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

#### ljmcdonald

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
C = lambda/T

3. 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.
1. The problem statement, all variables and given/known data
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.

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

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

3. 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.

#### berkeman

Mentor
1. The problem statement, all variables and given/known data
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?

2. Relevant equations
C = lambda/T

3. 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.
1. The problem statement, all variables and given/known data
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.

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

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

3. 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?

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