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To calculate the frequency of radio waves detected by an aerial, we can use the formula:

frequency = speed of light / wavelength

Given that the speed of light (C) is 300,000,000 m/s and the aerial length is a quarter wavelength, we can find the wavelength as follows:

wavelength = 4 * aerial length

Substituting the values:

wavelength = 4 * 1.5m = 6m

Now, we can calculate the frequency:

frequency = 300,000,000 m/s / 6m = 50,000,000 Hz

Therefore, the frequency of the radio waves detected by the 1.5m long aerial is 50,000,000 Hz or 50 MHz.

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