Analysis of sound frequency and sound intensity in the cylindrical musical instrument using audacity software
D N S Handayani1,* and Y Pramudya1
1Program Studi Magister Pendidikan Fisika, Universitas Ahmad Dahlan, Jl. Pramuka 42, Sidikan, Umbulharjo, Yogyakarta 55161
*Corresponding author: [email protected]
Abstract. The aim of the research is to investigate the value of the sound frequency and the sound intensity generated from the cylindrical percussion instruments using Audacity software and the effect of membrane diameter on the sound frequency and sound intensity of cylindrical percussion instruments. The material of membrane is a leather and mica plastic. The sound was recorded and analyzed by Audacity software. For the leather membrane diameter of 13.5 ± 0.1 cm, the sound frequency is 293.2 ± 16.3 Hz, and the sound intensity is -13.7 ± 1.0 dB. For the leather membrane diameter of 20.5 ± 0.1 cm, the sound frequency is 166.1 ± 7.9 Hz, and the sound intensity is -9.2 ± 1.5 dB. For the mica plastic membrane diameter of 13.5 ± 0.1 cm, the sound frequency is 315,9 ± 7.0 Hz, and the sound intensity is -14,5 ± 1.5 dB. For the mica plastic membrane diameter of 20.5 ± 0.1 cm, the sound frequency is 304,3 ± 14.8 Hz, and the sound intensity is -13.4 ± 1.1 dB. The effect of membrane diameter on cylinder-shaped instrument shows that the smaller the diameter, the lower the resulting sound intensity value, but the higher the resulting sound frequency.
1. Introduction In everyday life, vibration occurs on many objects. An interesting phenomenon to be discussed in a vibrating object in a two-dimensional case is a musical instrument in the shape of a circle or square. Some examples of musical instruments that can be found on circular membranes are drums, ketipung, and tambourine. The wave equation can be formulated using two wave-polynomial methods for vibrations that propagate on the square membrane and circular or rounded membranes [1]. The wave research on the two-dimensional case of the drumhead vibration has been done. The research is more focused on the correction of experimental results with the theoretical results [2]. The Audio Frequency Generator (AFG) can be used the sound to exit the wave on the drumhead. The peak of the wave occurs at the center of the drumhead. There are circle nodes at the edges. The resulting frequency depends on the size, type, and material that is used for the experiment [3]. For measuring the frequency of traditional musical instruments, Audacity software can be employed. The software was able to record and analyze the sound data from BonangBarung. Bonangbarung is a part of gamelan ensemble [4]. The differences in superposition waveform and spectrum of various timbres can be analyzed using Audacity software and MATLAB software. Superposition waveform of the mixed waveform and simultaneous struck have similar value. Hence, two superposition waveform produce the similar sound. They generate the similar value of frequencies and amplitudes. Although, there is a phase difference[5].An audacity is a tool in the form of a simple audio editor that produces a sound
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frequency; the frequency ratio produces a different musical tone. And as a learning tool in assessing the frequency ratio visually on the PC screen to increase students' understanding on the topic of the scale of music[6]. This study specifically examines the cylindrical instrument. Experimental research conducted to investigate the value of the sound frequency and the sound intensity generated from the cylindrical percussion instruments using Audacity software and the effect of membrane diameter on the sound frequency and sound intensity of cylindrical percussion instruments.
2. Theoretical description of vibrating drum 2.1. Circular Membrane One type of musical instrument that vibrates in a musical instrument is the vibration of the circular membrane. Some examples that can be found in circular membranes are vibration drums, ketipung, drum, and tambourine. For a circular membrane, a solution can be found using the Cartesian coordinate system. By choosing polar coordinate, the solution will be simplified, and the equation becomes: 2 1 1 2 1 2 2 2 2 2 2 for 0 ≤ r ≤ a, 0 ≤ θ ≤ 2π (1) r r r r cm t where a is the radius of the drum and θ is the radial position, cm is equal to the speed of sound in air. By using variable separation, the wave equation can be solved by assuming. r,,t R(r)()T(t) (2) By substitution equation (2) to equation (1) the wave equation can be written as: c 2 d 2 R 1 dR c 2 1 d 2 1 d 2T m m (3) 2 2 2 2 R dr r dr r dt T dt 1 d 2T Where, 2 .Because the left and right segments are two functions of different variables. T dt2 The right-hand side of equation (3) is a two-dimensional differential equation with the periodic function. The periodic function in the form of cost andsint . It can be replaced by -ω2. The similar way can be applied to the second term of the left-hand side (3). It is also the periodic function. By 1 d 2 using 2 and the wave equation can be written as: m 2 k d cm d 2 R 1 dR m 2 2 k 2 R 0 (4) dr r dr r This is known as Bessel’s equation; this relation has the general solution
Rr AJ m kr B m (5) While (4) is the general solution of (5), a membrane that extends across the origin must have the finite displacement at r = 0. This requires B = 0 so that
Rr AJ m kr (6)
Application of the boundary condition R(a) = 0 requires J m ka 0. If the values of the argument of
jmn Jm that cause it to be equal zero are denoted by jmn, then k assumes the discrete values k . mn a Where a is the radius of the membrane and j is the root of the Bessel function. The natural frequencies are [7]: c k 1 c j f m m mn (7) 0n wavelength 2 a
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wheref0n is the frequency in vibrating mode, cm is equal to the speed of sound in air, and a is the radius of the membrane.
2.2. Intensity The intensity l of a sound wave at a surface is the average rate per unit area at which energy is transferred by the wave through or onto the surface. The intensity can be formulated as P I (8) A which P is the time rate of energy transfer (the power) of the sound wave and A is the area of the surface intercepting the sound. Thus, instead of speaking of the intensity I of a sound wave, it is much more convenient to speak of its sound level훽, defined as I 10 log (9) I o
Where dB is the abbreviation for decibel, the unit of sound level.Io is a standard reference intensity 1,0 × 10-12 W/m2 [8].
