Wavelengths of a laser pulse and inductance in tuning of an FM radio

In summary, the conversation discusses two problems regarding pulsed lasers and FM radio tuning circuits. For the first problem, the wavelength and pulse duration are given, and the goal is to determine the number of wavelengths within the pulse and the minimum pulse duration needed for only one wavelength. For the second problem, a fixed capacitor and frequency range are given, and the goal is to calculate the range of inductance values needed for tuning and find the minimum and maximum inductance in nH. Further calculations and possible calculator entry errors are mentioned.
  • #1
ljmcdonald
1
0

Homework Statement


Pulsed lasers used for science and medicine produce very brief bursts of electromagnetic energy. If the laser light wavelength is 532 nm, and the pulse lasts for 37 ps,
(a) how many wavelengths are found within the laser pulse?

(b) How brief would the pulse need to be to fit only one wavelength?


Homework Equations


C = lambda/T


The Attempt at a Solution



This problem seemed straightforward to me. I need to find wavelengths, so I divided 532 * 10^-9 / 37 * 10 ^-12. I got 14378.378 wavelengths. This is marked incorrect. For part b, I assume C is 1 and so the time would have to equal the length of the wavelength. Therefore time should be 532 ns, or 532*10^-9 s. This was also incorrect.

Problem 2.

Homework Statement


A certain FM radio tuning circuit has a fixed capacitor C = 635 pF. Tuning is done by a variable inductance.
What range of values must the inductance have to tune stations from 88 MHz to 108 MHz?
Find Lmin and Lmax in nH.

Homework Equations


f = 1/sqrt(LC)/2pi.

I solved for L and got the equation L = 1/((2*pi*f)^2 * C)


The Attempt at a Solution



Plugging the numbers in I get 1/((2 * pi * 88*10^6)^2 * 635 * 10^-12)

This gives me 5.15 nH and I get 3.419 nH for 108 MHz. These are both marked incorrect.

Any help appreciated.
 
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  • #2
ljmcdonald said:

Homework Statement


Pulsed lasers used for science and medicine produce very brief bursts of electromagnetic energy. If the laser light wavelength is 532 nm, and the pulse lasts for 37 ps,
(a) how many wavelengths are found within the laser pulse?

(b) How brief would the pulse need to be to fit only one wavelength?


Homework Equations


C = lambda/T


The Attempt at a Solution



This problem seemed straightforward to me. I need to find wavelengths, so I divided 532 * 10^-9 / 37 * 10 ^-12. I got 14378.378 wavelengths. This is marked incorrect. For part b, I assume C is 1 and so the time would have to equal the length of the wavelength. Therefore time should be 532 ns, or 532*10^-9 s. This was also incorrect.

Problem 2.

Homework Statement


A certain FM radio tuning circuit has a fixed capacitor C = 635 pF. Tuning is done by a variable inductance.
What range of values must the inductance have to tune stations from 88 MHz to 108 MHz?
Find Lmin and Lmax in nH.

Homework Equations


f = 1/sqrt(LC)/2pi.

I solved for L and got the equation L = 1/((2*pi*f)^2 * C)


The Attempt at a Solution



Plugging the numbers in I get 1/((2 * pi * 88*10^6)^2 * 635 * 10^-12)

This gives me 5.15 nH and I get 3.419 nH for 108 MHz. These are both marked incorrect.

Any help appreciated.

On problem #1, you need to use the speed of light as part of the calculations.

On problem #2, I think it may just be a calculator entry issue. I think your equation for L is correct, but I got 5.151nH and 3.420nH. How many sig figs are you supposed to put in your answer?
 

What is the relationship between the wavelengths of a laser pulse and inductance in tuning of an FM radio?

The wavelengths of a laser pulse and inductance in tuning of an FM radio are not directly related. The wavelength of a laser pulse refers to the distance between two consecutive peaks or troughs of the laser's electromagnetic wave, while inductance in tuning of an FM radio refers to the ability of the radio's circuit to store energy in the form of a magnetic field. However, both wavelengths and inductance can affect the frequency of the electromagnetic waves being emitted or received, which can impact the functionality of a laser or FM radio.

How does the wavelength of a laser pulse affect its characteristics?

The wavelength of a laser pulse can affect its characteristics in several ways. For example, shorter wavelengths typically have higher energy and can penetrate or interact with materials more easily. Longer wavelengths, on the other hand, may be better for long-distance communication as they can travel through the atmosphere with less interference. The exact characteristics of a laser pulse also depend on the specific type of laser being used.

How does inductance play a role in tuning an FM radio?

Inductance is an essential component in the circuit of an FM radio. It helps to regulate the flow of current and maintain a stable frequency for the radio's reception. The inductance of the circuit can be adjusted by changing the number of coils or the size of the coils, which allows for tuning to different frequencies. Without inductance, an FM radio would not be able to receive or transmit signals accurately.

Can the wavelengths of a laser pulse be tuned or adjusted?

Yes, the wavelength of a laser pulse can be tuned or adjusted in certain types of lasers. For example, in a tunable laser, the wavelength can be changed by adjusting the optical cavity or the refractive index of the laser's medium. This allows for a more precise control of the laser's output and enables it to be used for various applications.

What factors can affect the inductance in tuning of an FM radio?

Several factors can impact the inductance in tuning of an FM radio, including the number and size of coils, the type of material used for the coils, and the surrounding environment. Changes in these factors can alter the inductance and, therefore, affect the frequency of the radio's reception. Additionally, interference from other electronic devices or nearby objects can also impact the inductance and tuning of the FM radio.

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