1. Write the standard form of a standing wave

A standing wave produced by two identical waves moving in opposite directions is written as

$y(x,t)=2A\sin(kx)\cos(\omega t)$

where:

• $k$ is the wave number,
• $\omega$ is the angular frequency.

The corresponding travelling wave speed is

$v=\frac{\omega}{k}$

2. Compare with the given equation

Given:

$y(x,t)=0.5\sin\left(\frac{5\pi}{4}x\right)\cos(200\pi t)$

Comparing with $2A\sin(kx)\cos(\omega t)$, we get:

$k=\frac{5\pi}{4}\ \text{rad/m}$

and

$\omega=200\pi\ \text{rad/s}$

3. Calculate the wave speed

$v=\frac{\omega}{k}$

Substitute the values:

$v=\frac{200\pi}{5\pi/4}$

$v=200\pi\times\frac{4}{5\pi}$

$v=160\ \text{m/s}$

4. Match with the options

$160\ \text{m/s}$ corresponds to:

Option A

5. Comparison with stored correct answer

Stored correct answer: A

Our derived answer: A

So, the answer agrees with the stored correct answer.