Question

A television is tuned to a station broadcasting at a frequency of 6.60×10^7 Hz . For best reception, the rabbit-ear antenna used by the TV should be adjusted to have a tip-to-tip length equal to half a wavelength of the broadcast signal.
Find the optimum length of the antenna.

Answer 1

Answer:

The optimum length of the antenna is 2.27 m

Explanation:

Given:

Broadcasting frequency $f = 6.60 \times 10^{7}$ Hz

From the formula of wavelength in terms of frequency,

  $v = f \lambda$

Where $v =$ speed of light $= 3 \times 10^{8} \frac{m}{s}$

  $\lambda = \frac{v}{f}$

  $\lambda = \frac{3 \times 10^{8} }{6.60 \times 10^{7} }$

  $\lambda = 4.54$ m

For finding the length of antenna,

   $l = \frac{\lambda}{2}$

   $l = \frac{4.54}{2}$

   $l = 2.27$ m

Therefore, the optimum length of the antenna is 2.27 m