An Ultraviolet Wave Traveling Through A Vacuum Has A Wavelength Of 4.0 × 10 − 7 M 4.0 \times 10^{-7} \, \text{m} 4.0 × 1 0 − 7 M . The Wave's Frequency, Written In Scientific Notation To Two Significant Figures, Is □ × 10 14 Hz \square \times 10^{14} \, \text{Hz} □ × 1 0 14 Hz .

Mar 9, 2025 by ADMIN 280 views

Understanding the Relationship Between Wavelength and Frequency of Ultraviolet Waves

Introduction

In the realm of physics, the study of electromagnetic waves is a fundamental concept that has far-reaching implications in various fields, including optics, electronics, and quantum mechanics. One of the key aspects of electromagnetic waves is the relationship between their wavelength and frequency. In this article, we will delve into the world of ultraviolet waves and explore how their wavelength and frequency are interconnected.

The Wavelength of Ultraviolet Waves

The wavelength of an electromagnetic wave is a measure of the distance between two consecutive peaks or troughs of the wave. In the case of the ultraviolet wave mentioned in the problem, its wavelength is given as $4.0 \times 10^{-7} \, \text{m}$ . This value represents the distance between two consecutive peaks or troughs of the wave, and it is a fundamental property of the wave that determines its behavior and interactions with matter.

The Frequency of Ultraviolet Waves

The frequency of an electromagnetic wave, on the other hand, is a measure of the number of oscillations or cycles of the wave per second. It is typically denoted by the symbol $f$ and is measured in units of hertz (Hz). In the case of the ultraviolet wave mentioned in the problem, its frequency is given as $\square \times 10^{14} \, \text{Hz}$ . This value represents the number of oscillations or cycles of the wave per second, and it is a critical property of the wave that determines its energy and interactions with matter.

The Relationship Between Wavelength and Frequency

The relationship between the wavelength and frequency of an electromagnetic wave is given by the speed of light equation, which states that the speed of light in a vacuum is equal to the product of the wavelength and frequency of the wave. Mathematically, this can be expressed as:

$c = \lambda \times f$

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

Solving for Frequency

Using the given wavelength of $4.0 \times 10^{-7} \, \text{m}$ and the speed of light in a vacuum of $3.0 \times 10^8 \, \text{m/s}$ , we can solve for the frequency of the ultraviolet wave using the speed of light equation:

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

Substituting the given values, we get:

$f = \frac{3.0 \times 10^8 \, \text{m/s}}{4.0 \times 10^{-7} \, \text{m}}$

Simplifying the expression, we get:

$f = 7.5 \times 10^{14} \, \text{Hz}$

Therefore, the frequency of the ultraviolet wave is $7.5 \times 10^{14} \, \text{Hz}$ .

Conclusion

In conclusion, the relationship between the wavelength and frequency of an electromagnetic wave is a fundamental concept in physics that has far-reaching implications in various fields. By understanding this relationship, we can determine the frequency of an electromagnetic wave given its wavelength, and vice versa. In this article, we have explored the relationship between the wavelength and frequency of an ultraviolet wave and have solved for its frequency using the speed of light equation.

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.

Discussion

What are some real-world applications of the relationship between wavelength and frequency of electromagnetic waves? How does this relationship impact our understanding of the behavior of light and other forms of electromagnetic radiation? Share your thoughts and insights in the comments below!
Frequently Asked Questions: Understanding the Relationship Between Wavelength and Frequency of Ultraviolet Waves

Introduction

In our previous article, we explored the relationship between the wavelength and frequency of ultraviolet waves and solved for the frequency of a given wave. In this article, we will address some of the most frequently asked questions related to this topic and provide a deeper understanding of the concepts involved.

Q&A

Q: What is the relationship between wavelength and frequency of electromagnetic waves?

A: The relationship between wavelength and frequency of electromagnetic waves is given by the speed of light equation, which states that the speed of light in a vacuum is equal to the product of the wavelength and frequency of the wave. Mathematically, this can be expressed as:

$c = \lambda \times f$

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

Q: How do I determine the frequency of an electromagnetic wave given its wavelength?

A: To determine the frequency of an electromagnetic wave given its wavelength, you can use the speed of light equation:

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

Substitute the given values of $c$ and $\lambda$ into the equation and solve for $f$ .

Q: What is the significance of the speed of light in the relationship between wavelength and frequency?

A: The speed of light is a fundamental constant that determines the relationship between wavelength and frequency of electromagnetic waves. It is a measure of the speed at which electromagnetic waves propagate through a vacuum and is a critical component of the speed of light equation.

Q: Can the frequency of an electromagnetic wave be greater than the speed of light?

A: No, the frequency of an electromagnetic wave cannot be greater than the speed of light. The speed of light is a fundamental limit that determines the maximum speed at which electromagnetic waves can propagate through a vacuum.

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

A: The relationship between wavelength and frequency of electromagnetic waves has numerous real-world applications, including:

Optics: Understanding the relationship between wavelength and frequency is crucial in the design and development of optical systems, such as telescopes and microscopes.
Electronics: The relationship between wavelength and frequency is essential in the design and development of electronic devices, such as radios and televisions.
Medical Imaging: The relationship between wavelength and frequency is critical in medical imaging techniques, such as MRI and CT scans.

Q: How does the relationship between wavelength and frequency impact our understanding of the behavior of light and other forms of electromagnetic radiation?

A: The relationship between wavelength and frequency has a profound impact on our understanding of the behavior of light and other forms of electromagnetic radiation. It allows us to predict the behavior of electromagnetic waves in various situations and has far-reaching implications in various fields, including optics, electronics, and medical imaging.

Conclusion

In conclusion, the relationship between wavelength and frequency of electromagnetic waves is a fundamental concept that has far-reaching implications in various fields. By understanding this relationship, we can determine the frequency of an electromagnetic wave given its wavelength, and vice versa. In this article, we have addressed some of the most frequently asked questions related to this topic and provided a deeper understanding of the concepts involved.

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.

Discussion

What are some other real-world applications of the relationship between wavelength and frequency of electromagnetic waves? How does this relationship impact our understanding of the behavior of light and other forms of electromagnetic radiation? Share your thoughts and insights in the comments below!

An Ultraviolet Wave Traveling Through A Vacuum Has A Wavelength Of 4.0 × 10 − 7 M 4.0 \times 10^{-7} \, \text{m} 4.0 × 1 0 − 7 M . The Wave's Frequency, Written In Scientific Notation To Two Significant Figures, Is □ × 10 14 Hz \square \times 10^{14} \, \text{Hz} □ × 1 0 14 Hz .

Introduction

The Wavelength of Ultraviolet Waves

The Frequency of Ultraviolet Waves

The Relationship Between Wavelength and Frequency

Solving for Frequency

Conclusion

References

Further Reading

Discussion

Introduction

Q&A

Q: What is the relationship between wavelength and frequency of electromagnetic waves?

Q: How do I determine the frequency of an electromagnetic wave given its wavelength?

Q: What is the significance of the speed of light in the relationship between wavelength and frequency?

Q: Can the frequency of an electromagnetic wave be greater than the speed of light?

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

Q: How does the relationship between wavelength and frequency impact our understanding of the behavior of light and other forms of electromagnetic radiation?

Conclusion

References

Further Reading

Discussion