Physics - Wave on String Question with Solution | TestHub

The equation of a given progressive wave is $$y=5\sin (100\pi t-0.4\pi x)$$ The standard equation of a progressive wave is $$y=a\sin (\omega t-kx)$$ Comparing (i) and (ii), we get $$a=5\mathrm{m},\omega =100\pi \mathrm{rad}{\mathrm{s}}^{-1},k=0.4\pi {\mathrm{m}}^{-1}$$ (1) Amplitude of the wave, $a=5\mathrm{m}$ (2) Wavelength of the wave, $$\lambda =\frac{2\pi }{k}=\frac{2\pi }{0.4\pi }=5\mathrm{m}$$ (3) Frequency of the wave, $$v=\frac{\omega }{2\pi }=\frac{100\pi }{2\pi }=50\mathrm{Hz}$$ (4) Velocity of the wave, $$v=v\lambda =\left(50{\mathrm{s}}^{-1}\right)(5\mathrm{m})=250\mathrm{m}{\mathrm{s}}^{-1}$$