Equation of two simple harmonic waves is given by \(\mathrm{Y}_1=2 \sin 8 \pi\left(\frac{\mathrm{t}}{0.2}-\frac{\mathrm{x}}{2}\right) \mathrm{m}\) and \(\mathrm{Y}_2=4 \sin 8 \pi\left(\frac{\mathrm{t}}{0.16}-\frac{\mathrm{x}}{1.6}\right) \mathrm{m}\) then both waves have

The two equations can be written as
\(Y_1=2 \sin 2 \pi\left(\frac{4 t}{0.2}-\frac{4 x}{2}\right)=2 \sin 2 \pi\) \(\left(\frac{\mathrm{t}}{0.05}-\frac{\mathrm{x}}{0.5}\right)\)
\(\text {and } Y_2=4 \sin 2 \pi\left(\frac{4 \mathrm{t}}{0.16}-\frac{4 \mathrm{x}}{1.6}\right)=2 \sin 2 \pi\) \(\left(\frac{\mathrm{t}}{0.04}-\frac{\mathrm{x}}{0.4}\right)\)
Comparing with standard equation
\(
\mathrm{Y}=\mathrm{A} \sin 2 \pi\left(\frac{\mathrm{t}}{\mathrm{T}}-\frac{\mathrm{x}}{\lambda}\right)
\)
We get, for the first wave,
\(
\mathrm{T}=0.05 \mathrm{~s} \text { and } \lambda=0.5 \mathrm{~m}
\)
For the second wave,
\(
\mathrm{T}=0.04 \mathrm{~s} \text { and } \lambda=0.4 \mathrm{~m}
\)
Hence their periods (hence frequencies) are not same.
Their wavelength is also not same.
For first wave, velocity \(=\frac{\lambda}{\mathrm{T}}=\frac{0.5}{0.05}=10 \mathrm{~m} / \mathrm{s}\)
For second wave, velocity \(\frac{0.4}{0.04}=10 \mathrm{~m} / \mathrm{s}\)
Hence velocity in same