Question

what is the wavelength of an electromagnetic wave that travels at 3 × 10⁸ m/s and has a frequency of 60 mhz? (1 mhz = 1,000,000 hz)
○ 60 mhz, 300,000,000 m/s
○ 300,000,000 m/s / 60,000,000 hz
○ no answer can be determined from the information given.
○ 60,000,000 hz / 300,000,000 m/s

Explanation:

Step1: Convert frequency unit

Given \( f = 60\ MHz\). Since \(1\ MHz=10^{6}\ Hz\), then \(f = 60\times10^{6}\ Hz=60000000\ Hz\). The speed of electromagnetic wave \(v = 3\times10^{8}\ m/s = 300000000\ m/s\).

Step2: Use the formula \(v=\lambda f\)

We know that the formula for the speed of a wave is \(v = \lambda f\), where \(v\) is the speed of the wave, \(\lambda\) is the wavelength, and \(f\) is the frequency. Rearranging the formula for \(\lambda\), we get \(\lambda=\frac{v}{f}\).
Substitute \(v = 300000000\ m/s\) and \(f = 60000000\ Hz\) into the formula: \(\lambda=\frac{300000000}{60000000}\ m\).

Step3: Calculate the wavelength

\(\frac{300000000}{60000000}=5\ m\). The general formula form for the options is \(\frac{v}{f}\), where \(v = 300000000\ m/s\) and \(f = 60000000\ Hz\)

Answer:

\(\frac{300000000\ m/s}{60000000\ Hz}\)