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

Question

Equation of a progressive wave is y=a sin (10 π x+11 π t+(π/3)) The wavelength of the wave is (A) 0.2 unit (B) 0.1 unit (C) 0.5 unit (D) 1 unit

Tardigrade Admin · Accepted Answer

Given, wave equation y(x, t)=a sin (10 π x+11 π t+π / 3) Comparing Eq. (i) with the general equation of wave y=A sin (k x+ω t+φ), text we get k=10 π We know that, Wavelength of the wave, λ=(2 π/k) ⇒ λ=(2 π/10 π)=0.2 text unit

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

$0.2$ unit

$0.1$ unit

$0.5$ unit

1 unit

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

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

0.2 unit

0.1 unit

0.5 unit

1 unit

Given, wave equation y(x,t)=asin(10πx+11πt+π/3) Comparing Eq. (i) with the general equation of wave y=Asin(kx+ωt+ϕ), we get k=10π We know that, Wavelength of the wave, λ=k2π​ ⇒λ=10π2π​=0.2 unit

$0.2$ unit

$0.1$ unit

$0.5$ unit

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