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Compare 960 on the AM dial to 97.3 on the FM dial. Which has the longer wavelength? By what factor is it larger?

Answer :

In order to compare the wavelengths of 960 kHz on the AM dial and 97.3 MHz on the FM dial, we need to use the formula for wavelength (λ):

λ=fc​

where:

  • λ is the wavelength
  • c is the speed of light (approximately $3 \times 10^8$ meters/second)
  • f is the frequency
    Let's perform the calculation step-by-step.

For AM radio (960 kHz):

  1. Convert the frequency to Hertz.
    960 kHz=960×103 Hz=960,000 Hz
  2. Calculate the wavelength.
    λAM​=960,000 Hz3×108 m/s​≈312.5 meters

For FM radio (97.3 MHz):

  1. Convert the frequency to Hertz.
    97.3 MHz=97.3×106 Hz=97,300,000 Hz
  2. Calculate the wavelength.
    λFM​=97,300,000 Hz3×108 m/s​≈3.08 meters

Comparison:

We observe that the wavelength for AM radio at 960 kHz is approximately 312.5 meters, while the wavelength for FM radio at 97.3 MHz is approximately 3.08 meters. Therefore, the AM wavelength is much longer.

Factor comparison:

To find out by what factor the AM wavelength is larger than the FM wavelength, we divide the AM wavelength by the FM wavelength:
Factor=λFM​λAM​​=3.08 meters312.5 meters​≈101.47

So, the wavelength at 960 kHz on the AM dial is approximately 101.47 times larger than the wavelength at 97.3 MHz on the FM dial.

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