The Physics
Hypertextbook
Opus in profectus

# Electromagnetic Spectrum

## Problems

### practice

1. Write something.
2. Write something.
3. Write something.
4. Write something completely different.

### conceptual

1. An analogy
1. What is the separation between the scratches on a diffraction grating that would be used in a typical high school or undergraduate physics lab?
2. What is the wavelength of the approximate center of the visible spectrum?
3. What is the separation between the pickets of a picket fence?
4. For what wavelength could a picket fence be used like a diffraction grating?
5. What is the frequency of the electromagnetic wave with the wavelength calculated in part d?
6. What kind of electromagnetic radiation is this?
2. Two simple facts
1. What is the source of all magnetism?
2. What is the source of all electromagnetic waves?
3. The door on a microwave oven is basically a double layer of safety glass with a perforated metal foil layer in between. The perforations allow you to see the food inside while at the same time keeping the microwaves trapped inside. How is this possible? Why is it that the light can escape the oven, but the microwaves can't?
4. Why are TV broadcasts in the very high frequency (VHF) range more easily received in areas of marginal reception than broadcasts in the ultra high frequency (UHF) range? Remember, UHF frequencies are higher than VHF frequencies. Assume that both types of frequencies are broadcast under identical conditions.

### numerical

1. A typical household microwave oven operates at a frequency of 2.45 GHz.
1. What is the wavelength of this radiation?
2. Hotspots in a microwave oven are caused by the formation of standing waves within the cooking chamber.
1. On what part of a standing wave do the hotspots in a microwave oven form?
2. What is the separation between hotspots in a 2.45 GHz microwave oven?
3. How is the problem of hotspots dealt with in the design of microwave ovens or in the cooking techniques employed by the people that use them?
2. The lowest frequency of electromagnetic radiation used for communication purposes is at 76 Hz. This lies in the extremely low frequency (ELF) part of the radio spectrum.
1. Who uses this frequency and for what purpose?
2. What is the wavelength of this radiation?
3. How long would a dipole antenna have to be to broadcast at this frequency?
4. How does the antenna length you calculated in part c. compare to the circumference of the Earth?
5. How long is the actual antenna used for ELF communication?
3. Sound is a longitudinal mechanical wave and radio is a transverse electromagnetic wave. Humans and other animals have organs called ears for receiving sound waves. They do not have organs for receiving radio waves. Such a device is called a radio receiver or just a radio. Analog radio relies one of two basic techniques to encode sound information into a radio signal — by varying the amplitude of the radio signal (amplitude modulation or AM) or by varying the frequency of the radio signal (frequency modulation or FM).
1. AM radio broadcasts in the US are allocated frequencies from 530 to 1710 kHz. What range of wavelengths correspond to these frequencies? About how big is this?
2. FM radio broadcasts in the US are allocated frequencies from 88 to 108 MHz. What range of wavelengths correspond to these frequencies? About how big is this?
4. Mobile phone companies use many frequencies, but across the Americas the core of the system are the 800 MHz and 1900 MHz bands. The 800 MHz band is the original "Cellular" band, introduced in 1983. The 1900 MHz band is the newer "Personal Communications Service" (PCS) band, introduced in 1994.
1. The Cellular band spans frequencies from 824 to 894 MHz. What range of wavelengths correspond to these frequencies? About how big is this?
2. The PCS band spans frequencies from 1850 to 1990 MHz. What range of wavelengths correspond to these frequencies? About how big is this?
5. Mobile phone companies use many frequencies, but across Africa, Asia, Australia, and Europe the core of the system are the Global System for Mobile Communications (GSM) bands. The original GSM band was centered around 900 MHz and was introduced in 1991. The second GSM band, sometimes called the Digital Cellular System (DCS) band, centered around 1800 MHz was added in 1993.
1. The original GSM band spans frequencies from 880 to 960 MHz. What range of wavelengths correspond to these frequencies? About how big is this?
2. The DCS band spans frequencies from 1710 to 1880 MHz. What range of wavelengths correspond to these frequencies? About how big is this?
6. Mobile phone companies use many frequencies, but across the Americas, some combination of four different bands is used — the Global System for Mobile Communications or GSM bands. Given the range of frequencies in megahertz in the table below, compute the corresponding range of wavelengths for each band to the nearest centimeter.
name range (MHz) range (cm) notes
GSM‑850 824–894   The original analog "Cellular" band in the US, introduced in 1983.
GSM‑900 880–960   The original GSM band in Europe, introduced in 1991.
GSM‑1800 1710–1880   Also known as the Personal Communications Service (PCS) band in the US, added in 1994.
GSM‑1900 1850–1990   Also known as the Digital Cellular System (DCS) band in Europe, added in 1993.
7. The wireless networking standard known as Wi-Fi encompasses several frequency bands in the microwave part of the electromagnetic spectrum. The two most common are the 2.4 GHz and 5 GHz bands.
1. Wi-Fi channels in the 2.4 GHz band range from 2.401 GHz to 2.473 GHz in the US. What range of wavelengths correspond to these frequencies? About how big is this?
2. Wi-Fi channels in the 5 GHz band range from 5.170 GHz to 5.835 GHz in the US. What range of wavelengths correspond to these frequencies? About how big is this?
8. Bluetooth is a wireless technology standard for exchanging data over short distances using ultrahigh frequency radio waves (UHF) in one of the internationally reserved industrial, scientific, and medical radio bands (ISM). Equipment operating in an ISM band must tolerate interference generated by other users, which limits its use to short range, low power applications like Bluetooth, Wi-Fi, microwave ovens, and and medical diathermy (therapeutic heating). The Bluetooth band is divided into 79, 1 MHz channels that start at 2402 MHz and end at 2480 MHz. What range of wavelengths correspond to these frequencies? About how big is this?
9. Police, fire, and other emergency services in New York City communicate mostly using ultra high frequency (UHF) narrowband frequency modulation (NFM) push-to-talk two way radios. Frequencies used range from 451.3 MHz to 487.5 MHz. What range of wavelengths correspond to these frequencies? About how big is this?
10. The satellites in the US Global Positioning System (GPS) broadcast microwave signals that enable GPS receivers on or near the Earth's surface to determine their location and time and to derive their velocity (speed and bearing). All GPS satellites currently broadcast on two frequencies: L1 at 1.57542 GHz and L2 at 1.22760 GHz. (L3 is a legacy system for detonating nuclear warheads, L4 is currently experimental, and L5 is for more demanding tasks like landing airplanes.) Determine the corresponding wavelengths of the L1 and L2 GPS frequencies. About how big is this?

### investigative

1. Determine the one-way transit time for a signal received on Earth today if it originated from…
1. a satellite in geosynchronous orbit
2. the Moon
3. the Sun
4. Voyager 1 or Voyager 2
5. Proxima Centauri
6. the Large Magellanic Cloud
7. the Andromeda Galaxy (a.k.a. M81)
8. the edge of the observable universe
2. Calculate the "round trip light time" for the following astronomical objects. That is, how long would it take a signal to travel from the Earth to the object and back?
1. the Moon
2. the Sun
3. Mars (when closest to the Earth)
4. Pluto (when farthest from the Earth)