You are tuned to 790 on AM radio. This station is broadcasting at a frequency of \(790 \mathrm{kHz}\left(7.90 \times 10^{5} \mathrm{Hz}\right) .\) You switch to 98.3 on \(\mathrm{FM}\) radio. This station is broadcasting at a frequency of \(98.3 \mathrm{MHz}\left(9.83 \times 10^{7} \mathrm{Hz}\right)\) a. What are the wavelengths of the AM and FM radio signals? b. Which broadcasts at higher frequencies: AM or FM? c. What are the photon energies of the two broadcasts?

Frequency refers to the number of cycles of a wave that pass a given point per unit of time. It's usually measured in Hertz (Hz). For any wave, whether it's sound, light, or radio, the frequency determines its pitch, color, or station on the dial. When tuning into a radio station, you're selecting a specific frequency that the station is broadcasting. The frequency for AM and FM stations is measured in kilohertz (kHz) and megahertz (MHz) respectively.
We have:

• AM frequency: 790 kHz or 790,000 Hz
• FM frequency: 98.3 MHz or 98,300,000 Hz

Higher frequencies mean that more cycles pass a given point per second. Therefore, FM radio, which operates in MHz, has a much higher frequency than AM radio.

Wavelength is the distance between successive crests (or troughs) of a wave. It's inversely related to frequency, meaning that as the frequency of the wave increases, its wavelength decreases. The relationship between wavelength (\( \text{λ} \)) and frequency (\( \text{f} \)) can be expressed by the equation:
\( \text{λ} = \frac{c}{f} \)
where \( c \) is the speed of light (\( 3 \times 10^8 \) meters/second). Using this formula, we calculated:

• AM wavelength: 379 meters
• FM wavelength: 3.05 meters

AM signals have longer wavelengths compared to FM signals, leading to differences in how they travel and are received.

Photon energy is the energy carried by a single photon and is directly related to its frequency. Higher frequency waves carry higher energy photons. The energy of a photon (\( \text{E} \)) is given by:
\( \text{E} = hf \)
where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) Joules·second). We calculated:

• AM photon energy: \( 5.23 \times 10^{-28} \) Joules
• FM photon energy: \( 6.51 \times 10^{-26} \) Joules

Thus, FM signals carry photons with significantly more energy than AM signals due to their higher frequencies.

AM (Amplitude Modulation) radio is a type of radio transmission in which the amplitude of the carrier wave is varied in proportion to the sound signal being transmitted. AM radio stations operate in the kilohertz range, specifically between 530 to 1700 kHz. The long wavelengths of AM radio allow it to travel long distances, especially at night when these waves bounce off the ionosphere.
Because of its longer wavelengths, AM radio can often be picked up in locations far from the transmitter, which is especially beneficial in rural areas. However, AM signals are more susceptible to noise and interference due to the variation in the signal's amplitude.

FM (Frequency Modulation) radio is a type of radio transmission in which the frequency of the carrier wave is varied in accordance with the sound signal being transmitted. FM radio stations operate in the megahertz range, typically between 88 to 108 MHz. FM signals have much shorter wavelengths compared to AM, leading to higher sound quality and less susceptibility to interference from environmental noise.
FM radio provides better sound reproduction and fidelity, making it more suitable for music. However, FM signals are generally not able to travel as far as AM signals because they primarily propagate through the sky rather than reflecting off the ionosphere. Therefore, FM stations usually require a network of repeaters to cover larger areas effectively.