Final answer:
The wavelength of radio waves with a frequency of 106.7 kHz is calculated using the formula λ = c/f, where λ is the wavelength, f is the frequency, and c is the speed of light. The calculated wavelength is 2.81 km, making option a) the correct answer.
Step-by-step explanation:
Radio waves are the waves having the longest wavelength in the electromagnetic spectrum. These waves are a kind of electromagnetic radiation and have a frequency from high 300 GHz to low as 3 kHz, though somewhere it is defined as above 3 GHz as microwaves. At 300 GHz, the wavelength is 1 mm, and at 3 kHz is 100 km.
To find the wavelength of radio waves with a given frequency, you can use the formula c = λf, where λ is the wavelength, f is the frequency, and c is the speed of light in a vacuum (approximately 3.00 × 108 m/s). Solving for wavelength (λ), we get λ = c/f.
In this question, the frequency (f) is given as 106.7 kHz, which is 106.7 × 103 Hz. Thus, the calculation for the wavelength (λ) will be as follows: λ = (3.00 × 108 m/s) / (106.7 × 103 Hz), λ = 2812.92 meters, which can be rounded to 2.81 kilometers (km), making option a) 2.81 km the correct answer.