Calculate the range of wave length corresponding to the baseband audio and frequency range (20hz −20khz) and…

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Calculate the range of wave length corresponding to the baseband audio and frequency range (20hz −20khz) and comment on the implications on the size of antenna requirements Solve in English

ScanSolve AI Tutor · Accepted Answer

To calculate the range of wavelengths, we use the formula $\lambda = \frac{c}{f}$ , where $c$ is the speed of light ( $3 \times 10^8$ m/s) and $f$ is the frequency. The given frequency range for baseband audio is 20 Hz to 20 kHz.

Calculate the wavelength for the minimum frequency (20 Hz)
The minimum frequency is $f_{min} = 20$ Hz.
$\lambda_{max} = \frac{c}{f_{min}}$ $\lambda_{max} = \frac{3 \times 10^8 \text{ m/s}}{20 \text{ Hz}}$ $\lambda_{max} = 0.15 \times 10^8 \text{ m}$ $\lambda_{max} = 15 \times 10^6 \text{ m}$ $\lambda_{max} = 15 \text{ Mm}$
Calculate the wavelength for the maximum frequency (20 kHz)
The maximum frequency is $f_{max} = 20 \text{ kHz} = 20 \times 10^3 \text{ Hz}$ .
$\lambda_{min} = \frac{c}{f_{max}}$ $\lambda_{min} = \frac{3 \times 10^8 \text{ m/s}}{20 \times 10^3 \text{ Hz}}$ $\lambda_{min} = \frac{3}{20} \times 10^{8-3} \text{ m}$ $\lambda_{min} = 0.15 \times 10^5 \text{ m}$ $\lambda_{min} = 15000 \text{ m}$ $\lambda_{min} = 15 \text{ km}$
State the range of wavelengths
The range of wavelengths corresponding to the baseband audio frequency range (20 Hz - 20 kHz) is from 15 km to 15 Mm.
Comment on the implications for antenna size
Antennas are typically designed to be a significant fraction of the wavelength (e.g., $\frac{1}{2}\lambda$ , $\frac{1}{4}\lambda$ ).
For the calculated wavelengths:
- A wavelength of 15 km would require an antenna on the order of kilometers long.
- A wavelength of 15 Mm (15,000 km) would require an antenna on the order of thousands of kilometers long.
These dimensions are impractically large for any terrestrial antenna. This is why baseband audio frequencies are not directly transmitted as RF signals. Instead, they are used to modulate a much higher frequency carrier wave, which has a significantly smaller wavelength, making antenna design feasible.

The range of wavelengths is $\boxed{\text{15 km to 15 Mm}}$ .
The implication is that antennas for direct transmission of these wavelengths would be extremely large and impractical.

Calculate the range of wave length corresponding to the baseband audio and frequency range (20hz -20khz) and comment on the implications on the size of antenna requirements Solve in English

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Step-by-step solution

Calculate the wavelength for the minimum frequency (20 Hz)

Calculate the wavelength for the maximum frequency (20 kHz)

State the range of wavelengths

Comment on the implications for antenna size

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