What will be the wavelength of the electromagnetic waves transmitted from the source, if a source is transmitting electromagnetic wave of frequency `8.2 xx 10^6` Hz ?

Options

A. 36.6 m
B. 40.5 m
C. 42.3 m
D. 50.9 m

Explanation

To find the wavelength of the electromagnetic waves transmitted from the source, we can use the formula that relates the speed of light (C), frequency (ν), and wavelength (λ):

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

**Step 1: Identify the values.**
- The speed of light (C) is approximately \(3 \times 10^8\) meters per second.
- The frequency (ν) given in the problem is \(8.2 \times 10^6\) Hz.

**Step 2: Substitute the values into the formula.**
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{8.2 \times 10^6 \text{ Hz}} \]

**Step 3: Perform the division.**
\[ \lambda = \frac{3 \times 10^8}{8.2 \times 10^6} \]

Calculating the division:
\[ \lambda = \frac{3}{8.2} \times \frac{10^8}{10^6} = \frac{3}{8.2} \times 10^{8-6} = \frac{3}{8.2} \times 10^2 \]

Now, calculate \(\frac{3}{8.2}\):
\[ \frac{3}{8.2} \approx 0.36585 \]

Then multiply by \(10^2\):
\[ \lambda \approx 0.36585 \times 100 = 36.585 \text{ meters} \]

**Step 4: Round the answer.**
Rounding to one decimal place, we get:
\[ \lambda \approx 36.6 \text{ meters} \]

Thus, the wavelength of the electromagnetic waves transmitted from the source is approximately **36.6 meters**.

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