91Ó°ÊÓ

Inductance,$L=0.253\mathrm{μ}\text{H}=0.253×{10}^{-6}\text{H}$ .

Capacitance,$C=25.0\text{pF}=25.0×{10}^{-12}\text{F}$.

The velocity of light, $c=3×{10}^8\text{m/s}$.

Figure 33-3 shows an arrangement for generating a traveling electromagnetic wave in the radio region of the spectrum. It shows that an LC oscillator produces a sinusoidal current in the antenna, which generates the wave. The wavelength of electromagnetic waves emitted by an oscillator-antenna system can be calculated using the formula for frequency in terms of inductance and capacitance.

Formula:

$f=1/2\mathrm{Ï€}\sqrt{LC}$

To calculate, we have,

$f=1/2\mathrm{Ï€}\sqrt{LC}$ (1)

But, $f=\frac{c}{\mathrm{λ}},$i.e.,

$\mathrm{λ}=c/f$ (2)

From equations 1 and 2, we can write the formula for wavelength as,

$\begin{array}{rcl}\mathrm{λ}& =& \frac{c}{1/2\mathrm{π}\sqrt{LC}}\\ \mathrm{λ}& =& 2\mathrm{π}c\sqrt{LC}\end{array}$

Substitute the values in the above expression, and we get,

$\begin{array}{rcl}\mathrm{λ}& =& 2\left(3.14\right)\left(3×{10}^8\right)\sqrt{\left(0.253×{10}^{-6}\right)\left(25.0×{10}^{-12}\right)}\\ & =& 4.74\mathrm{m}\end{array}$

Thus, the wavelength of the electromagnetic wave emitted by the oscillator is $4.74\mathrm{m}$.