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 130 MHz . One microwave generator is set to emit microwaves with a wavelength of 1.250cm. If the second generator emits the longer wavelength, what is that wavelength? Express your answer to four significant figures and include the appropriate units.

Answer 1

To find the wavelength of the second microwave generator emitting the longer wavelength, we can rearrange the formula Wavelength = wave speed / frequency and solve for the second frequency. Using the given values, the wavelength of the second generator is approximately 1.2875 cm.

Step-by-step explanation:

To find the wavelength of the microwave generator emitting the longer wavelength, we can use the formula:

Wavelength = wave speed / frequency

We are given the beat frequency (130 MHz) and the wavelength of the first generator (1.250 cm). The beat frequency is the difference between the frequencies of the two generators:

Beat frequency = frequency2 - frequency1

We can rearrange the formula to solve for the second frequency:

Frequency2 = beat frequency + frequency1

Using the given values, we get:

Frequency2 = 130 MHz + 900 MHz = 1030 MHz

Now we can use the formula for wavelength, using the second frequency:

Wavelength2 = wave speed / frequency2

Substituting the known values:

Wave speed = wavelength2 * frequency2 = 1.250 cm * 1030 MHz

Calculating the wave speed:

Wave speed = 1.250 cm * 1030 MHz = 1.2875 cm

Therefore, the wavelength of the second microwave generator emitting the longer wavelength is approximately 1.2875 cm.

Answer 2

The wavelength of second generator is found to be 1.257 cm.

Step-by-step explanation:

Let,

fb = beat frequency

f1 = frequency of given wave

f2 = frequency of second generator

λ1 = wavelength of given generator = 1.250 cm = 0.0125 m

λ2 = wavelength of second generator

since,

fb = |f1 - f2|

therefore,

fb = c/λ1 - c/λ2

1/λ2 = 1/λ1 - fb/c

1/λ2 = 1/0.0125 m - (130,000,000 Hz)/(300,000,000 m/s) + 1/0.0125 m

λ2 = 1/79.566

λ2 = 0.01257 m = 1.257 cm