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STD 11 - 14. waves and sound — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 14. waves and sound4 Marks
MCQ
A longitudinal wave is represented by $x =10 \sin 2 \pi\left( nt -\frac{ x }{\lambda}\right) \,cm$. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to .....................
  • A
    $2 \pi$
  • ✓
    $5 \pi$
  • C
    $\pi$
  • D
    $\frac{5 \pi}{2}$
✓

Answer

Correct option: B.
$5 \pi$
b
$V _{ P } \max =4 V _{\text {wave }}$

$\omega A =4\left(\frac{\omega}{ k }\right) \Rightarrow A =\frac{4 \lambda}{2 \pi}$

$\lambda=\frac{2 \pi A }{4} \Rightarrow \frac{20 \pi}{4} \Rightarrow 5 \pi$

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