# B Beats frequency question

1. May 7, 2017

### Isaac0427

Consider this: two singers are both singing an A4. These singers, like any human, are not perfect. One sings 440 Hz and one sings 441 Hz. So, theoretically, I should hear an amplitude oscillation with a frequency of one second, right? I never seem to hear this kind of effect, though it should happen if both members of a duet sing the same note, right? It would seem highly improbable that both singers would be singing the same exact frequency. Why do I never hear beats?

The same thing for an orchestra. If the violin section is all playing the same note, if any of the violins are not tuned to the same exact frequency, there should be a beat. I don't hear these beats in orchestras either. Would the violins (or singers in the first example) just be 100% in tune or is there another physics concept explaining the absence of beats.

It just feels a little weird that no violin would even be a tenth of a hertz off.

Thanks.

2. May 7, 2017

If you have ever tuned up a musical instrument such as a guitar, the "beats" is what you listen for as you bring the string you are tuning to match the same note played (on a higher fret) of an adjacent string. When some members of an orchestra play notes out of tune, I think the disharmonious sound that you hear is often these "beats".

3. May 7, 2017

### Staff: Mentor

What is the lower range of your hearing? Can you hear a 1 hertz beat?

Wikipedia says that the lower range of human hearing is 31 hertz.

4. May 7, 2017

You hear a volume change that occurs at the "beat" frequency. The volume cycles up and down. You hear the note such as the 440 Hz A, but instead of a steady volume, if there is a f=435 Hz sound accompanying it, you'll get a volume change at 5 Hz.

Last edited: May 7, 2017
5. May 7, 2017

### pixel

Singers use vibrato, which might mask any beat frequency present. Violin players also.

6. May 7, 2017

### Isaac0427

That makes sense. The last question I just thought of is this: I simultaneously play an A4 and an A#4 on a piano. I should get about a 27 Hz beat frequency, but it doesn't appear to have that. I know that a frequency like that is hard to tell but when my computer generates it I can definitely tell the beats. Is there something about most musical instruments that beats can be masked?

7. May 7, 2017

### Staff: Mentor

Ok, I guess I was wrong. But hearing can be complex. What about a 440 tone and a 500 tone. Do you hear two pure tones with no interference? Or a 60 hz volume swing? Or 440/500/60 hertz tones?

Different effects at different beat frequencies? The OP was about 1 hertz beat.

When I push 1 on a phone, I hear the dual tone 697 and 1209 hertz. I hear no 512 hertz beat.

8. May 7, 2017

The "beat" that you hear in tuning a guitar string often starts out a several Hertz and in the process of getting it in tune, (by adjusting the tuning peg), you'll hear the beat frequency decrease steadily to zero= beats almost absent as you match the frequencies. $\\$ Editing... I think some of the harmonious sound that you hear when you play a C and a G at the same time is a combination of beat frequencies at higher frequencies that are subharmonics of the fundamental notes.

9. May 7, 2017

### Isaac0427

About the beats being "almost absent," if you play 440 Hz and 440.01 Hz at the same time, after ~40 seconds would you get a ~20 second period of a very low amplitude? That just seems weird to me, but it seems like it would be true. The weirder thing is it's implications on acoustics: even if your tuner is accurate to the .0001 Hz, if you need to play a note for a long time, the note will be nearly inaudible for quite a while. Am I understanding this correctly?

10. May 7, 2017

A very good question...I'm not an acoustics expert, but one problem that occurs with trying to make an ideal model of two point sources each at an individual frequency is that the wavelengths involved are reasonably large and the receiver, such as the human hearing the sound has two ears, so that the person who is the receiver isn't localized at a single point in space. If you use a simple model of the sounds though, intensity $I=(Acos(\omega_1 t)+Acos(\omega_2 t))^2=4 A^2(cos^2((\omega_1+\omega_2)t/2) cos^2((\omega_1-\omega_2)t/2)$. This last beat frequency term is $cos^2((\omega_1-\omega_2)t/2)= (1+cos((\omega_1-\omega_2)t))/2$ where $\omega=2 \pi f$ in all cases. This case would represent what I think would be considered 100% amplitude modulation. In practice, the modulation of the beats never cancels completely, and in many cases, e.g. if the notes are almost in tune, it can be harder to pick it up=i.e. I think the percentage of amplitude modulation might be much less, but it might take someone with more expertise in acoustics to give a more complete answer.

11. May 7, 2017

### Staff: Mentor

How far apart would you expect them to be, and why?

I would recommend that you take a sample of the same piano playing the same note once with a very long sustain and once staccato. Then look at the FFT of each sample.

Similarly with the beats that you expect to hear but are not hearing. Analyze the signals to get a good intuition for the topic

Last edited: May 7, 2017