An FM Radio Station Broadcasts At $9.23 \times 10^7 , \text{Hz}$. Given That The Radio Waves Travel At $3.00 \times 10^8 , \text{m/s}$, What Is The Wavelength Of These Waves?A. 0.308 M B. 2.77 M C. 3.25 M D. 6.50 M

Introduction

Radio waves are a type of electromagnetic wave that is commonly used for communication purposes. They have a wide range of applications, including broadcasting, navigation, and wireless communication. In this article, we will explore the relationship between the frequency and wavelength of radio waves, and use this knowledge to calculate the wavelength of radio waves broadcast by a given FM radio station.

The Relationship Between Frequency and Wavelength

The frequency and wavelength of a wave are two fundamental properties that are closely related. The frequency of a wave is defined as the number of oscillations or cycles per second, and is typically measured in units of hertz (Hz). The wavelength of a wave, on the other hand, is defined as the distance between two consecutive points on the wave that are in phase with each other, and is typically measured in units of meters (m).

The relationship between frequency and wavelength is given by the speed of the wave, which is a constant for a given medium. In the case of radio waves, the speed is approximately equal to the speed of light in a vacuum, which is $3.00 \times 10^8 \, \text{m/s}$. This relationship can be expressed mathematically as:

$$\lambda = \frac{c}{f}$$

where $\lambda$ is the wavelength, $c$ is the speed of the wave, and $f$ is the frequency.

Calculating the Wavelength of Radio Waves

Given that the radio waves broadcast by the FM radio station have a frequency of $9.23 \times 10^7 \, \text{Hz}$, and the speed of the wave is $3.00 \times 10^8 \, \text{m/s}$, we can use the equation above to calculate the wavelength of these waves.

Plugging in the values, we get:

$$\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{9.23 \times 10^7 \, \text{Hz}}$$

Simplifying the expression, we get:

$$\lambda = 3.25 \, \text{m}$$

Therefore, the wavelength of the radio waves broadcast by the FM radio station is $3.25 \, \text{m}$.

Conclusion

In this article, we have explored the relationship between the frequency and wavelength of radio waves, and used this knowledge to calculate the wavelength of radio waves broadcast by a given FM radio station. We have shown that the wavelength of these waves is $3.25 \, \text{m}$, which is a fundamental property of the wave that is determined by its frequency and speed.

Discussion

The calculation of the wavelength of radio waves is an important application of the relationship between frequency and wavelength. It is used in a wide range of fields, including physics, engineering, and telecommunications. In addition to calculating the wavelength of radio waves, this relationship is also used to design and optimize communication systems, such as radio transmitters and receivers.

References

• [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics (10th ed.). John Wiley & Sons.
• [2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers (10th ed.). Cengage Learning.

Glossary

• Frequency: The number of oscillations or cycles per second, typically measured in units of hertz (Hz).
• Wavelength: The distance between two consecutive points on the wave that are in phase with each other, typically measured in units of meters (m).
• Speed: The rate at which a wave propagates through a medium, typically measured in units of meters per second (m/s).
• Radio waves: A type of electromagnetic wave that is commonly used for communication purposes.
  

Introduction

In our previous article, we explored the relationship between the frequency and wavelength of radio waves, and used this knowledge to calculate the wavelength of radio waves broadcast by a given FM radio station. In this article, we will answer some of the most frequently asked questions about radio waves and wavelength.

Q: What is the relationship between frequency and wavelength?

A: The relationship between frequency and wavelength is given by the speed of the wave, which is a constant for a given medium. In the case of radio waves, the speed is approximately equal to the speed of light in a vacuum, which is $3.00 \times 10^8 \, \text{m/s}$. This relationship can be expressed mathematically as:

$$\lambda = \frac{c}{f}$$

where $\lambda$ is the wavelength, $c$ is the speed of the wave, and $f$ is the frequency.

Q: How do I calculate the wavelength of a radio wave?

A: To calculate the wavelength of a radio wave, you need to know the frequency of the wave and the speed of the wave. You can use the equation above to calculate the wavelength:

$$\lambda = \frac{c}{f}$$

For example, if the frequency of the wave is $9.23 \times 10^7 \, \text{Hz}$ and the speed of the wave is $3.00 \times 10^8 \, \text{m/s}$, the wavelength of the wave would be:

$$\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{9.23 \times 10^7 \, \text{Hz}}$$

Simplifying the expression, we get:

$$\lambda = 3.25 \, \text{m}$$

Q: What is the difference between wavelength and frequency?

A: Wavelength and frequency are two fundamental properties of a wave that are closely related. The frequency of a wave is defined as the number of oscillations or cycles per second, and is typically measured in units of hertz (Hz). The wavelength of a wave, on the other hand, is defined as the distance between two consecutive points on the wave that are in phase with each other, and is typically measured in units of meters (m).

Q: Can I use the same equation to calculate the wavelength of different types of waves?

A: Yes, the equation above can be used to calculate the wavelength of different types of waves, including radio waves, light waves, and sound waves. However, the speed of the wave will be different for each type of wave. For example, the speed of light in a vacuum is approximately $3.00 \times 10^8 \, \text{m/s}$, while the speed of sound in air is approximately $343 \, \text{m/s}$.

Q: What are some real-world applications of the relationship between frequency and wavelength?

A: The relationship between frequency and wavelength has many real-world applications, including:

• Designing and optimizing communication systems, such as radio transmitters and receivers
• Calculating the wavelength of radio waves broadcast by FM radio stations
• Understanding the behavior of light waves and their interaction with matter
• Designing and optimizing optical communication systems, such as fiber optic cables

Conclusion

In this article, we have answered some of the most frequently asked questions about radio waves and wavelength. We have shown that the relationship between frequency and wavelength is a fundamental property of waves that is used in a wide range of applications. We hope that this article has been helpful in understanding this important concept.

References

• [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics (10th ed.). John Wiley & Sons.
• [2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers (10th ed.). Cengage Learning.

Glossary

• Frequency: The number of oscillations or cycles per second, typically measured in units of hertz (Hz).
• Wavelength: The distance between two consecutive points on the wave that are in phase with each other, typically measured in units of meters (m).
• Speed: The rate at which a wave propagates through a medium, typically measured in units of meters per second (m/s).
• Radio waves: A type of electromagnetic wave that is commonly used for communication purposes.