A certain cellular telephone transmits at a frequency of 825 MHz and receives at a frequency of 875 MHz. (a) What is the wavelength of the transmitted signal in cm?

Verified step by step guidance

1. Step 1: Understand that the speed of light (c) is constant and is equal to 3.00 x 10^8 m/s or 3.00 x 10^10 cm/s. The frequency (f) is given in the problem as 825 MHz, which is equivalent to 825 x 10^6 Hz. The wavelength (λ) is what we are trying to find.
2. Step 2: Recall the formula that relates speed of light, frequency, and wavelength: c = λf. We can rearrange this formula to solve for wavelength: λ = c/f.
3. Step 3: Substitute the given values into the formula. Remember to convert the frequency to Hz (1 MHz = 10^6 Hz) and the speed of light to cm/s (1 m = 100 cm) to match the units of the desired answer.
4. Step 4: Perform the division to calculate the wavelength. Do not forget to check your units to ensure they are consistent.
5. Step 5: The result is the wavelength of the transmitted signal in cm.

Key Concepts

Wave Properties

Waves, including electromagnetic waves like radio signals, have properties such as frequency and wavelength. The frequency is the number of cycles per second, while the wavelength is the distance between successive peaks of the wave. These properties are inversely related; as frequency increases, wavelength decreases, and vice versa.

Speed of Light

The speed of light in a vacuum is a constant value, approximately 3.00 x 10^8 meters per second. This speed is crucial for calculating the wavelength of a signal when its frequency is known. The relationship between speed (c), frequency (f), and wavelength (λ) is given by the equation c = f × λ.

Unit Conversion

In scientific calculations, it is often necessary to convert units to ensure consistency. In this case, the frequency is given in megahertz (MHz), which must be converted to hertz (Hz) for calculations. Additionally, the final wavelength should be expressed in centimeters (cm), requiring conversion from meters (m) to centimeters.