Physics - Wave on String Question with Solution | TestHub

Key Idea : The sign between two terms in argument of sine will define its direction. Writing the given wave equation $y=0.25\sin (10\pi x-2\pi t)$ The minus $(-)$ between $(10\pi x)$ and $(2\pi t)$ implies that the wave is travelling along positive $x$ direction. Now comparing Eq. (i) with standard wave equation $y=a\sin (kx-\omega t)$ We have $\begin{array}{l}a=0.25\mathrm{m},\omega =2\pi ,k=10\pi \mathrm{m}\\ \therefore \frac{2\pi }{T}=2\pi \\ \Rightarrow f=1\mathrm{Hz}\end{array}$ Also, $\lambda =\frac{2\pi }{k}=\frac{2\pi }{10\pi }=0.2\mathrm{m}$ Therefore, the wave is travelling along +ve $x$ direction with frequency $1\mathrm{Hz}$ and wavelength $0.2\mathrm{m}$