Question

All electromagnetic waves travel at the speed of light (300,000,000 m/s) Calculate the wavelength of each of the following types of EM waves: 88,000,000 Hz, 600,000,000,000 Hz, and 3,000,000,000,000,000,000 Hz.

a) 3.41 m, 5 x 10^-7 m, 1 x 10^-10 m
b) 2.27 m, 5 x 10^-8 m, 1 x 10^-11 m
c) 3.41 m, 5 x 10^-8 m, 1 x 10^-11 m
d) 2.27 m, 5 x 10^-7 m, 1 x 10^-10 m

Answer 1

The wavelengths for the electromagnetic waves with frequencies 88,000,000 Hz, 600,000,000,000 Hz, and 3,000,000,000,000,000,000 Hz are 3.41 m, 5 x 10⁻⁷ m, and 1 x 10⁻¹⁰ m, respectively, corresponding to option a).

Step-by-step explanation:

The wavelength of electromagnetic waves can be calculated using the formula c = λ x f, where c is the speed of light, λ is the wavelength, and f is the frequency. Since the speed of light c is a constant 3.00 × 10⁸ m/s, we can rearrange the equation to find the wavelength as λ = c / f.

For the frequencies given:

1. 88,000,000 Hz: λ = 3.00 × 10⁸ m/s / 88,000,000 Hz = 3.41 m
2. 600,000,000,000 Hz: λ = 3.00 × 10⁸ m/s / 600,000,000,000 Hz = 5 x 10⁻⁷ m
3. 3,000,000,000,000,000,000 Hz: λ = 3.00 × 10⁸ m/s / 3,000,000,000,000,000,000 Hz = 1 x 10⁻¹⁰ m

Therefore, the correct wavelengths of electromagnetic waves corresponding to the given frequencies are 3.41 m, 5 x 10⁻⁷ m, and 1 x 10⁻¹⁰ m, which matches option a).