What is the frequency of the sum of several sine waves?

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SUMMARY

The combined frequency of the sine waves represented by the equation y(t) = sin(2π10t) + sin(2π50t) + sin(2π100t) is determined by the lowest frequency component, which is 10 Hz. While the individual frequencies of 10 Hz, 50 Hz, and 100 Hz exist, the overall waveform is periodic with a fundamental period of 0.1 seconds, dictated by the 10 Hz sine wave. The concept of the least common multiple (LCM) does not apply in this context, as the resulting waveform is not a simple sinusoidal wave but a complex periodic waveform.

PREREQUISITES
  • Understanding of sine wave properties and frequencies
  • Knowledge of periodic functions and their characteristics
  • Familiarity with concepts of least common multiple (LCM) and highest common factor (HCF)
  • Basic grasp of waveform analysis in signal processing
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  • Study the concept of Fourier series to analyze complex waveforms
  • Learn about harmonic frequencies and their impact on signal composition
  • Explore the principles of signal superposition in wave theory
  • Investigate the effects of phase shifts on combined sine waves
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Students and professionals in physics, electrical engineering, and signal processing who are interested in understanding the behavior of combined waveforms and their frequencies.

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I am given three sine waves with individual frequency being 10 Hz, 50 Hz, and 100 Hz.
What is the frequency of the following :

y(t) = sin(2π10t) + sin(2π50t) + sin(2π100t)​

Is it simply 100, the LCM of all the sin waves? If not, How to calculate the frequency of y(t) ?​
 
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I would say 10Hz, the HCF of the frequencies.
All three frequencies are still present, combining to give a non-sinusoidal waveform. This combined waveform is periodic over 0.1sec, due to the 10Hz component.
 

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