2.3. Software Audacity Audacity is free, open source software for recording and editing sounds. We can use Audacity to record live audio through a microphone or a mixer, to edit sound files, to cut, to copy or to mix the sounds, to change the speed or the pitch of the recording, and more [9]. And Audacity software can record voice signals, display and measure frequencies, and measure the sound intensity and can be used in physics learning. In the Audacity software, there is Fourier transformation analysis facilities so that it can display the frequency spectrum visually and numerically [10]. Also, the audacity of the signal model is filtered from background noise and the sound waveform of a sine wave. The analysis result from sound recording on Audacity is a graph of sound intensity and frequency.
3. Methodology 3.1. Experimental Materials This research was conducted on four pieces of space (cylindrical shape) with the same height (18.0 ± 0.1) cm and two different the diameter, i.e., the diameter (13.5 ± 0.1) cm and (20.5 ± 0.1) cm. They are leather membranes and mica plastic membranes of each diameter. The membrane was struck by hands, and the frequency and intensity were the measurements by Audacity software. There are two different diameters as shown in Figure 1.
Figure 1. The cylindrical percussion instruments with two different diameter
3.2 Experimental Procedure 1. Tools and materials are arranged as shown in Figure 2.
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Cylinder dan membranelingkaran Computer Poles
Microphone
Figure 2. Experimental scheme
2. The circular membrane attached to the cylinder is struck by hand in 10 times. The cylinder height (18.0 ± 0.1) cm and the circular membranes used were mica plastic membranes in diameters (13.5 ± 0.1) cm and (20.5 ± 0.1) cm. 3. The sound is recorded by Audacity. 4. The data is analyzed using Audacity. 5. Is repeated with a different type of the leather membrane.
4. Result and Discussion The results of experiments that have been done in this study by with the experimental scheme that has been established with variations in diameter and type of membrane and height of cylinder used the same, then obtained the sound recording on cylindrical instruments. The recorded sound recording produces images that can be seen in Figure 3.From Figure 3 we get a sound recording of almost equal sound waves for each variation in diameter and type of membrane.
Figure 3. Sound source recording of the circular membrane
Recorded sound sources that have been analyzed to produce the frequency and intensity of sound.The intensity of sound of the membrane in the graph a shown in Figure 4.
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Figure 4. Results of sound source analysis on a circular membrane
Cylindrical musical instruments with the cylinder height (18.0 ± 0.1) cm and the circular membranes used were the leather and mica plastic membranes in diameters (13.5 ± 0.1) cm and (20.5 ± 0.1) cm. The circular membrane attached to the cylinder is struck by hand in 10 times and recorded. The result, analyzed spectrum with Audacity software then averaged so that the sound frequency of the leather and mica plastic membrane for its diameter can be seen in Table 1.For the mica plastic membrane, the frequencies are similar on two diameters. However, there is frequency different on two diameters for the leather membrane.
Table 1. Sound frequency data on cylindrical instrument mica plastic membrane Diameter leather membrane frequency frequency (cm) (Hz) (Hz) 13,5± 0,1 315,9± 7,0 293,2± 16,3
20,5± 0,1 304,3± 14,8 166,1± 7,9
The circular membrane attached to the cylinder is struck by hand in 10 times and recorded. The result analyzed spectrum with Audacity software then averaged so that the sound intensity of mica plastic of lower than the leather membrane can be seen in Table 2. For the mica plastic membrane, the intensities are similar on two diameters. However, there is intensity different on two diameters for the leather membrane.
Table 2. Sound intensity data on cylindrical instrument Intensity of mica plastic Intensity of leather membrane Diameter (cm) membrane (dB) (dB) 13,5± 0,1 -14,5± 1,5 -13,7± 1,0 20,5± 0,1 -13,4± 1,1 -9,2± 1,5
Differences in the sound frequency and intensity of sound for the four cylindrical instruments are caused by several factors. Different membranes and diameters (shapes) are factors that could be different and make them sound different on musical instruments [11]. The cause of the first difference is the quality of the material used for the circular membrane of a cylindrical instrument. In term of sound intensity of the leather, the membrane is better than mica plastic. The sound produced from the
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leather membrane is more comfortable to hear than the sound on the mica plastic membrane. Therefore, the quality of materials used as a membrane on cylindrical musical instruments greatly affects the quality of the sound produced from the instrument. The second factor is diameter used for the circular membrane of a cylindrical instrument. For both membranes, the sound frequency of small diameter is higher than the large diameter. It is predicted by equation (7). For both membranes, the sound intensity of the small diameter is smaller than small the diameter.
5. Conclusion This experiment can be concluded that for leather membrane diameter of 13.5 ± 0.1 cm, the sound frequency is 293.2 ± 16.3 Hz and the sound intensity is -13.7 ± 1.0dB. For leather membrane diameter of 20.5 ± 0.1 cm, the sound frequency is 166.1 ± 7.9Hz, and the sound intensity is -9.2 ± 1.5 dB. For mica plastic membrane diameter of 13.5 ± 0.1 cm, the sound frequency is 315,9 ± 7.0 Hz, and the sound intensity is -14,5 ± 1.5dB. For mica plastic membrane diameter of 20.5 ± 0.1 cm, the sound frequency is 304,3 ± 14.8Hz, and the sound intensity is -13.4 ± 1.1 dB. The effect of membrane diameter on cylinder-shaped instrument shows that the smaller the diameter, the lower the resulting sound intensity value, but the higher the resulting sound frequency.
6. References
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