Answer
(a) $\lambda = 628~nm$
(b) $f = 4.77\times 10^{14}~Hz$
(c) $E_0 = 900~V/m$
Work Step by Step
We can write the general equation for a magnetic wave:
$B = B_0~sin(kx-\omega t)$
We can write the equation for this magnetic wave:
$B = (3.00~\mu T)~sin[(1.00\times 10^7)x-\omega t]$
(a) We can find the wavelength:
$\lambda = \frac{2\pi}{k}$
$\lambda = \frac{2\pi}{1.00\times 10^7}$
$\lambda = 6.28\times 10^{-7}~m$
$\lambda = 628~nm$
(b) We can find the frequency:
$f = \frac{c}{\lambda}$
$f = \frac{3.0\times 10^8~m/s}{6.28\times 10^{-7}~m}$
$f = 4.77\times 10^{14}~Hz$
(c) We can find the electric field amplitude:
$E_0 = c~B_0$
$E_0 = (3.0\times 10^8~m/s)(3.00\times 10^{-6}~T)$
$E_0 = 900~V/m$
