An electromagnetic wave has a frequency of 500 MHz and a wavelength of 60 cm.
(a) Calculate the speed of the wave.
(b) Name the medium through which it is travelling.

Answer

To solve the problem step by step, we will address both parts of the question: calculating the speed of the electromagnetic wave and identifying the medium through which it is traveling.

### Step-by-Step Solution

**(a) Calculate the speed of the wave.**

1. **Identify the given values:**
- Frequency (f) = 500 MHz
- Wavelength (λ) = 60 cm

2. **Convert the frequency from megahertz to hertz:**
- 1 MHz = \(10^6\) Hz
- Therefore, \(500 \text{ MHz} = 500 \times 10^6 \text{ Hz} = 5 \times 10^8 \text{ Hz}\)

3. **Convert the wavelength from centimeters to meters:**
- 1 cm = 0.01 m
- Therefore, \(60 \text{ cm} = 60 \times 0.01 \text{ m} = 0.6 \text{ m}\)

4. **Use the formula for the speed of a wave:**
\[ v = f \times \lambda \]
where:
- \(v\) = speed of the wave
- \(f\) = frequency
- \(\lambda\) = wavelength

5. **Substitute the values into the formula:**
\[ v = (5 \times 10^8 \text{ Hz}) \times (0.6 \text{ m}) \]

6. **Calculate the speed:**
\[ v = 3 \times 10^8 \text{ m/s} \]

**(b) Name the medium through which it is travelling.**

7. **Identify the medium:**
- Electromagnetic waves travel through various media, including vacuum, air, and other materials. Given that the speed of light in a vacuum is approximately \(3 \times 10^8 \text{ m/s}\), and since the wave is traveling at this speed, we can conclude that it is traveling in air.

### Final Answers:
- (a) The speed of the wave is \(3 \times 10^8 \text{ m/s}\).
- (b) The medium through which it is traveling is air.