Are there any ways to alter the frequency of wave? I want to know how can we change the frequency of wave, both sound and light, and what is the nature of "changing frequency".
Such as, any material could absorb and re-emit wave in another wavelength. Or any kind of field could make an interference in a way that making new wave in difference frequency.
PS please exclude refraction (which is not really change frequency, just a change in wavelength and speed) and Doppler shift.
 A: Here are some topics to read about:


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*Frequency doubling, also called second-harmonic generation as Johannes mentions. Here, you put one wave into a medium, and some fraction of it is converted to a wave with a different frequency. By carefully engineering the medium you can get quite a high conversion percentage.

*Other nonlinear optical processes, not just frequency doubling, but includes difference frequency generation, optical parametric oscillators, N-wave mixing, etc. These involve putting one or more waves with different frequencies into a medium and, getting an additional wave out with a frequency that you didn't put in.

*Raman scattering which is spontaneous, and its stimulated equivalents CARS and CSRS. In Raman scattering you don't really get a coherent wave out; you just put one wave into a medium and a tiny portion of the scattering has a different frequency. CARS and CSRS use the same mechanism (a molecule absorbing a photon, using its energy to transition to a different level, then re-emitting a photon with the excess energy) but they are types of four-wave mixing and really belong in the previous point.

A: Although normally considered as photon interactions, any inelastic scattering process will result in the alteration of the frequency of the electromagnetic radiation.
An obvious example is Compton scattering, where high energy (X-rays+) light scatters from free electrons. The scattered light has lower energy and longer wavelengths than the light incident upon the electrons.
Raman scattering of (often optical or infrared) light from molecules results in the scattered light having a slightly lower frequency, corresponding to a transition between energy levels in the molecule.
A: Yes.
Materials that absorb electromagnetic radiation and emit it in a different frequency are known as fluorescent. You probably see them as the coating on the inside of fluorescent tubes, where they absorb ultra-violet light and emit a lower frequency visible light.
A: If you have light that is reasonably monochromatic, then you can shift its frequency using two types of related devices: acousto-optic modulators (AOMs) and electro-optic modulators (EOMs). Strictly speaking, these fit within the categories of ptomato's answer as nonlinear optical processes, but they are distinct enough that they are typically considered on their own.
The basic idea is to have a material (say, quartz, or lithium niobate) whose refractive index depends on the local elastic strain (for AOMs) or on the local (quasi-)DC electric field (for EOMs). If you then make the elastic strain (resp. electric field) oscillate, by using an acoustic wave (resp. an RF field), then you have light travelling through a medium with a time-dependent refractive index, which can and does alter the frequency of the light.
As a general rule, EOMs can achieve larger frequency shifts (as much as several GHz) than AOMs, but they're more complex and harder to work with. Both types of modulators are in common use when you want a laser that is very narrow-band (i.e. has a very well-defined frequency) but you want at least some ability to tune its frequency so that you can e.g. lock it to some specific transition in an atom or molecule of interest.
