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

The optimum length of the antenna is 2.27 m

Step-by-step explanation:

Given:

Broadcasting frequency
`f = 6.60 * 10^(7)` Hz

From the formula of wavelength in terms of frequency,

`v = f \lambda`

Where
`v =` speed of light
`= 3 * 10^(8) (m)/(s)`

`\lambda = (v)/(f)`

`\lambda = (3 * 10^(8) )/(6.60 * 10^(7) )`

`\lambda = 4.54` m

For finding the length of antenna,

`l = (\lambda)/(2)`

`l = (4.54)/(2)`

`l = 2.27` m

Therefore, the optimum length of the antenna is 2.27 m