Question

The spacing between bands of color in a chemical wave from an oscillating reaction is measured to be 1.2 cm, and a new wave appears every 42 s. Calculate the speed of propagation of the chemical waves.

Short answer

The chemical wave's propagation speed is 0.028 cm/sec.

Step-by-step solution

Speed of wave

The wave equation gives the formula to calculate the speed of the wave, which is expressed in m/sec or cm/sec, as shown below;

$\mathbf{Speed}\mathbf{=}\left(\mathbf{\lambda }\right)\mathbf{wavelength}\mathbf{\times }\left(\mathbf{\upsilon }\right)\mathbf{frequency}$

Speed of chemical wave

The formula to calculate the speed of the propagation of the chemical wave is;

$Speed=wavelength\left(\lambda \right)\times frequency\left(\upsilon \right)$

The frequency of the wave is calculated as;

$$\begin{gathered} \upsilon \text{=}\frac{\text{1}}{\text{T}} \\ \text{=}\frac{\text{1}}{42\text{sec}} \\ \text{=} 0.023{\text{sec}}^{\text{- 1}} \end{gathered}$$

Here,

The wavelength of the water wave is 1.2 cm.

The frequency of the water wave is$0.023{\sec }^{-1}$.

Substituting the known value in the formula ofthe speed of the wave;

$$\begin{gathered} Speed=\lambda \times \nu \\ =1.2cm\times 0.023s^{-1} \\ =0.028cm{s}^{-1} \end{gathered}$$