Question

Two microwave signals of nearly equal wavelengths can generate a beat frequency if both are directed onto the same microwave detector. In an experiment, the beat frequency is 100 MHz. One microwave generator is set to emit microwaves with a wavelength of 1.250 cm. If the second generator emits a longer wavelength, what is that wavelength?

Short answer

The wavelength of the second wave is 1.255 cm.

Step-by-step solution

Write the given information 

The beat frequency is f_b= 100 M Hz

The wavelength of one of the waves is λ₁= 1.250 cm = 0.0125m

The speed of the wave is c = 3x 10⁸ m/s

To determine the wavelength of the second wave 

Let the frequency of the second wave is λ₂
The frequency of the beat is given as
$$\begin{gathered} f_b=|f_1-f_2| \\ 100\times {10}^{6}Hz=\frac{c}{{\lambda }_1}-\frac{c}{{\lambda }_2} \\ {10}^8=3\times {10}^8\left(\frac{1}{0.0125}-\frac{1}{{\lambda }_2}\right) \\ {\lambda }_2=1.255cm \end{gathered}$$

Thus, the wavelength of the second wave is 1.255 cm and it is longer than the first one.