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  • A longitudinal wave is represented by <img alt="x=10 \sin 2 \pi\left(\mathrm{nt}-\frac{x}{\lambda}\right) \mathrm{cm}" src="/latex-image/?x%3D10%20%5Csin%202%20%5Cpi%5Cleft%28%5Cmathrm%7Bnt%7D-%5Cf

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

Option: 1

2 \pi


Option: 2

5 \pi


Option: 3

\pi


Option: 4

\frac{5 \pi}{2}


Answers (1)

best_answer

\mathrm{x=10 \sin 2 \pi\left(n t-\frac{x}{\lambda }\right) \mathrm{cm}}

Particle velocity \mathrm{=\frac{\partial x}{\partial t}}

maximum particle velocity \mathrm{=(2\pi n)\times10}

wave velocity=n\lambda

As given in the question

\mathrm{2\pi n\times10=n\lambda \times 4}

\mathrm{\lambda =5\pi}

Hence, the correct answer is Option (2)

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