Question

A radio station has two channels. One is AM at 1020 kHz and the other is FM at 89.5 MHz. For good results you will use

• A. longer antenna for the AM channel and shorter for the FM
• B. shorter antenna for the AM channel and longer for the FM
• C. same length antenna will work for both
• D. information given is not enough to say which one to use for which

Hint:

Antenna length \(\propto \lambda\). Lower frequency (AM) needs longer antenna, higher frequency (FM) needs shorter antenna.

Answer 1

The Correct Option is A

Step 1: Recall relation between antenna length and wavelength.
Antenna length is usually proportional to wavelength, typically \(\lambda/4\).
Step 2: Compare wavelengths of AM and FM.
\[ \lambda = \frac{c}{f} \]
AM frequency \(f_{AM}=1020\,kHz\) is much smaller, so wavelength is very large.
FM frequency \(f_{FM}=89.5\,MHz\) is much higher, so wavelength is small.
Step 3: Conclusion based on wavelength.
Longer wavelength \(\Rightarrow\) longer antenna needed.
So AM requires longer antenna and FM requires shorter antenna.
Final Answer:
\[ \boxed{\text{(A) longer antenna for AM and shorter for FM}} \]