154k views
4 votes
Determine the maximum and minimum spectral frequencies received from a stationary transmitter that has a center frequency of 1.95GHz, assuming that the receiver is traveling at the speed of 1 km/hr.

User Jozef Izso
by
6.5k points

1 Answer

4 votes

Final answer:

The maximum frequency received is 3.9 GHz and the minimum frequency received is 0 Hz.

Step-by-step explanation:

The maximum and minimum spectral frequencies received from a stationary transmitter can be determined using the formula for Doppler shift. The formula is given by:

f' = f(v + u) / (v + u_s)

where f' is the observed frequency, f is the original frequency, v is the velocity of sound in air, u is the velocity of sound in the medium, and u_s is the velocity of the medium with respect to the observer. In this case, the original frequency is 1.95 GHz and the velocity of the medium is 1 km/hr. To find the maximum and minimum frequencies, we need to consider the observer moving towards the transmitter and away from the transmitter separately.

Maximum frequency:

f'_{max} = f(1 + v/u_s)

f'_{max} = 1.95 imes 10^9(1 + 348.7/348.7)

f'_{max} = 1.95 imes 10^9(2)

f'_{max} = 3.9 imes 10^9 Hz

So, the maximum frequency received is 3.9 GHz.

Minimum frequency:

f'_{min} = f(1 - v/u_s)

f'_{min} = 1.95 imes 10^9(1 - 348.7/348.7)

f'_{min} = 1.95 imes 10^9(0)

f'_{min} = 0 Hz

So, the minimum frequency received is 0 Hz.

User Tmagalhaes
by
7.7k points