Wave equation is a mathematical equation describing wave phenomena, which usually contains an unbiased differential equation and a set of initial conditions. This unbiased differential equation can be one-dimensional, two-dimensional or three-dimensional, and the specific form depends on the type and environment of the wave under study. Wave equation describes the behavior of wave propagation in space and time.
For one-dimensional wave, the wave equation can be written as: y/? x？ = 1/v？ *y/？ t？ .
Where y is the displacement along the x axis, t is the time and v is the wave velocity.
For one-dimensional vibration, the vibration equation can be written as:
m*d？ x/dt？ +c*dx/dt+k*x=0
Where x is the displacement of the particle, t is the time, m is the mass of the particle, c is the damping coefficient and k is the elastic coefficient.
Although both wave equation and vibration equation involve the change of displacement with time, their forms and application backgrounds are different. Wave equation is suitable for describing the propagation behavior of waves, such as water waves and sound waves. The vibration equation is suitable for describing the vibration phenomenon of objects, such as spring oscillator and pendulum.
Difference between wave equation and vibration equation
1, physical phenomenon:
Wave equation describes the propagation behavior of waves, such as water waves, sound waves and electromagnetic waves. Wave equation studies the characteristics of wave propagation speed, amplitude and frequency.
The vibration equation describes the vibration phenomena of objects, such as spring oscillator and pendulum. Vibration equation studies the displacement, velocity, acceleration and other characteristics of vibrating objects.
2. Equation form:
Wave equation is usually a partial differential equation, involving the partial derivatives of space coordinates and time; Such as wave equation y/? x？ = 1/v？ *y/？ t？ .
The vibration equation is usually an ordinary differential equation, which only involves the derivative of time; For example, the vibration equation m*d of simple harmonic vibration? x/dt？ +c*dx/dt+k*x=0 .