What is an expression for the standing wave that is produced by adding the two waves

(2.5 cm)sin[(3.0 m-1)x - (27 s-1 )t]
and
(2.5 cm)sin[(3.0 m-1)x + (27 s-1)t]

To find the expression for the standing wave produced by adding the two waves, you need to use the concept of superposition. When two waves superpose, the displacements of each wave add up at each point in space and time. In this case, we have two waves:

Wave 1: A*sin(kx - ωt)
Wave 2: A*sin(kx + ωt)

Where A is the amplitude, k is the wave number, x is the position, ω is the angular frequency, and t is the time.

To find the expression for the standing wave, we need to add these two waves together:

Wave 1 + Wave 2 = A*sin(kx - ωt) + A*sin(kx + ωt)

Using the trigonometric identity for the sum of two sine functions, we get:

2A*sin(kx)*cos(ωt)

So the expression for the standing wave produced by adding the two waves is:

(2.5 cm) * sin(3.0 m^(-1)x) * cos(27 s^(-1)t)