A wave in a string has an amplitude of $2\,\, cm.$ The wave travels in the $+ve$ direction of $x-$ axis with a speed of $128\,\, m/s$ and it is noted that $5$ complete waves fit in $4\,\, m$ length of the string. The equation describing the wave is
AIPMT 2009, Medium
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Amplitude $=2 \mathrm{cm}=0.02 \mathrm{m}, v=128 \mathrm{m} / \mathrm{s}$
$\lambda=\frac{4}{5}=0.8 \mathrm{m} ; \mathrm{v}=\frac{128}{0.8}=160 \mathrm{Hz}$
$\omega=2 \pi \mathrm{v}=2 \pi \times 160=1005 ; \quad k=\frac{2 \pi}{\lambda}=\frac{2 \pi}{0.8}=7.85$
$\therefore \quad y=0.02 \sin (7.85 x-1005 t)$
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