The electron field portion of an electromagnetic wave is given by (all variables in SI units) E = 10-4 sin ( 6 × 105 t - 0.01 x) . The frequency (f) and the speed (ν) of electromagnetic wave are

Question

The electron field portion of an electromagnetic wave is given by (all variables in SI units) E = 10-4 sin ( 6 × 105 t - 0.01 x) . The frequency (f) and the speed (ν) of electromagnetic wave are (A) f = 30 / π kHz and ν =1.5 × 107m / s-1 (B) f = 90 / π kHz and ν =6.0 × 107m / s-1 (C) f = 300 / π kHz and ν =6.0 × 107m / s-1 (D) f = 600 / π kHz and ν =7.5 × 107 m / s-1

Tardigrade Admin · Accepted Answer

ω=6 × 105 =2 π f f =(6/2 π) × 105=(3/π) × 105 Hz =(300/π) × 103 Hz =(300/π) kHz Wave speed = (ω/k) = (6 × 105/0.01)=6 × 107 m / s

Q. The electron field portion of an electromagnetic wave is given by (all variables in SI units) $E = 1 0^{- 4} sin (6 \times 1 0^{5} t - 0.01 x)$ . The frequency $(f)$ and the speed $(ν)$ of electromagnetic wave are

$f = 30/ π k Hz$ and $ν = 1.5 \times 1 0^{7} m / s^{- 1}$

$f = 90/ π k Hz$ and $ν = 6.0 \times 1 0^{7} m / s^{- 1}$

$f = 300/ π k Hz$ and $ν = 6.0 \times 1 0^{7} m / s^{- 1}$

$f = 600/ π k Hz$ and $ν = 7.5 \times 1 0^{7} m / s^{- 1}$

$f = 900/ π k Hz$ and $ν = 8.0 \times 1 0^{7} m / s^{- 1}$

$ω = 6 \times 1 0^{5} = 2 π f$
$f = \frac{6}{2 π} \times 1 0^{5} = \frac{3}{π} \times 1 0^{5} Hz$
$= \frac{300}{π} \times 1 0^{3} Hz$
$= \frac{300}{π} k Hz$
Wave speed $= \frac{ω}{k}$
$= \frac{6 \times 1 0 ^{5}}{0.01} = 6 \times 1 0^{7} m / s$

Q. The electron field portion of an electromagnetic wave is given by (all variables in SI units) E=10−4sin(6×105t−0.01x) . The frequency (f) and the speed (ν) of electromagnetic wave are

f=30/πkHz and ν=1.5×107m/s−1

f=90/πkHz and ν=6.0×107m/s−1

f=300/πkHz and ν=6.0×107m/s−1

f=600/πkHz and ν=7.5×107m/s−1

f=900/πkHz and ν=8.0×107m/s−1

ω=6×105=2πf f=2π6​×105=π3​×105Hz =π300​×103Hz =π300​kHz Wave speed =kω​ =0.016×105​=6×107m/s