What is the frequency in kiloHertz of a radio wave that is 40 meters long?

What is the frequency in kiloHertz of a radio wave that is 40 meters long?

• A. 10 kHz
• B. 15 kHz
• C. 7,500 kHz
• D. 25 kHz

Answer: (C)

To determine the frequency of a radio wave based on its wavelength, you can use the wave equation, which relates wavelength and frequency through the speed of light. The formula is: \[ f = \frac{c}{\lambda} \] where: - \( f \) is the frequency in hertz (Hz), - \( c \) is the speed of light in meters per second (approximately \( 3 \times 10^8 \) m/s), - \( \lambda \) is the wavelength in meters. In this case, the given wavelength is 40 meters. By substituting into the wave equation: \[ f = \frac{3 \times 10^8 \text{ m/s}}{40 \text{ m}} \] Calculating this gives: \[ f = 7.5 \times 10^6 \text{ Hz} \] To convert hertz to kilohertz, divide by 1,000: \[ f = 7,500 \text{ kHz} \] Thus, the frequency of the radio wave that is 40 meters long is 7,500 kHz. This calculation highlights that option C correctly reflects the relationship between wavelength and frequency for electromagnetic waves.

To determine the frequency of a radio wave based on its wavelength, you can use the wave equation, which relates wavelength and frequency through the speed of light. The formula is:

[ f = \frac{c}{\lambda} ]

where:

• ( f ) is the frequency in hertz (Hz),

• ( c ) is the speed of light in meters per second (approximately ( 3 \times 10^8 ) m/s),

• ( \lambda ) is the wavelength in meters.

In this case, the given wavelength is 40 meters. By substituting into the wave equation:

[ f = \frac{3 \times 10^8 \text{ m/s}}{40 \text{ m}} ]

Calculating this gives:

[ f = 7.5 \times 10^6 \text{ Hz} ]

To convert hertz to kilohertz, divide by 1,000:

[ f = 7,500 \text{ kHz} ]

Thus, the frequency of the radio wave that is 40 meters long is 7,500 kHz. This calculation highlights that option C correctly reflects the relationship between wavelength and frequency for electromagnetic waves.