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Chapter 31: Problem 58

What is the wavelength of the electromagnetic waves used for cell phone communications in the 850 -MHz band?

Short Answer

Expert verified
Answer: The approximate wavelength of the electromagnetic waves used for cell phone communications in the 850 MHz band is 35.29 centimeters.

Step by step solution

01

Convert frequency to Hz

The frequency given is 850 MHz. To convert it to Hz, we need to multiply it by 10^6 (since there are one million Hz in a MHz). 850 MHz = 850 * 10^6 Hz = 8.50 * 10^8 Hz
02

Apply the formula to calculate the wavelength

We have the frequency (f) in Hz now, and the speed of light (c) is 3.00 * 10^8 m/s. We can apply the formula λ = c / f to find the wavelength. λ = (3.00 * 10^8 m/s) / (8.50 * 10^8 Hz)
03

Calculate the result

Dividing the speed of light by the frequency, we get: λ = 3.00 * 10^8 m/s / 8.50 * 10^8 Hz = 0.3529 * 10^0 m
04

Express the wavelength in an appropriate unit

The calculated wavelength is in meters. However, it's more appropriate to express the result in a smaller unit like centimeters. To convert the wavelength from meters to centimeters, we need to multiply it by 100 (since there are 100 centimeters in a meter). λ = 0.3529 m * 100 cm/m = 35.29 cm The wavelength of the electromagnetic waves used for cell phone communications in the 850 MHz band is approximately 35.29 centimeters.

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