JEE Main 2014 · 9 Apr · Shift 1 · Physics Q15

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A transverse wave is represented by :
$y=\frac{10}{\pi}\sin\left(\frac{2\pi}{T}t-\frac{2\pi}{\lambda}x\right)$
For what value of the wavelength the wave velocity is twice the maximum particle velocity ?

40 cm

20 cm

10 cm

60 cm

Answer and worked solution

Official answer: A

Maximum particle speed: $A\omega=\dfrac{10}\pi\cdot\dfrac{2\pi}T=\dfrac{20}T$ .
Wave speed: $\dfrac\lambda T$ .

$\dfrac\lambda T=2\cdot\dfrac{20}T$ gives $\lambda=40$ (in the length unit of $y$ , cm).

Topics:Wave equation and progressive waves

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JEE Main 2014 · 9 Apr · Shift 1, Physics question 15