Question

Radio waves of frequency 1.667 GHz arrive at two telescopes that are connected by a computer to perform interferometry. One portion of the same wave front travels 1.080 m farther than the other before the two signals are combined Part A Will the two waves combine constructively or destructively? Destructively O Constructively Submit Request Answer Part B Calculate the value of m for the path difference between the two signals Express your answer as an integer Submit Request Answer

Answer 1

Answer:

constructively

6

Explanation:

c = Speed of light = $3\times 10^8\ m/s$

$\nu$ = Frequency = 1.667 GHz

$\Delta x$ = Path difference = 1.08 m

Wavelength is given by

$\lambda=\frac{c}{\nu}\\\Rightarrow \lambda=\frac{3\times 10^8}{1.667\times 10^9}\\\Rightarrow \lambda=0.17996\ m$

Path difference is given by

$\Delta x=m\lambda\\\Rightarrow m=\frac{\Delta x}{\lambda}\\\Rightarrow m=\frac{1.08}{0.17996}\\\Rightarrow m=6.00133\approx 6$

As the integral multiple of wavelength gives path difference the waves will combine constructively.

The value of m is 6