An FM radio station generates radio waves that have a frequency of 95.5 MHz. The frequency of the waves from a competing station have a frequency of 102.7 MHz. What is the difference in wavelength between the waves emitted from the two stations ?

Options

A. 0.22 m
B. 0.84 m
C. 0.45 m
D. 2.4 m

Answer

To find the difference in wavelength between the waves emitted from the two FM radio stations, we can follow these steps:

### Step 1: Convert Frequencies to Hertz
The frequencies of the two stations are given in megahertz (MHz). We need to convert these frequencies to hertz (Hz) for our calculations.

- For the first station (FM radio station):
\[ f_1 = 95.5 \, \text{MHz} = 95.5 \times 10^6 \, \text{Hz} \]

- For the second station (competing station):
\[ f_2 = 102.7 \, \text{MHz} = 102.7 \times 10^6 \, \text{Hz} \]

### Step 2: Use the Wave Equation
The relationship between wavelength (λ), frequency (f), and the speed of light (c) is given by the equation:
\[ \lambda = \frac{c}{f} \]
Where \(c\) is the speed of light in air, approximately \(3 \times 10^8 \, \text{m/s}\).

### Step 3: Calculate Wavelengths
Now we can calculate the wavelengths for both stations.

- For the first station:
\[ \lambda_1 = \frac{c}{f_1} = \frac{3 \times 10^8 \, \text{m/s}}{95.5 \times 10^6 \, \text{Hz}} \approx 3.14 \, \text{m} \]

- For the second station:
\[ \lambda_2 = \frac{c}{f_2} = \frac{3 \times 10^8 \, \text{m/s}}{102.7 \times 10^6 \, \text{Hz}} \approx 2.92 \, \text{m} \]

### Step 4: Calculate the Difference in Wavelengths
Now, we find the difference in wavelength between the two stations:
\[ \Delta \lambda = \lambda_1 - \lambda_2 \approx 3.14 \, \text{m} - 2.92 \, \text{m} = 0.22 \, \text{m} \]

### Final Answer
The difference in wavelength between the waves emitted from the two stations is approximately **0.22 meters**.

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