What Frequencies Arise from a 4 ms Waveform Cycle?

[jon9986]

A complex waveform repeats every 4 ms. What are the frequencies of its Fourier components?

Thanks in advance.

 

[Andre]

So what would be the base frequency for a period of 4msec and how would you get the same sequence again.

What would be the lowest frequency that could be added to the first and that would repeat the same sequence again?

 

[M98Ranger]

The frequencies of the Fourier components of a complex waveform that repeats every 4 ms can be calculated using the formula: f = 1/T, where f is the frequency and T is the period. In this case, the period is 4 ms, so the frequency would be 1/0.004 = 250 Hz. This means that the waveform contains a fundamental frequency of 250 Hz.

In addition to the fundamental frequency, there will also be harmonics present in the waveform. Harmonics are integer multiples of the fundamental frequency, so in this case, the harmonics would be 500 Hz, 750 Hz, 1000 Hz, and so on. This is because the waveform repeats every 4 ms, so it also has a period of 4 ms.

It is important to note that the amplitudes of the harmonics may vary and can be affected by factors such as the shape and material of the vibrating object producing the sound. This is why different instruments or voices can produce different harmonics and have unique sounds.

In conclusion, the frequencies of the Fourier components of a complex waveform that repeats every 4 ms would include a fundamental frequency of 250 Hz and harmonics at integer multiples of this frequency.