How is the Angular Frequency of a Sine Wave Calculated?

Finally, remember that the angular frequency (in radians / second) is the same as 2 * PI * F (in Hz).In summary, the conversation discusses finding the angular frequency from a given picture and mentions the value of 1571 as the answer. It also suggests a misprint in the given data and provides a way to calculate the frequency and angular frequency using the period and complete cycle of a sinewave.
  • #1
randomuser241
1
0

Homework Statement



Please see the attached picture. I need help finding the angular frequency. The answer is 1571 but I don't know how they arrived at the solution. From the picture it looks like the period is 2pi but this would give an angular freq. of 1.


Homework Equations



w=2pi(f)=2pi/T


The Attempt at a Solution


see above
 

Attachments

  • sine wave.jpg
    sine wave.jpg
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  • #2
welcome to pf!

hi randomuser241! welcome to pf! :smile:

(have a pi: π :wink:)
randomuser241 said:
I need help finding the angular frequency. The answer is 1571 but I don't know how they arrived at the solution. From the picture it looks like the period is 2pi but this would give an angular freq. of 1.

well, 1571 = 500 π :rolleyes: …

i think that 8mA at the bottom must be a misprint for 8 ms (or is it 4 ms?) :smile:​
 
  • #3
4 mS I think. Sloppy misprint.

To get the frequency (in Hz) you can work out F = 1 / T where T = period = 0.004 seconds.

Then, one complete cycle of a sinewave is 2 * PI radians or 6.28318 radians.

So, you can work out how many radians occur per second at this frequency.
 

FAQ: How is the Angular Frequency of a Sine Wave Calculated?

What is the formula for calculating the angular frequency of a sine wave?

The formula for calculating the angular frequency of a sine wave is ω = 2πf, where ω is the angular frequency in radians per second and f is the frequency in cycles per second (Hz).

How does the angular frequency affect the shape of a sine wave?

The angular frequency determines the rate at which the sine wave oscillates. A higher angular frequency results in a shorter period and a more condensed waveform, while a lower angular frequency results in a longer period and a more spread out waveform.

What is the relationship between angular frequency and wavelength in a sine wave?

The angular frequency and wavelength are inversely proportional in a sine wave. This means that as the angular frequency increases, the wavelength decreases, and vice versa.

Can the angular frequency of a sine wave be negative?

Yes, the angular frequency of a sine wave can be positive or negative. A positive angular frequency indicates a clockwise rotation, while a negative angular frequency indicates a counterclockwise rotation.

How does the amplitude of a sine wave affect the angular frequency?

The amplitude of a sine wave does not affect the angular frequency. The angular frequency is solely determined by the frequency of the wave and is independent of its amplitude.

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