Wave Number Range: 633nm Laser & 100MHz Radio

• Winzer
In summary, the wave number range in a 633nm laser and a 100MHz radio refers to the frequencies that these devices are capable of producing. Wave numbers are inversely proportional to wavelength and directly proportional to frequency, meaning that as the wave number increases, the wavelength decreases and the frequency increases. While a 633nm laser may also produce other wavelengths, its primary wavelength is 633nm. The frequency of a 100MHz radio is determined by its design and components, and this frequency is commonly used for communication purposes.
Winzer

Homework Statement

A 1ns pulse of electromagnetic waves would be 30cm long.
a) Consider such a pulse of 633 nm wavelength laser light. Find its central wavenumber and the range of wave numbers it is comprised of.
b) Repeat a except for a 1ns pulse of 100MHz radio
waves.

Homework Equations

$$k=\frac{2\pi}{\lambda}$$

The Attempt at a Solution

I got the central wavenumber with the above equation. But I am at a lost on where to go from there.

Do I have to deal with the gaussian wave packet & fouier transform?

The central wavenumber for the 633nm laser light would be 9.95 x 10^6 m^-1. To find the range of wave numbers, we need to consider the frequency range of the pulse. Since it is a 1ns pulse, the frequency would be 1 GHz (1/1ns). Using the relation v=fλ, we can find the wavelength range to be 0.3m to 300m. Plugging these values into the wavenumber equation, we get a range of 3.33 x 10^6 m^-1 to 3.33 x 10^9 m^-1. This means that the pulse of 633nm laser light is comprised of a range of wave numbers from 3.33 x 10^6 m^-1 to 3.33 x 10^9 m^-1.

For the 1ns pulse of 100MHz radio waves, the central wavenumber would be 3 x 10^8 m^-1 (using the equation k=\frac{2\pi}{\lambda}). The frequency range for this pulse would be 100MHz to 100GHz, giving a wavelength range of 3m to 3 x 10^4 m. Plugging these values into the wavenumber equation, we get a range of 3.33 x 10^7 m^-1 to 3.33 x 10^11 m^-1. This means that the pulse of 100MHz radio waves is comprised of a range of wave numbers from 3.33 x 10^7 m^-1 to 3.33 x 10^11 m^-1.

1. What is the significance of the wave number range in a 633nm laser and a 100MHz radio?

The wave number range refers to the range of frequencies that can be produced by a specific type of laser or radio. In the case of a 633nm laser, this refers to the range of frequencies within the visible light spectrum, specifically in the red-orange range. For a 100MHz radio, this range refers to the frequencies within the radio wave spectrum, which is typically used for communication purposes.

2. How are wave numbers related to wavelength and frequency?

Wave numbers, or wavenumbers, are inversely proportional to wavelength and directly proportional to frequency. This means that as the wave number increases, the wavelength decreases, and the frequency increases. This relationship is governed by the equation: wave number = 1/wavelength = frequency/c.

3. Can a 633nm laser also produce other wavelengths besides 633nm?

Yes, a 633nm laser can produce a range of wavelengths depending on the specific design and capabilities of the laser. However, the primary wavelength produced will be 633nm, as this is the specific frequency that the laser is designed to emit.

4. How is the frequency of a 100MHz radio determined?

The frequency of a radio is determined by the design and components of the radio itself. In the case of a 100MHz radio, this means that the radio is designed to produce radio waves with a frequency of 100 million hertz (MHz), or 100 million cycles per second. This frequency is typically set and regulated by the radio's internal oscillator.

5. What applications are these specific wave number ranges commonly used for?

The 633nm laser is commonly used in various scientific and industrial applications, such as microscopy, spectroscopy, and laser printing. The 100MHz radio frequency is often used for communication purposes, such as AM and FM radio, television broadcasting, and mobile phone networks.

Replies
5
Views
2K
Replies
3
Views
1K
Replies
4
Views
2K
Replies
5
Views
1K
Replies
7
Views
1K
Replies
10
Views
1K
Replies
14
Views
2K
Replies
1
Views
2K
Replies
7
Views
1K
Replies
1
Views
1K