# Distinguishing the difference between the same note on different instruments

1. Dec 30, 2008

### clairez93

1. The problem statement, all variables and given/known data

The "A" on a trumpet and a clarinet have the same pitch, but the two are clearly distinguishable. Which property is most important in enabling one to distinguish between these two instruments?

A) intensity
B) fundamental frequency
C) displacement amplitude
D) pressure amplitude
E) harmonic content

2. Relevant equations

n/a

3. The attempt at a solution

I defined the terms.

Intensity: the rate at which sound waves transmit energy per unit area
Fundamental frequency:the first standing wave for which the harmonic number n is 1
Displacement amplitude: the maximum displacement a wave travels
Pressure amplitude: the places of maximum pressure for a sound wave
Harmonic content: the number and relative intensity of the upper harmonics present in the sound

I am not sure how these terms relate to the sound or pitch of an "A" note, however.

2. Dec 30, 2008

### marcusl

Well, which ones matter to your ear in determining which instrument produced the sound?
In a previous post, you discussed certain properties pertaining to sound produced by a string. How might a trumpet differ from the string?

3. Dec 30, 2008

### clairez93

I think I can rule out intensity, because that is just the loudness of a sound, as well as pressure, since I don't think that has anything to do with how the ear picks up the sound. Perhaps, fundamental frequency too because this doesn't determine the pitch of the "A" note?
A trumpet is different because it consists of sound tubes, so the waves are longitudinal, not transverse like in a string.

4. Dec 30, 2008

### marcusl

Excellent so far! How about c and d, think about how they relate to a.

True, but I was thinking more about constraints on the wave. A string is fixed on both ends, and that determines which harmonics are allowed. How about a trumpet? What can you say about constraints on the column of air inside?

5. Dec 30, 2008

### clairez93

The displacement amplitude, I think that is what determines the fundamental frequency of a sound, and I think the pressure amplitude determines the intensity.

A trumpet is a sound tube with one end closed, so the harmonic numbers would have to be odd?

6. Dec 30, 2008

### marcusl

No, amplitudes are related to intensity--in fact, intensity is generally the square of an amplitude.
Exactly! Compare that to a string, where all harmonics are allowed and you see one reason (answer "E") that instruments sound different. Clarinets and trumpets are both stopped tubes, however, so the differences between their sounds have to do with additional changes in the harmonic structure due to:
* different materials (wood absorbs some sounds, brass generally does not)
* different excitation (vibrating lips and vibrating wooden reeds are different)
* finger holes (opening a small hole in the side of the clarinet alters the properties of the stopped tube)
* differing pipe cross-sections versus length

Last edited: Dec 30, 2008
7. Jan 1, 2009

### Gnosis

Of your choices, “harmonic content” is the best of the available choices, but it is merely one vital property of several that bear great significance in identifying an instrument by the nature of its audio. An overall term known as “timbre” refers to an instrument’s tone, as well as its harmonic content and its unique wave-shape (ADSR envelope).

When programming the ADSR (Attack, Delay, Sustain, Release) envelope of a synthesizer (for which I have decades of experience), it becomes abundantly evident that these 4 attributes are of significant importance in reproducing the type of sound that an instrument makes. For instance, by merely shortening the decay and sustain rates of a piano wave-shape, the piano timbre can be made to sound like a couple of wood blocks or sticks being clicked together, which of course, is an altogether different sound from that of a piano even though the tone and harmonic values have not been altered.

The sound of a trumpet can easily be made to sound like an organ simply by altering the ADSR envelope even though the identical tone and harmonics are still present at the same intensities. This makes the ADSR envelope a key aspect of an instrument’s timbre though it could never exclusively do so, as timbre requires appropriate tone as well as harmonics. For instance, retaining the same ADSR settings used to produce the envelope of a Tuba would be impossible if the timbre were changed to a mellow flute voice. I hope this was helpful.