A longitudinal wave is represented by x = 10 | vedclass

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Question

(B) The wave equation is given by $y = A \sin 2 \pi (nt - \frac{x}{\lambda})$.Here,the amplitude $A = 10 \, cm$.The maximum particle velocity is given

Vedclass · Accepted Answer

$5 \pi$

Vedclass · Answer

(B) The wave equation is given by $y = A \sin 2 \pi (nt - \frac{x}{\lambda})$.Here,the amplitude $A = 10 \, cm$.The maximum particle velocity is given by $V_{p, 	ext{max}} = \omega A = (2 \pi n) A$.The wave velocity is given by $V_{	ext{wave}} = n \lambda = \frac{\omega}{k} = \frac{2 \pi n}{2 \pi / \lambda} = n \lambda$.According to the problem,$V_{p, 	ext{max}} = 4 V_{	ext{wave}}$.Substituting the expressions: $(2 \pi n) A = 4 (n \lambda)$.Simplifying,we get $2 \pi A = 4 \lambda$.Therefore,$\lambda = \frac{2 \pi A}{4}$.Substituting $A = 10 \, cm$: $\lambda = \frac{2 \pi (10)}{4} = \frac{20 \pi}{4} = 5 \pi \, cm$.

$A$ longitudinal wave is represented by $x = 10 \sin 2 \pi (nt - \frac{x}{\lambda}) \, cm$. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to .....................

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