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$\cdot$ The electromagnetic spectrum. Electromagnetic waves, which include light, consist of vibrations of electric and magnetic fields, and they all travel at the speed of light. (a) FM radio. Find the wavelength of an FM radio station signal broadcasting at a frequency of 104.5 $\mathrm{MHz}$ . (b) $\mathrm{X}$ rays. X rays have a wavelength of about 0.10 $\mathrm{nm}$ . What is their frequency? (c) The Big Bang. Microwaves with a wavelength of 1.1 $\mathrm{mm}$ , left over from soon after the Big Bang, have been detected. What is their frequency? (d) Sunburn. Sunburn (and skin cancer) are caused by ultraviolet light waves having a frequency of around $10^{16} \mathrm{Hz}$ . What is their wavelength? (e) SETI. It has been suggested that extraterrestrial civilizations (if they exist) might try to communicate by using electromagnetic waves having the same frequency as that given off by the spin flip of the electron in hydrogen, which is 1.43 GHz. To what wave-length should we tune our telescopes in order to search for such signals? (f) Microwave ovens. Microwave ovens cook food with electromagnetic waves of frequency around 2.45 $\mathrm{GHz}$ . What wavelength do these waves have?

a) 2.87$m$b) $3 \times 10^{18} H z$c) $2.72 \times 10^{11} H z$d) 0.122 $\mathrm{m}$

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

Rutgers, The State University of New Jersey

University of Washington

McMaster University

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So here velocity is going to be equal to see the speed of light. And this will be 3.0 times 10 to the eighth meters per second. And we know that the velocity is equal to the wavelength times the frequency. So we can say that for party. We're trying to find the wavelength of the FM radio waves. We have the wavelength equals C over f, and this will be 3.0 times 10 to the eighth, divided by the frequency of 100 for megahertz. So we either 104.5 megahertz. So 104.5 times 10 to the sixth hurts, and this is giving us 2.87 meters. So this is the wavelength of FM radio waves. And then for part B, they're asking us for the frequency of X rays. Ah, the frequency of X rays would be equal to the speed of light divided by Lambda. And this will be simply the speed of light divided by the wavelength of the X ray. So 0.10 nano meters, or 0.10 times 10 to the negative ninth meters, and this is equaling 3.0 times. 10 to the 18th hurts penny. And this is for X rays for see micro waves left over from the big bang we have the frequency equals sea over the land of the wavelength and this equals c divided by here. It will be 1.1 times 10 to the negative third meters and this is giving us 2.7 times 10 to the 11th. Kurtz And this will be for the macro waves left over from the Big Bang and then for party. They want the wavelength of UV rays, so this will be the speed of light divided by the frequency. So this will be sii divided by 10 to the 16th hurts. And this is giving us 30 nano meters and this will be the wavelength for UV rays. And then for part ee, they want the wavelength of he spend flip of lee electron and hydrogen. So the wavelength will be equal to again the speed of light, the about about the frequency. And this will simply be see the speed of light divided by the frequency of 1.43 times 10 to the ninth hurts no. And we're getting a wavelength of 21.0 centimeters. Again. This is for the spin flip of the electron and the hydrogen atom. And then for part F Lastly, we have the wave link of microwave ovens. So this will be see divided by F. And we have again see the speed of light threepio 0.0 times 10 to the eighth meters per second, divided by the frequency of 2.45 times 10 to the ninth hurts. And this is giving microwave oven wavelengths 0.1 to 2 meters. So these will be again for microwave ovens. That is the end of the solution. Thank you for washing.

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