Final answer:
The distance a 1MHz signal will travel into the tunnel before its signal intensity drops by 30 dB can be calculated using the formula d = lambda / (4 * pi * R), where d is the distance, lambda is the wavelength of the signal, and R is the signal loss per unit distance in dB. Using the given values, the distance is approximately 23886.76 meters.
Step-by-step explanation:
The signal intensity of a 1 MHz signal will drop by 30 dB after it travels a certain distance into the tunnel. To find this distance, we can use the formula:
d = lambda / (4 * pi * R)
Where d is the distance, lambda is the wavelength of the signal, and R is the signal loss per unit distance in dB.
Since the signal loss is given as 30 dB, we can convert it to a linear scale by using the formula:
R = 10^(R/10)
This gives us R = 10^(-3) = 0.001.
For a 1 MHz signal, the wavelength lambda = c / f, where c is the speed of light and f is the frequency. Plugging in the values, we get lambda = 3x10^8 / 10^6 = 300 meters.
Substituting these values into the first formula, we find that
d = 300 / (4 * pi * 0.001) = 23886.76 meters.