A progressive wave equation is given by y (x,t) = 5 sin (2πt + πx), where x and y is in meter (m) and t is in second(s)

Question

1. Determine the period of the wave.

(2 marks)

1. Calculate the wavelength during one complete cycle.

(2 marks)

1. Find the magnitude of wave velocity.

Answer 1

In this problem the equation of the wave has a form

y(x,t) = 5sin (2πt + πx), m (1)

The "+" sign tells us that the progressive wave is moving to the left.

The equation of the progressive wave in general form looks like

y(x,t) = Asin 2π(x/λ + t/T)

or

y(x,t) = A sin (2πt/T + 2πx/λ) (2)

Compare equation (1) and (2), we see that

2π/T = 2π

Hence

T = 1 s

Then

2π/λ = π

So,

λ = 2 m

To find the magnitude of wave's velocity, we use the formula

v = λ / T

Plugging in the numbers, we get

v = 2 m/s