## Calculate the range of wavelengths for the frequencies found on the FM band. Take a look at the “whip” radio antennas on cars, comment on th

Question

Calculate the range of wavelengths for the frequencies found on the FM band. Take a look at the “whip” radio antennas on cars, comment on the size of the wavelength and the antenna. {2.8 – 3.4 m}

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1 year 2021-09-02T07:18:42+00:00 1 Answers 14 views 0

2.8m-3.4m

Explanation:

Radio waves are electromagnetic waves and they all travel with a speed of

$$3*10^8m/s$$ in air.

The range of frequencies in the FM band is from 88MHz to 108MHz.

Generally, the relationship between velocity, frequency and wavelength for electromagnetic waves is given by equation (1);

$$v=\lambda f…………..(1)$$

From equation (1), we can write,

$$\lambda=\frac{v}{f}……………(2)$$

For the upper frequency of 108MHz, the wavelength is given by;

$$\lambda_1=\frac{3*10^8}{108*10^6}\\\lambda_1=0.02778*10^2\\\lambda_1=2.78m$$

Similarly, for the lower frequency of 88MHz, the wavelength is given by;

$$\lambda_2=\frac{3*10^8}{88*10^6}\\\lambda_2=0.0341*10^2\\\lambda_2=3.41m$$

The range of wavelength therefore  is $$\lambda_1-\lambda_2=2.8m-3.4m$$ approximately.

$$108MHz=108*10^6Hz\\88MHz=88*10^6Hz$$