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  4. Equation of a progressive wave is y=a sin (10 π x+11 π t+(π/3)) The wavelength of the wave is

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Q. Equation of a progressive wave is $$ y=a \sin \left(10 \pi x+11 \pi t+\frac{\pi}{3}\right) $$ The wavelength of the wave is

Waves

Solution:

Given, wave equation
$y(x, t)=a \sin (10 \pi x+11 \pi t+\pi / 3)$
Comparing Eq. (i) with the general equation of wave
$y=A \sin (k x+\omega t+\phi), \text { we get } $
$k=10 \pi$
We know that,
Wavelength of the wave, $\lambda=\frac{2 \pi}{k}$
$\Rightarrow \lambda=\frac{2 \pi}{10 \pi}=0.2 \text { unit }$