Question 434: Waves

Question

A simple harmonic progressive wave is given by $$Y=Y_0 \sin 2 \pi\left(n t-\frac{x}{\lambda}ight)$$. If the wave velocity is $$\left(\frac{1}{8}ight)^{	ext {th }}$$ the maximum particle velocity then the wavelength is

Accepted Answer

Maximum particle velocity $$=Y_0 \omega=2 \pi n Y_0$$
Wave velocity $$=n \lambda$$
$$\begin{aligned}
& 	herefore \frac{2 \pi n Y_0}{8}=n \lambda \
& 	herefore \lambda=\frac{\pi Y_0}{4}
\end{aligned}$$

Answer

$$\frac{\pi Y_0}{2}$$

Answer

$$\frac{\pi Y_0}{4}$$

Answer

$$\frac{\pi \mathrm{Y}_0}{8}$$

Answer

$$\frac{\pi Y_0}{16}$$

Waves

A simple harmonic progressive wave is given by $Y=Y_0 \sin 2 \pi\left(n t-\frac{x}{\lambda}\right). If the wave velocity is \left(\frac{1}{8}\right)^{\text {th }}$ the maximum particle velocity then the wavelength is

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