Skip to main content
Ch 17: Superposition
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 17: SuperpositionProblem 13
Chapter 17, Problem 13

A carbon dioxide laser is an infrared laser. A CO2 laser with a cavity length of 53.00 cm oscillates in the m=100,000 mode. What are the wavelength and frequency of the laser beam?

Verified step by step guidance
1
The wavelength of the laser beam can be determined using the relationship between the cavity length and the mode number. For a standing wave in a laser cavity, the wavelength is given by: λ=2mL, where L is the cavity length and m is the mode number.
Substitute the given values into the formula: λ=2100,000(53.00) cm. Ensure the cavity length is in meters for consistency in SI units.
To find the frequency of the laser beam, use the relationship between the speed of light, wavelength, and frequency: c=λf, where c is the speed of light (approximately 3.00×10^8 m/s), λ is the wavelength, and f is the frequency.
Rearrange the formula to solve for frequency: f=cλ. Substitute the calculated wavelength and the speed of light into this equation.
Perform the calculations to determine the wavelength in meters and the frequency in hertz. Ensure all units are consistent throughout the process.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Laser Operation

Lasers operate on the principle of stimulated emission, where an excited atom or molecule releases a photon of light, which then stimulates other excited atoms to emit more photons. This process creates a coherent beam of light, characterized by its monochromaticity and directionality. In the case of a CO2 laser, the specific gas mixture and cavity design determine the wavelength and frequency of the emitted light.
Recommended video:
Guided course
08:22
Operations with Significant Figures

Wavelength and Frequency Relationship

Wavelength and frequency are inversely related properties of electromagnetic waves, described by the equation c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency. This relationship indicates that as the wavelength increases, the frequency decreases, and vice versa. Understanding this relationship is crucial for calculating the wavelength and frequency of the laser beam based on its mode of oscillation.
Recommended video:
Guided course
05:08
Circumference, Period, and Frequency in UCM

Mode of Oscillation

The mode of oscillation in a laser refers to the specific standing wave patterns that can form within the laser cavity. Each mode is characterized by a quantum number, which in this case is m=100,000 for the CO2 laser. The mode number helps determine the wavelength of the emitted light, as it relates to the length of the cavity and the number of wavelengths that fit within it, influencing the laser's output characteristics.
Recommended video:
Guided course
04:26
Oscillations in an LC Circuit
Related Practice
Textbook Question

A bass clarinet can be modeled as a 120-cm-long open-closed tube. A bass clarinet player starts playing in a 20° C room, but soon the air inside the clarinet warms to where the speed of sound is 352m/s . Does the fundamental frequency increase or decrease? By how much?

1
views
Textbook Question

What are the three longest wavelengths for standing waves on a 60 cm long string that is fixed at both ends?

1
views
Textbook Question

The two highest-pitch strings on a violin are tuned to 440 Hz (the A string) and 659 Hz (the E string). What is the ratio of the mass of the A string to that of the E string? Violin strings are all the same length and under essentially the same tension.

1
views
Textbook Question
The fundamental frequency of an open-open tube is 1500 Hz when the tube is filled with 0°C helium. What is its frequency when filled with 0°C air?
1
views
Textbook Question

Standing waves on a 1.0-m-long string that is fixed at both ends are seen at successive frequencies of 36 Hz and 48 Hz. Draw the standing-wave pattern when the string oscillates at 48 Hz.

2
views
Textbook Question

The lowest note on a grand piano has a frequency of 27.5 Hz. The entire string is 2.00 m long and has a mass of 400 g. The vibrating section of the string is 1.90 m long. What tension is needed to tune this string properly?

6
views