Question

explain mathematical expression of a wave​

Answer 1

here's your answer ⭐

To find the amplitude, wavelength, period, and frequency of a sinusoidal wave, write down the wave function in the form y(x,t)=Asin(kx−ωt+ϕ). The amplitude can be read straight from the equation and is equal to A. The period of the wave can be derived from the angular frequency (T=2πω).

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Answer 2

 A wave can be mathematically expressed as a function of time and position. The most common form of this expression is the sinusoidal wave, which can be represented as:

      y(x,t) = A sin(kx - ωt + φ)

Where,

• y(x,t) is the value of the wave at position x and time t.

• A is the amplitude of the wave, which determines its maximum displacement from its equilibrium position.

• k is the wavenumber, which determines the spatial frequency of the wave.

• x is the position of the point along the wave.

• ω is the angular frequency, which determines the temporal frequency of the wave.

• t is the time at which the wave is evaluated.
  
• φ is the phase angle, which determines the position of the wave relative to a reference point.

• The sinusoidal wave is just one example of a mathematical expression of a wave, but it is a very useful and versatile one that can describe many types of waves, including sound waves, light waves, and water waves. Other types of waves may have different mathematical expressions, but the basic principles of amplitude, frequency, and phase are common to all waves.

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