Problem 13 - Applied Physics

Question

Find the frequency of an electromagnetic wave with wavelength \(1.50 \mathrm{~m}\).

Step-by-Step Solution

Answer

The frequency of the wave is \(2.00 \times 10^8\) Hz.

Step 1: Understand the formula

The frequency of an electromagnetic wave can be found using the formula \( c = \lambda \cdot f \), where \( c \) is the speed of light in vacuum (approximately \( 3.00 \times 10^8 \) m/s), \( \lambda \) is the wavelength, and \( f \) is the frequency. We need to solve for \( f \).

Step 2: Rearrange the formula

To find the frequency \( f \), rearrange the formula: \( f = \frac{c}{\lambda} \).

Step 3: Substitute the known values

Now substitute the known values into the equation: \( f = \frac{3.00 \times 10^8 \, \text{m/s}}{1.50 \, \text{m}} \).

Step 4: Calculate the frequency

Perform the division: \( f = \frac{3.00 \times 10^8}{1.50} = 2.00 \times 10^8 \) Hz.

Key Concepts

Wavelength Calculation

Wavelength is a crucial characteristic of any wave, including electromagnetic waves like light and radio waves. It refers to the distance between consecutive peaks of a wave. To find the frequency of an electromagnetic wave, you first need to understand its wavelength, denoted by the Greek letter \( \lambda \). In our specific exercise, the wavelength is given as \(1.50 \, \text{m}\). A longer wavelength usually means a lower frequency because wavelength and frequency are inversely related. Knowing the wavelength allows you to calculate the frequency, especially when you also know the speed of the wave, in this case, the speed of light. Once these values are in hand, you can proceed with your calculation by using appropriate formulas.

Speed of Light

The speed of light, denoted by \( c \), is one of the most fundamental constants in physics. It is the speed at which electromagnetic waves travel through the vacuum of space. For most calculations involving electromagnetic waves, the speed of light is approximated as \( 3.00 \times 10^8 \, \text{m/s}\). This speed is incredibly fast and is consistent across all forms of electromagnetic radiation in a vacuum, whether they are visible light, radio waves, or X-rays. This constant not only helps us calculate the frequency of electromagnetic waves but also plays a vital role in Einstein’s theory of relativity. This constancy allows scientists to use the speed of light to determine distances in space and fully understand the behavior of light.

Physics Formulas

Physics equations are tools that help us solve specific questions about the world around us. One of the most common and useful formulas in physics for electromagnetic waves is the equation \( c = \lambda \cdot f \). Here’s a breakdown of this formula:

• \( \lambda \) (wavelength) is the distance between two wave peaks.
• \( f \) (frequency) is the number of wave crests that pass a point per second.
• \( c \) is the speed of light in a vacuum.

By rearranging the formula to \( f = \frac{c}{\lambda} \), you can easily solve problems that ask for the frequency, given the wavelength and speed of light. This approach shows the relationship between these three parameters and allows you to find any one value if the other two are known, making it an essential formula for physics students.