Question

A plane progressive wave is given by the equation y = cos (2πt -πx). Find the equation of the wave with a triple of the amplitude. (All other factors are same)
1. y = 3 cos (2πt -πx)
2. y = 1/3 cos (2πt - πx)
3. y = 6 cos (2πt + πx)
4. y = 9 cos (2πt - πx)

Answer 1

Correct Answer - Option 1 : y = 3 cos (2πt -πx)

CONCEPT:

The general equation of wave motion is given by:

y =  Asin (kx - ωt)

where A = amplitude, ω = angular frequency, k = angular wavenumber, t = time, and x is position

• Wavelength (λ): Distance between two nearest particles vibrating in the same phase.
• Frequency (f): Number of vibrations complete by a particle in one second.
• Time Period (T): Time taken by the wave to travel a distance equal to one wavelength.
• Amplitude (A): Maximum displacement of vibrating particles from the mean position.

The relationship between frequency (f), wavelength (λ), and velocity (v) of a wave is given by:

f × λ = v 

CALCULATION:

Given that:

y = cos (2πt -πx)

By comparing a given equation with a general equation we get 

A = 1; ω = 2π; k = π

Now the new wave equation has triple the amplitude that's mean:

A' = 3 × 1

A' = 3

The new wave equation with triple amplitude of the initial one:

y = 3 cos (2πt - πx)

• Hence option 1 is correct.