Physics - Wave on String Question with Solution | TestHub

The given wave equation is $y=10\cos \pi \left(\frac{x}{4}+\frac{t}{2}\right)$

Rewriting the equation, we get $y=10\cos \left(\frac{\pi }{4}x+\frac{\pi }{2}t\right)$

Comparing with the standard wave equation $y=A\cos (kx+\omega t)$, we get:

Angular frequency $\omega =\frac{\pi }{2}\text{rad/s}$

Wave number $k=\frac{\pi }{4}{\text{m}}^{-1}$

Frequency $f=\frac{\omega }{2\pi }=\frac{\pi /2}{2\pi }=0.25\text{Hz}$

Wavelength $\lambda =\frac{2\pi }{k}=\frac{2\pi }{\pi /4}=8\text{m}$

Wave velocity $v=f\lambda =0.25\times 8=2\text{m/s}=200\text{cm/s}$

Thus, the only correct statement is frequency $=0.25\text{Hz}$.

Answer: frequency $=0.25\text{Hz}$