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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 string is clamed at both the ends and it is vibrating in its $4^{th}$ harmonic. The equation of the stationary wave is $Y =0.3\,sin\,(0.157\,x) \,cos\,(200\pi t)$. The length of the string is ..... $m$ (all quantities are in $SI$ units)
  • A
    $60$
  • ✓
    $80$
  • C
    $40$
  • D
    $20$
✓

Answer

Correct option: B.
$80$
b
$4^{\text {th }}$ harmonic

$4 \frac{\lambda}{2}=\ell \quad ; 2 \lambda=\ell$

From equation $\frac{2 \pi}{\lambda}=0.157$

$\lambda=40 ; \quad \ell=2 \lambda=80 \mathrm{m}$

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