A 50 Hz vibrator is used to generate waves in a ripple tank. If the speed of the waves in two different regions of the tank are 1.0 ms-1 and 0.4 ms-1, calculate the difference in their wavelengths.

The relationship between wave speed ($v$), frequency ($f$), and wavelength ($\lambda$) is given by:

$$v = f\lambda$$

We are given the frequency $f = 50 \, \text{Hz}$.
The speed of waves in the first region is $v_1 = 1.0 \, \text{ms}^{-1}$.
The speed of waves in the second region is $v_2 = 0.4 \, \text{ms}^{-1}$.

Rearrange the wave equation to solve for wavelength: $\lambda = \frac{v}{f}$.

$$\lambda_1 = \frac{v_1}{f}$$ $$\lambda_1 = \frac{1.0 \, \text{ms}^{-1}}{50 \, \text{Hz}}$$ $$\lambda_1 = 0.02 \, \text{m}$$

$$\lambda_2 = \frac{v_2}{f}$$ $$\lambda_2 = \frac{0.4 \, \text{ms}^{-1}}{50 \, \text{Hz}}$$ $$\lambda_2 = 0.008 \, \text{m}$$

Difference in wavelengths $= |\lambda_1 - \lambda_2|$

$$|\lambda_1 - \lambda_2| = |0.02 \, \text{m} - 0.008 \, \text{m}|$$ $$|\lambda_1 - \lambda_2| = 0.012 \, \text{m}$$

The difference in their wavelengths is $\text{0.012 m}$.