The wavelength (in SI units) for an electromagnetic wave is given as ψ(x, t)=103 sin π(3 × 106 x-9 × 1014 t) The speed of the wave is y × 107 m / s. Find y.

Question

The wavelength (in SI units) for an electromagnetic wave is given as ψ(x, t)=103 sin π(3 × 106 x-9 × 1014 t) The speed of the wave is y × 107 m / s. Find y. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Ψ(x, t)=103 sin π(3 × 106 x-9 × 1014 t) Ψ(x, t)=103 sin (3 π × 106 x-9 π × 1014 t) speed =v=(ω/k)=(9 π × 1014/3 π × 106) =3 × 108 m / s

Q. The wavelength (in $S I$ units) for an electromagnetic wave is given as $ψ (x, t) = 1 0^{3} sin π (3 \times 1 0^{6} x - 9 \times 1 0^{14} t)$ The speed of the wave is $y \times 1 0^{7} m / s$ . Find $y$ .

$Ψ (x, t) = 1 0^{3} sin π (3 \times 1 0^{6} x - 9 \times 1 0^{14} t)$
$Ψ (x, t) = 1 0^{3} sin (3 π \times 1 0^{6} x - 9 π \times 1 0^{14} t)$
speed $= v = \frac{ω}{k} = \frac{9 π \times 1 0 ^{14}}{3 π \times 1 0 ^{6}}$
$= 3 \times 1 0^{8} m / s$

Q. The wavelength (in SI units) for an electromagnetic wave is given as ψ(x,t)=103sinπ(3×106x−9×1014t) The speed of the wave is y×107m/s. Find y.

Ψ(x,t)=103sinπ(3×106x−9×1014t) Ψ(x,t)=103sin(3π×106x−9π×1014t) speed =v=kω​=3π×1069π×1014​ =3×108m/s

Q. The wavelength (in $S I$ units) for an electromagnetic wave is given as $ψ (x, t) = 1 0^{3} sin π (3 \times 1 0^{6} x - 9 \times 1 0^{14} t)$ The speed of the wave is $y \times 1 0^{7} m / s$ . Find $y$ .

$Ψ (x, t) = 1 0^{3} sin π (3 \times 1 0^{6} x - 9 \times 1 0^{14} t)$
$Ψ (x, t) = 1 0^{3} sin (3 π \times 1 0^{6} x - 9 π \times 1 0^{14} t)$
speed $= v = \frac{ω}{k} = \frac{9 π \times 1 0 ^{14}}{3 π \times 1 0 ^{6}}$
$= 3 \times 1 0^{8} m / s$