A wave represented by X=0.4cos(8t-y÷2),where x and y are in meters t in second. Calculate the speed of the wave?

Answer 1

The general form of a wave equation is:

y = A cos(kx - wt)

where:
y = displacement of the wave from its equilibrium position
A = amplitude of the wave
k = wave number
x = position of the particle on the wave
w = angular frequency
t = time

Comparing this with the given equation:

y = 0.4cos(8t - y/2)

We can see that:
A = 0.4
k = 1 (since y/2 is equivalent to (1/2)x)
w = 8

The wave speed is given by the following formula:

v = w/k

Substituting the values of k and w, we get:

v = 8/1

v = 8 m/s

Therefore, the speed of the wave is 8 m/s.