Answer
(a) $f = 8.6\times 10^8~Hz$
(b) $\lambda = 23~cm$
Work Step by Step
(a) We can find the frequency of the waves as they travel through the air.
$f = \frac{v}{\lambda}$
$f = \frac{3.0\times 10^8~m/s}{0.35~m}$
$f = 8.6\times 10^8~Hz$
We know that the frequency of a wave does not change when moving from one medium to another medium. Therefore, the frequency as the signal travels through the glass is $8.6\times 10^8~Hz$.
(b) We can find the speed of the signal as it travels through glass. The index of refraction of glass is $n = 1.5$. Therefore;
$v = \frac{c}{n}$
$v = \frac{3.0\times 10^8~m/s}{1.5}$
$v = 2.0\times 10^8~m/s$
We can find the wavelength as:
$\lambda = \frac{v}{f}$
$\lambda = \frac{2.0\times 10^8~m/s}{8.6\times 10^8~Hz}$
$\lambda = 0.23~m = 23~cm$
