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

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 14. waves and sound4 Marks
Question
In a transverse wave the distance between a crest and neighbouring trough at the same instant is $4.0\, cm$ and the distance between a crest and trough at the same place is $1 .0\, cm$ . The next crest appears at the same place after a time interval of $0.4\,s$. The maximum speed of the vibrating particles in the medium is
✓

Answer

Transverse wave equation

$y=a \sin (\omega t+k x)$

Next crest appears at time interval of $0.4 \mathrm{s}$

So, the time period $T=0.4$

$\therefore$ Angular Frequency $\omega=\frac{2 \pi}{T}=\frac{2 \pi}{0.4}$

$\therefore$ Speed of the particle

$\nu=\frac{d y}{d t}=a \omega \sin (\omega t+k x)$

$\nu_{\max }=a \omega$

$a=1 / 2 c m$

$=\frac{1}{2} \times \frac{2 \pi}{0.4}=\frac{2 \pi}{8} \times 10$

$=\frac{5 \pi}{2} \mathrm{cm} / \mathrm{s}$

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