Two waves are represented by the following equations: y₁ = 5sin2π(10t − 0.1x) and y₂ = 10sin2π(10t − 0.1x). The ratio of intensities I₂: I₁ will be

Given: A₁ = 5, A₂ = 10, 

We know that the magnitude of intensity depends on the strength and amplitude of a wave under propagation and I ∝ A ² where I is intensity and A is the amplitude.

then 

$\frac{{\mathrm{I}}_2}{{\mathrm{I}}_1}={\left(\frac{{\mathrm{A}}_2}{{\mathrm{A}}_1}\right)}^2={\left(\frac{10}{5}\right)}^2=4$

Therefore, the required ratio is 4: 1.