A plane wave has the equation y=25sin(120t-4x). Find (a) amplitude (b) wave length (c) frequency (d) speed

a) The amplitud of the plain wave is 25, b) The wave length of the plain wave is , c) The frequency of the plain wave is , d) The speed of propagation of the plain wave is 0.082.

Step-by-step explanation:

A plain wave is modelled after the following mathematical model as a function of time and horizontal position. That is:

Where:

- Vertical position wave with respect to position of equilibrium, dimensionless.

- Amplitude, dimensionless.

- Angular frequency, dimensionless.

- Wave length, dimensionless.

After comparing this expression with the equation described on statement, the following information is obtained:

, and

a) The amplitude of the plain wave is 25.

b) The wave length associated with the plain wave is found after some algebraic handling:

The wave length of the plain wave is .

c) The frequency can be calculated in term of angular frequency, that is:

Where is the frequency of the plain wave.

If , then:

The frequency of the plain wave is .

d) The speed of propagation is equal to the product of wave length and frequency:

Given that and , the speed of propagation is:

The speed of propagation of the plain wave is 0.082.