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

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$π$

$\frac{5 π}{2}$

5 $π$

2 $π$

answer is B.

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Detailed Solution

$\begin{array}{l} V_{P} max = 4 V_{wave} \\ ωA = 4 (\frac{ω}{k}) \Rightarrow A = \frac{4 λ}{2 π} \\ λ = \frac{2 πA}{4} \Rightarrow \frac{20 π}{4} \Rightarrow 5 π \end{array}$

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