In order to explore the physics behind a trumpet's sound production, we must first understand the basic background knowledge about sound and its properties, so.....
What Is Sound?
Sound is a form of energy produced by vibrating objects detectable by sensory organs; our ears. Sound waves are mechanical waves, meaning there must be a medium for the energy of sound to travel in. In instruments, the transmission of sound is typically by air.
When traveling through gas, the waves consist of differences in pressure as energy pass through the medium. Regions where particles are closer (higher pressure) are called compressions and regions where they are farther apart (lower pressure) are called rarefaction. |
Diagram displays these regions of pressure differences
This Characteristic is found in longitudinal waves; waves which particle vibrates parallel to the direction of the flow of energy |
Characteristics of a wave
Viewing the wave on a graph, we can see some of the characteristics it displays.
(NOTE; graph represents horizontal displacement in the case of a sound wave) -Amplitude; the maximum displacement of a wave from its equilibrium point, determines the energy and also the volume in a sound wave NOTE; it is only the energy that travels through the medium, the actual particles are fixed and do not travel with the wave. -Wave length; the distance between two similar points in successive identical cycles Although not shown in the picture -Frequency; the number of complete cycles that occur in a unit of time. (measured in hertz; # of cycles/ per 1 second) The frequency determines the pitch of a sound; the higher the frequency, the higher the pitch |
To find the speed of a sound wave, the universal wave equation is used:
speed (m/s)= Frequency(Hz) x wavelength(m) It is important to note that speed is determined by the medium. For sound, typically the waves will travel by air. Thus, the air as well as its temperature will influence the speed that the sound waves will travel in. Therefore, when sound is travelling in the same medium, the speed will always be the same. No matter how different the frequencies are from other waves, the wave-length will change to compensate the difference and vice versa. This maintains the same speed according to the formula. |
Standing Waves
Standing waves is the pattern of interference produced by an incoming and reflected wave, making it appear stationary.
But why is it important for an instrument? Well, standing wave patterns are caused by the natural frequencies of an object (the frequency that an object tends to vibrate). Each standing wave pattern requires specific frequencies of vibration to form, which are also known as harmonics Any frequencies other than harmonics are irregular, whereas harmonic frequencies vibrate in a more regular and periodic pattern, giving instruments a more pleasant sound. Plus, each harmonic frequencies are related to each other in whole number ratios. |
The nodes are the locations where the particles are at rest, and the antinodes are the locations where the particles move with the greatest speed
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Harmonics and Overtone
Although Harmonics was mentioned above, lets expand on it.
Remember that harmonics are related to each other by whole number ratios, these whole numbers are multiples of the fundamental frequency (the lowest frequency that can produce a standing wave in a medium) which is also known as the first harmonic. Notice how the number of harmonic is equal to the number of anti-nodes between the end of the string in Fig. 1 Overtone, which is very similar to harmonics, is a sound resulting from a string that vibrates with more than one frequency. (overtone refers to the sound, thus even if two instruments play in the same note; in the same frequency yet have different overtones, their sound will be different.) Notice how the number of overtone is equal to the number of nodes between the end of the string in Fig 1 (not counting those at the ends) |
Regarding the purple texts above, that aspect is only true if the ends are nodes. However, in many wind instruments, the instrument sets up a standing wave pattern in an open air column, where both ends are half an anti-node.
Thus as illustrated from the diagram to the right, the opposite is true. The number of overtone can be counted by the number of anti-nodes between the ends (not counting the anti-node at the ends), and the number of harmonics refer to the number of nodes between the ends In a trumpet, one end is a node and the other is half an anti-node; in this special case, the harmonics are odd number multiples of the fundamental frequency. We will explore more on this in the "Trumpet" Section, as we uncover how the instrument compensates for this irregularity . |