FM radio broadcasts at 900 KHz. What wavelength does this corresponds to ?

Options

A. 333m
B. `3.03xx10^(-3)`m
C. 330cm
D. 3300m

Answer

To find the wavelength corresponding to a frequency of 900 KHz, we can follow these steps:

### Step 1: Convert Frequency to Hertz
The frequency given is 900 KHz. To convert this to Hertz (Hz), we multiply by 1,000 (since 1 KHz = 1,000 Hz).

\[ \text{Frequency} (f) = 900 \text{ KHz} = 900 \times 10^3 \text{ Hz} = 900,000 \text{ Hz} \]

### Step 2: Use the Wave Equation
The relationship between the speed of light (C), frequency (f), and wavelength (λ) is given by the equation:

\[ C = f \times \lambda \]

Where:
- \(C\) is the speed of light (approximately \(3 \times 10^8\) meters per second),
- \(f\) is the frequency in Hertz,
- \(\lambda\) is the wavelength in meters.

### Step 3: Rearrange the Equation to Solve for Wavelength
To find the wavelength (λ), we can rearrange the equation:

\[ \lambda = \frac{C}{f} \]

### Step 4: Substitute the Values
Now we can substitute the values of \(C\) and \(f\) into the equation:

\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{900 \times 10^3 \text{ Hz}} \]

### Step 5: Perform the Calculation
Calculating the above expression:

\[ \lambda = \frac{3 \times 10^8}{900 \times 10^3} = \frac{3 \times 10^8}{9 \times 10^5} = \frac{3000}{9} \text{ m} \]

Calculating \(3000 \div 9\):

\[ \lambda \approx 333.33 \text{ m} \]

### Step 6: Round the Result
Rounding \(333.33\) meters gives us approximately:

\[ \lambda \approx 333 \text{ meters} \]

### Final Answer
The wavelength corresponding to a frequency of 900 KHz is approximately **333 meters**.

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