Question

If the equation of a sound wave is given as $y=0.0015\sin (62.8x+316t)$, then wave length of this wave is:

• A. 0.1 unit
• B. 0.2 unit
• C. 0.4 unit
• D. 0.5 unit

Answer 1

Answer: (A)

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
$y=0.0015\sin (62.8x+316t)0$ ...(ii)
Comparing Eqs. (i) and (ii), we get
$\frac{2\pi x}{\lambda }=62.8x$
$\Rightarrow \lambda =\frac{2\pi }{62.8}=0.1$ unit