What is the physical meaning of frequency in the wave concept?

Let us take the classical electromagnetic picture in which our 3d space is permeated by an electromagnetic field. This basically means that at any point in space we may define a field strength and direction $mathbf{E}$ of the electric field, and also an associated magnetic field strength and direction $mathbf{B}$. Let us for the moment assume that these strengths are fixed in time. Any charged particle located in this spatial point will then feel a Coulomb force, proportional to the strength of the field and along its respective direction.

We speak of light as an electromagnetic wave since it produces a ripple through the electromagnetic field, much like a stone thrown into water produces ripples in the water's surface. Physically this means that at any point in space the value and direction of the electric and magnetic field oscillate with time. This also means that my charged particle will now feel a changing force where before it was fixed, and start moving with the wave. This is the actual observable effect of a ripple in the electromagnetic field, that we refer to as light.

Now the frequency of the light is related to how quickly this oscillation of the field strength occurs. One may imagine that the charged particle can be made to oscillate very quickly or very slowly, depending on how fast $mathbf{E}$ flips its sign.

In your question you refer to the concept of colour specifically. Our eyes take the frequency of the ripples in the electromagnetic field which interacts with particles in your eye, and translate this oscillation frequency to a sensation that we percieve as colour. Obviously this is a heavily simplified picture, and I am not so well versed in biophysics so maybe someone else can help you out with the specifics there. I hope that at least the physical picture is somewhat clearer now.

What is the physical meaning of frequency in wave concept?

A wave doesn't necessarily have a frequency though periodic waves will have a fundamental frequency. But not all waves are periodic. For example, consider a single wave packet which is oscillatory but not periodic (note: the replaying animation below should not be interpreted as periodic train of wave packets)

For the case of a periodic wave, the fundamental frequency is the inverse of the period which is essentially the time required for the traveling wave spatial pattern to return to its starting pattern (starting at some arbitrary time $t_0$).

Consider for example a traveling wave described by

$$psi(x,t) = cos(kx -omega t),quadomega = kc$$

where $c$ is the speed of the traveling wave. Now, since $cos(cdot)$ is periodic in its argument:

$$cos(phi + ncdot 2pi) = cos(phi)$$

where $n$ is an integer, it follows that

$$psileft(x,t_0 - frac{2pi}{omega}right) = cos(kx - omega t_0 + 2pi) = cos(kx - omega t_0) = psi(x,t_0)$$

Thus, this wave has a period $T$ of

$$T = frac{2pi}{omega} = frac{1}{nu}$$

where $nu = frac{omega}{2pi}$ is the frequency of the wave $psi(x,t)$. That is, the wave returns the starting spatial pattern after $T$ seconds. Since the frequency is the inverse of the period, the frequency of the wave tells one how many times per second the wave's spatial pattern returns to its starting pattern.

One has to define the type of wave . The simplest mathematical represenation of a wave is a sine or a cosine function. In sound waves Frequency is how many complete cycles per second pass a measuring point. A complet cycle is a period.

This is true for classical waves, including electromagnetic waves, which are described by sinusoidal solutions of the Maxwell equations.

We see that light with different frequency have different colour. But, why? In wave, what property or physical meaning does frequency provide?

There are the spectral colors, identified one to one with a given frequency, i.e. the number of periods per second, of light.

In a rainbow or the separation of colors by a prism we see the continuous range of spectral colors (the visible spectrum). A spectral color is composed of a single wavelength

Frequency and wavelength are mathematically related by the velocity of the traveling wave, light in this case $c=νλ$

BUT there is alsocolor perception , the way our eye sees color is not uniquely defined by the frequency, different frequencies impinging on the eye can give the color perception of the simple spectral colors.

Our eyes have cone cells - these cells have proteins which absorb light. Once the light is absorbed - the protein starts a chain of reactions which leads to a neurological impulse to the brain. Then brain treats these impulses as color.

Different materials absorb EM waves of different frequencies. Absorption happens when molecule particles vibrate with the same frequency as the EM wave. There are 3 types of proteins on cone cells - depending on the type they will absorb different frequencies better. So we have:

1. 3 types of cone cells. The type depends on which of the three proteins are located on those cells.
2. The brain is tuned to treat signals from 1st type as blue, signals from 2nd type as green and signals from 3d type as red color
3. So when a light of "red" frequency is absorbed by the respective cone cell - the signal is sent and brain recognizes this as red.

Though things are actually more complicated. We recognize more colors than just red-blue-green. This is because:

1. Typically the light consists of many different wavelengths. So more than one type of a cone cell is excited. Our brain draws some statistical conclusions ("compares" relative amounts of signals of different types) and deduces more colors.
2. Also it's not like 1 type of cone cells detects only 1 particular frequency. There are ranges of frequencies that excite these cells. And those ranges overlap between types of cone cells (so red-blue-green separation is a simplification). But a particular frequency is absorbed better by one type compared to another type of the cone cell. I assume this gives even more variety to which colors we can recognize.