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  4. 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

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Q. 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

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Solution:

Amplitude $=2 \,cm =0.02\, m , v=128 \,m / s$
$\lambda={ }_{5}^{4}=0.8 \,m ; v=\frac{128}{0.8}=160\, Hz$
$\omega=2 \pi v=2 \pi \times 160=1005 ; k=\frac{2 \pi}{\lambda}=\frac{2 \pi}{0.8}=7.85$
$\therefore y=0.02 \sin (7.85 x-1005 t) .$