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Thesis: The frequency and pitch of the recorder is dependent on the type of standing wave which occurs inside it and the loudness of the sound is affected by the amplitude of the standing wave.
Sound is a form of energy produced by vibrations of objects (Walding et. al. 2004). There are two types of waves called transverse and longitudinal waves. Transverse waves occur when the wave particles move at right angles to the motion of the wave (Walding et. al. 2004). Longitudinal waves occur when the waves move horizontally with the particles moving horizontally. An example is a slinky is on a long table with someone is holding it securely on one end while on the other end someone is sliding it back and forth causing the compressions and rarefactions to move along the slinky. When a wave is at its highest peak it is called a crest and when it is at its lowest point it is called a trough (Walding et. al. 2004). The height of a crest is known as amplitude. (Figure 1). The wave length can be measured by a Greek symbol called lambda (?). A wave length on a transverse wave can be measured at the top of one crest to the top of another crest. It can also be measured from the bottom of one trough to the bottom of another trough. (Figure 1). The wave length on a longitudinal wave is measured half way on one compression to half way on the next compression. Also it can be measured by half way on a rarefaction to half way on the next rarefaction. (Figure 2). It can be calculated by rearranging the universal wave equation shown in the following:

v is velocity of the wave (ms-1), f is frequency of the wave (Hz) and ? is wave length (m).

As stated in the above equations v is the velocity. Velocity of a wave is the measure of how fast the wave is travelling in metres per second (m/s-1). In figure 1, one full cycle of the wave is labelled on the picture. The time it take for a full time a wave takes to pass a point is known as the period (T). It is measured in seconds (s). This can be calculated by the following formula:

T is period (s) and f is frequency (Hz).

As shown in the above equation, were f is the frequency. It is measured in Hertz (Hz). The frequency is how many cycles that pass through a particular point per second. It can be calculated by rearranging the previous formula:

T is period (s) and f is frequency (Hz).

All of the musical instruments in the world can be split up into four groups. The four groups are aerophones, idiophones, membranophones and chordophones. Examples of aerophones are a recorder and an oboe. Examples of idiophones are xylophone and a harmonica. Examples of membranophones are a drum and a kazoo. Examples of chordophones are a piano and a cello (Classification of Musical Instruments, Music Appreciation, 2018). When these instruments are being played together to create different sounds it is called music. There are many different types of music. For example there is heavy metal, pop, rock and roll, rap and opera. They all created using different musical instruments. The instrument that this assignment will be examining is the recorder. The recorder is an instrument that is 300mm long open pipe with a diameter of 11mm. (Recorder (musical instrument), 2018). In order for the recorder to make sound when air is blown into it, there is a vibrating air column that is 270mm long. (Recorder (musical instrument), 2018). It has seven holes, where three are for the upper hand and four are for the lower hand. The holes are used for changing pitch so that different notes can be created to play a song.

Figure 3: A labelled diagram of a recorder.
The pitch of a recorder is caused by the frequency of the standing waves which occurs inside of the pipe. Standing waves are caused by interference between waves travelling in opposite directions inside the pipe. Wave interference occurs when two waves are travelling in the same medium. There are two types of wave interference, destructive interference and constructive interference. Destructive interference happens when two waves meet that have the same wave length and amplitude but are on opposite sides of the centre. Constructive interference happens when two waves meet which have that same wave length and amplitude and are on the same side of the centre (Walding et. al. 2004). A standing wave pattern has nodes and antinodes. Nodes occur when the two waves cancel each other out, called destructive interference. An antinode occurs when two waves build on each other called constructive interference. Inside a recorder a node is a place where there no movement of particles and an antinode is a place with maximum movement of particles.

The recorder is an open pipe which means its standing waves have an anti-node at each end of the pipe. There are many natural frequencies which can occur in the standing waves starting with the most simple called the fundamental frequency. The first five standing waves are shown in figure 5. These diagrams are a simplification where all the holes on the recorder are closed. The different patterns can be achieved when the musician blows into the recorder with more force.

The frequency of the first five harmonics can be calculated as shown in appendix 1, and the results are summarised in table 1.
Harmonic Frequency (Hz)
1st 570
2nd 1140
3rd 1710
4th 2280
5th 2850

Table 1: Indicating the frequencies for the five harmonics of a recorder, with all the holes closed.

The notes on a recorder can also be achieved by un covering the holes, with a C occurring when all the holes are closed. The actual frequency of C5 is 523 Hz (Frequencies for Equal-Tempered Scale, Physics of Music – Notes, 2018) which is different from the 570 Hz calculated. This is most likely because when the frequency was calculated the entire length of the recorder was used, whereas the frequencies only should be based on the length of the vibrating column. This will occur for every frequency calculated in this essay.

Figure 6: Indicating the notes played on a recorder when the indicated holes are closed.

Opening a hole on the recorder causes an antinode to happen at that position. This is because the pressure is released, allowing the air particles to move with the maximum amplitude. Opening one hole will cause the type of standing wave to change.

(Calculations)