In the equation $y=4 \cos \left(\frac{2 \pi x}{50}\right) \sin 100 \pi t$, where represents the disp

Question

In the equation $y=4 \cos \left(\frac{2 \pi x}{50}ight) \sin 100 \pi t$, where represents the displacement of a particle at a distance from the origin and at the time, the distance between consecutive nodes is\

Professor PC Thomas Classes · Answer

The given equation is\ $y=4 \cos \left(\frac{2 \pi x}{50}ight) \sin 100 \pi t(1)$\ The standard $=\mathrm{n}$ for a stationary wave is\ $\mathrm{Y}=2 \mathrm{~A} \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}ight) \sin \frac{2 \pi \mathrm{vt}}{\lambda}$ (2)\ Comparing $\lambda=50 \mathrm{~cm}$\ Distance between consecutive nodes is $\frac{\lambda}{2}=$ 25 cm\