Physics - Wave on String Question with Solution | TestHub

The two equations can be written as $$\begin{array}{rl}& Y_1=2\sin 2\pi \left(\frac{4t}{0.2}-\frac{4x}{2}\right)=2\sin 2\pi \left(\frac{\mathrm{t}}{0.05}-\frac{\mathrm{x}}{0.5}\right)\\ & \text{ and }{Y}_2=4\sin 2\pi \left(\frac{4\mathrm{t}}{0.16}-\frac{4\mathrm{x}}{1.6}\right)=2\sin 2\pi \left(\frac{\mathrm{t}}{0.04}-\frac{\mathrm{x}}{0.4}\right)\end{array}$$ 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