Physics - Wave on String Question with Solution | TestHub

The given equation of the progressive wave is $y=6\cos (100t-4x)$.

Comparing this with the standard wave equation $y=A\cos (\omega t-kx)$, we get:
Amplitude $A=6\mu \text{m}=6\times 10^{-6}\text{ m}$
Angular frequency $\omega =100\text{ rad/s}$
Wave number $k=4{\text{ m}}^{-1}$

The maximum particle velocity is given by $v_{p,\text{max}}=A\omega$.

The velocity of the wave is given by $v_w=\frac{\omega }{k}$.

The ratio of the maximum particle velocity to the wave velocity is:
$\frac{v_{p,\text{max}}}{v_w}=\frac{A\omega }{\frac{\omega }{k}}=Ak$

Substituting the values of $A$ and $k$:
$\text{Ratio}=(6\times 10^{-6})\times 4=24\times 10^{-6}=2.4\times 10^{-5}$

Answer: $2.4\times 10^{-5}$