Question

Suppose an AM talk radio station broadcasts radio waves with a frequency of 590. kHz . Calculate the wavelength of these radio waves. Round your answer to 3 significant digits.

Answer 1

The wavelength of a 590 kHz AM radio signal is approximately 508 meters when calculated using the speed of light and the given frequency.

Step-by-step explanation:

To calculate the wavelength of radio waves emitted by an AM radio station broadcasting at 590 kHz, we can use the formula:

c = λf

Where 'c' is the speed of light in a vacuum (approximately 3.00 x 108 m/s), 'λ' is the wavelength, and 'f' is the frequency in Hz. Since the broadcast frequency is given in kHz, we need to convert this to Hz by multiplying by 1,000. Thus:

f = 590 kHz x 1,000 = 590,000 Hz

Now the wavelength can be calculated as:

λ = c / f

λ = (3.00 x 108 m/s) / (590,000 Hz)

λ ≈ 508 m (rounded to three significant digits)

The wavelength of the radio waves broadcasted by the AM station with a frequency of 590 kHz is approximately 508 meters.