JEE MAIN - Physics (2022 - 29th June Morning Shift - No. 14)
A longitudinal wave is represented by $$x = 10\sin 2\pi \left( {nt - {x \over \lambda }} \right)$$ cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to :
2$$\pi$$
5$$\pi$$
$$\pi$$
$${{5\pi } \over 2}$$
Explanation
Particle velocity = $${{\partial x} \over {\partial t}}$$
$$\Rightarrow$$ Maximum particle velocity $$ = (2\pi n)\,(10)$$
$$ \Rightarrow (2\pi n)\,(10) = (n\lambda )\,(4)$$
$$ \Rightarrow \lambda = 5\pi $$
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