This means that even though the individual particles may have a longer distance to travel between wave crests, they still maintain the same speed of energy transmission.
In summary, the wavespeed is not affected by changes in the wavelength because it is determined by the properties of the medium and how it transfers energy, rather than the specific characteristics of the waveform itself.