Question

The equation of a transverse wave travelling in a string is given by

y(x,t) = (0.15 m) sin[(0.79 rad/m) x - (13 rad/s)t]

(a) What is the displacement at x = 2.3 m and t = 0.16 s?

Answer 1

To find the displacement at a specific point in the wave, substitute the given values into the equation for the wave function.

Step-by-step explanation:

The equation of a transverse wave in a string is given by y(x,t) = A sin(kx - wt), where A is the amplitude, k is the wave number, x is the position, w is the angular frequency, and t is the time.

In this case, the equation is y(x,t) = (0.15 m) sin[(0.79 rad/m) x - (13 rad/s)t]. To find the displacement at x = 2.3 m and t = 0.16 s, we substitute these values into the equation.

y(2.3,0.16) = (0.15 m) sin[(0.79 rad/m) * 2.3 - (13 rad/s) * 0.16]

Calculating this gives us the displacement at that point in the wave.