Question 377: Waves

Question

A transverse wave in a medium is given by $$y=A \sin 2(\omega t-k x)$$. It is found that the magnitude of the maximum velocity of particles in the medium is equal to that of the wave velocity. What is the value of $$A$$ ?

Accepted Answer

The given equation is $$y=A \sin 2(\omega t-k x)$$
$$	herefore \quad$$ Velocity of the particle, $$v=\frac{d y}{d t}$$
$$\begin{array}{ll} 
& =2 \mathrm{~A} \omega \cos 2(\omega \mathrm{t}-\mathrm{kx}) \
	herefore \quad & 	ext { Maximum velocity }=2 \mathrm{~A} \omega \
& 	ext { Velocity of the wave }=\frac{\omega}{\mathrm{k}}
\end{array}$$
$$\begin{aligned}
& 	ext { Given } 2 \mathrm{~A} \omega=\frac{\omega}{\mathrm{k}} \
& 	herefore \quad \mathrm{A}=\frac{1}{2 \mathrm{k}}=\frac{\lambda}{(2 \pi)^2}=\frac{\lambda}{4 \pi}
\end{aligned}$$

Answer

$$\frac{2 \lambda}{\pi}$$

Answer

$$\frac{\lambda}{\pi}$$

Answer

$$\frac{\lambda}{2 \pi}$$

Answer

$$\frac{\lambda}{4 \pi}$$

Waves

A transverse wave in a medium is given by $y=A \sin 2(\omega t-k x). It is found that the magnitude of the maximum velocity of particles in the medium is equal to that of the wave velocity. What is the value of A$ ?

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