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Q.
If the equation of a sound wave is given as $y=0.0015\, \sin (62.8 x+316\, t)$, then wave length of this wave is:
AFMCAFMC 2002
Solution:
Standard equation of progressive sound wave is
$y=a \sin 2 \pi\left(\frac{t}{T}+\frac{x}{\lambda}\right)$
For a wave travelling with amplitude $a$, wavelength $\lambda$ having periodic time $T$, the displacement equation at instant $t$ is given by
$y=a \sin 2 \pi\left(\frac{t}{T}+\frac{x}{\lambda}\right)$ ...(i)
Given, equation of wave is
$y=0.0015 \sin (62.8 x+316\, t)0$ ...(ii)
Comparing Eqs. (i) and (ii), we get
$\frac{2 \pi x}{\lambda} =62.8 x$
$\Rightarrow \lambda =\frac{2 \pi}{62.8}=0.1$ unit