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

In summary, the frequency of the sum of two sine waves is the average of the frequencies of the individual waves. To calculate the frequency of the sum of multiple sine waves, you need to add the frequencies of all the individual waves and divide by the total number of waves. When sine waves of different frequencies are added, the resulting frequency will be between the frequencies of the individual waves. No, the frequency of the sum of sine waves can never be lower than the frequencies of the individual waves. The amplitude of the sine waves does not affect the frequency of their sum.
  • #1
sherled
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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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  • #2
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.
 

1. What is the frequency of the sum of two sine waves?

The frequency of the sum of two sine waves is the average of the frequencies of the individual waves. For example, if one wave has a frequency of 10 Hz and the other has a frequency of 20 Hz, the frequency of their sum would be (10 + 20)/2 = 15 Hz.

2. How do you calculate the frequency of the sum of multiple sine waves?

To calculate the frequency of the sum of multiple sine waves, you need to add the frequencies of all the individual waves and divide by the total number of waves. For example, if you have three waves with frequencies of 10 Hz, 20 Hz, and 30 Hz, the frequency of their sum would be (10 + 20 + 30)/3 = 20 Hz.

3. What happens to the frequency when sine waves of different frequencies are added?

When sine waves of different frequencies are added, the resulting frequency will be between the frequencies of the individual waves. The exact value will depend on the specific frequencies being added.

4. Can the frequency of the sum of sine waves ever be lower than the frequencies of the individual waves?

No, the frequency of the sum of sine waves can never be lower than the frequencies of the individual waves. This is because the lowest frequency component in the sum will always contribute to the overall frequency.

5. How does the amplitude of the sine waves affect the frequency of their sum?

The amplitude of the sine waves does not affect the frequency of their sum. The frequency is solely determined by the frequencies of the individual waves being added.

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