Consider an antenna transmitting at 900 MHz. The receiver is traveling at a speed of 40km/h. Calculate its Doppler shift.
To calculate the Doppler shift, we need to know the relative velocity between the transmitter and the receiver, as well as the frequency of the transmitted signal. We can use the Doppler equation:
Doppler shift = (Frequency received - Frequency transmitted) / Frequency transmitted
In this case, we are given the frequency of the transmitted signal, which is 900 MHz (900 * 10^6 Hz). We also know that the receiver is traveling at a speed of 40 km/h.
To calculate the relative velocity between the transmitter and receiver, we need to convert the speed from km/h to m/s. We know that 1 km/h is equal to 0.27778 m/s. So, the relative velocity would be:
Relative velocity = 40 km/h * 0.27778 m/s/km/h
Relative velocity = 11.1111 m/s
Now, we can use this relative velocity and the frequency of the transmitted signal to calculate the Doppler shift:
Doppler shift = (Frequency received - Frequency transmitted) / Frequency transmitted
Since the problem does not provide the frequency received, we cannot calculate the exact Doppler shift without that information. However, if we are given the frequency received, we can substitute that into the formula to find the Doppler shift.
To calculate the Doppler shift, we'll use the formula:
Doppler Shift = fs * (v / c)
Where:
- fs is the source frequency (in this case, the transmitted frequency)
- v is the velocity of the receiver
- c is the speed of light in a vacuum (approximately 3 x 10^8 m/s)
First, we need to convert the speed of the receiver from km/h to m/s:
40 km/h = (40 * 1000) / 3600 m/s
= 11.11 m/s (rounded to two decimal places)
Now, we can substitute the given values into the formula:
Doppler Shift = 900 MHz * (11.11 m/s / 3 x 10^8 m/s)
Simplifying the equation:
Doppler Shift = 900 MHz * 11.11 / 3 x 10^8
Calculating the Doppler shift:
Doppler Shift = 3.33 x 10^-3 MHz
Therefore, the Doppler shift for the receiver traveling at 40 km/h is 3.33 x 10^-3 MHz.