# Same frequency sounding different

• vcsharp2003
In summary, the sounds emitted by a guitar and sitar are of the same frequency, but they sound different because the waveform of guitar string is different from waveform of sitar string.f

#### vcsharp2003

Homework Statement
Why would two sounds having same frequency and loudness sound different to the human ear?
Relevant Equations
None
I was always thinking that frequency decides the type of sound we hear ( ex: high pitched squeaky sound). But then I read somewhere that loudness i.e. intensity can also affect the sound we hear. Still the quality of sound should depend only on frequency since loudness would simply make it more or less loud like making our music device's volume high or low.
So, I'm unable to answer this question since the two different sounds have the same frequency/loudness and so should feel the same.

Homework Statement:: Why would two sounds having same frequency and loudness sound different to the human ear?
Relevant Equations:: None

I was always thinking that frequency decides the type of sound we hear ( ex: high pitched squeaky sound). But then I read somewhere that loudness i.e. intensity can also affect the sound we hear. Still the quality of sound should depend only on frequency since loudness would simply make it more or less loud like making our music device's volume high or low.
So, I'm unable to answer this question since the two different sounds have the same frequency/loudness and so should feel the same.
Perhaps, a sound may have multiple frequencies with one dominant frequency, and it is this that causes different sounds from two sources having the same frequency.

Could also be
• a non-linearity in either the source or your hearing (or both)
• some frequencies may be below your hearing threshold when quieter

And as you noted, differing non-dominant frequencies. If you have the opportunity, listen to a Sine Wave and to a Square Wave of the same frequency. The square wave has many harmonics and sounds quite different.

Also note, it is not uncommon that your two ears have different frequency responses, especially as you age.

Cheers,
Tom

• vcsharp2003
Two factors can alter the timbre, or character, of the sound as heard:-
The shape of sound waves, even though of the same frequency, will later the harshness of the sound. A sine wave gives the smoothest sound and a jagged wave shape gives a rough sound.
The amplitude (or intensity) of the sound alters the frequency response of the ear. So if the sound has many frequency components, as for example from an orchestra, the high and low frequencies are emphasised at high listening levels. Some amplifiers have a "loudness" control, which will emphasise high and low frequencies if listening at low level. Have a look at Fletcher-Munson equal loudness curves.

• vcsharp2003 and Tom.G
If you have the opportunity, listen to a Sine Wave and to a Square Wave of the same frequency.
Is the square wave resulting from multiple waves which superimpose?

Is the square wave resulting from multiple waves which superimpose?
There is no difference between a square wave which is the sum of an infinite series of sine waves of various frequencies and a plain old square wave.

• vcsharp2003
It all depends what you exactly mean by the term "frequency". Its a polymorphic term having multiple meaning depending on the context.

Here you use it for example with two meaning, the frequency of a sine wave and the frequency of a square wave.

Yes a square wave of some frequency f, will not sound to us the same way like a sine wave of the same frequency, because they have different wave forms. Or if you know abit about Fourier series or Fourier transforms, the Fourier series and the Fourier transform of a square wave is different than those of a sine wave (of the same frequency).

• vcsharp2003
There is no difference between a square wave which is the sum of an infinite series of sine waves of various frequencies and a plain old square wave.

I was just wondering how a musical string instrument can emit square wave. Is the source of sound emitting square wave or the square wave is being formed by multiple sine waves being emitted by the source a few milliseconds apart? I think it should the latter.

It all depends what you exactly mean by the term "frequency". Its a polymorphic term having multiple meaning depending on the context.

Here you use it for example with two meaning, the frequency of a sine wave and the frequency of a square wave.

Yes a square wave of some frequency f, will not sound to us the same way like a sine wave of the same frequency, because they have different wave forms. Or if you know abit about Fourier series or Fourier transforms, the Fourier series and the Fourier transform of a square wave is different than those of a sine wave (of the same frequency).
A typical question asked is why a guitar and sitar emit sounds of same frequency, yet they sound different. The answer should be that the waveform of guitar string is different from waveform of sitar string. Is that correct or there are other reasons?

• PhDeezNutz and Delta2
I was just wondering how a musical string instrument can emit square wave. Is the source of sound emitting square wave or the square wave is being formed by multiple sine waves being emitted by the source a few milliseconds apart? I think it should the latter.
https://en.wikipedia.org/wiki/Square_wave#Fourier_analysis

• vcsharp2003
A typical question asked is why a guitar and sitar emit sounds of same frequency, yet they sound different. The answer should be that the waveform of guitar string is different from waveform of sitar string. Is that correct or there are other reasons?
The way I understand the human sense of hearing, the inner ear is a spiral structure with fibers that resonate at various frequencies. The brain gets the input from all of them. Effectively it is a sampling of a large but finite number of frequency bands within the sound wave. It is a Fourier analysis implemented in flesh and bone.

• PhDeezNutz and Delta2
In the animation I see at above link, the sine waves must be coming from some source(s). My question is how a musical instrument like guitar or sitar can produce multiple sine waves that superimpose to produce a square wave?

In the animation I see at above link, the sine waves must be coming from some source(s). My question is how a musical instrument like guitar or sitar can produce multiple sine waves that superimpose to produce a square wave?
I do not think that you have grasped the concept.

It is mathematics. The wave form has a particular shape. That same shape can be approximated as a sum of sine waves of various frequencies and amplitudes.

The sine waves do not need to actually exist. However, they are really there in the sense that the cilia in your inner ear will resonate with them whether they exist or not.

The output from a stringed instrument will not be a square wave.

• vcsharp2003
A typical question asked is why a guitar and sitar emit sounds of same frequency, yet they sound different. The answer should be that the waveform of guitar string is different from waveform of sitar string. Is that correct or there are other reasons?
Yes that is correct. In order for two sounds to sound exactly the same they must have identical waveforms, which also means identical Fourier seriers and identical Fourier transforms.

• vcsharp2003
I do not think that you have grasped the concept.

It is mathematics. The wave form has a particular shape. That same shape can be approximated as a sum of sine waves of various frequencies and amplitudes.

The sine waves do not need to actually exist. However, they are really there in the sense that the cilia in your inner ear will resonate with them whether they exist or not.
So you're saying that some sources of sound are capable of producing a square wave? I'm still confused since I'm not getting a direct answer to my question. But I'll keep reading your answer to understand it more, in case I've missed something.

• Delta2
So you're saying that some sources of sound are capable of producing a square wave?
Note from the Wiki article:

"An ideal mathematical square wave changes between the high and the low state instantaneously, and without under- or over-shooting. This is impossible to achieve in physical systems, as it would require infinite bandwidth."

• vcsharp2003
Note from the Wiki article:

"An ideal mathematical square wave changes between the high and the low state instantaneously, and without under- or over-shooting. This is impossible to achieve in physical systems, as it would require infinite bandwidth."
If I'm getting this correctly, then it means that a source cannot produce a square wave. But a source can produce multiple sine waves that can produce a square wave due to superposition, or this statement is incorrect?

If I'm getting this correctly, then it means that a source cannot produce a square wave. But a source can produce multiple sine waves that can produce a square wave due to superposition, or this statement is incorrect?
Neither is correct. The perfect square wave requires infinite bandwidth, that means infinite range of frequencies (of sine waves , or simply called harmonic frequencies) which systems in nature simply can't do. A sound source can produce using its limited bandwidth a waveform that is approximately a square wave.

• jbriggs444 and vcsharp2003
Neither is correct. The perfect square wave requires infinite bandwidth, that means infinite range of frequencies (of sine waves , or simply called harmonic frequencies) which systems in nature simply can't do. A sound source can produce using its limited bandwidth a waveform that is approximately a square wave.
Thanks, that makes sense now.

Sorry for being too inquisitive, but is there a real world example of a source producing an approximate square wave?

Thanks, that makes sense now.

Sorry for being too inquisitive, but is there a real world example of a source producing an approximate square wave?
I am not aware of any musical instruments (my knowledge in that sector is very limited though) but using computer software we can make an approximate square wave form which then we can hear through our sound card and speakers.

• vcsharp2003
• Delta2
It would be nice if one could hear a square wave online using some simulator. It would be helpful to students like me.
The theory is gently presented in this one:

[Edit:]
My ears, headphones, or both, stop above 6kHz in the next one; also, laptop computers may not be audible at the first (100Hz) demo.
[/Edit]
You can actually hear the diffference in direct comparisons here:

The above were found with:
Which was the fifth entry in the Google search in I posted two posts above!

(The trick to finding such things is once you get some decent responses from Google, start following links down thru a few levels to find related responses. As you can see from all the above, it can take a bit of effort!)

Cheers,
Tom

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• • vcsharp2003 and Delta2
The theory is gently presented in this one:

[Edit:]
My ears, headphones, or both, stop above 6kHz in the next one; also, laptop computers may not be audible at the first (100Hz) demo.
[/Edit]
You can actually hear the diffference in direct comparisons here:

The above were found with: