8.1 Music and Musical Notes

It’s important to realize the difference between what is music and noise. Music is sound that originates from a vibrating source with one or more frequencies (usually harmonious and pleasant). Noise on the other hand is sound that originates from a source with constantly changing frequencies and is usually not ‘pleasant’ to the ear. On an oscilloscope, noise would not have a constant wave form or pattern.

Which of the following are musical and which are noise?

There are three main characteristics of musical sounds: pitch, loudness and quality. Each of these characteristics depends not only on the source of the musical sound, but also on the listener. Thus, they are called subjective characteristics.

Pitch is the perception of the highness or lowness of a sound; it depends primarily on the frequency of the sound.

Loudness is the perception of the intensity of sound.

Sound Quality is a property that depends on the number and relative intensity of harmonics that make up the sound.

In music, a pure tone is a sound where only one frequency is heard. Musical sounds are not normally pure tones; they usually consist of more than one frequency. In general, two or more sounds have consonance if their frequencies are in a simple ratio (simpler ratio produces more consonance). Harmonious pairs of sounds have high consonance; unpleasant pairs of sounds have high dissonance, or low consonance.

Unison is a set of sounds of the same frequency. An octave has sounds with double the frequency of the sounds in another frequency. For example, a 200-Hz sound is one octave above a 100-Hz sound.

The two common musical scales are the scientific musical scale, based on 256 Hz, and the musicians’ scale, based on 440 Hz.

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8.2 Vibrating StringsVibrating strings (examples?) are often used to produce musical sounds. The frequency of a vibrating string is determined by four factors: length, tension, diameter, and density. All of these factors are taken into consideration when designing stringed musical instruments, such as the piano, guitar, cello, harp, lute, mandolin, banjo and violin.

Increase length -> decrease frequency

Increase tension -> increase frequency

Increase diameter -> decrease frequency

Increase density -> decrease frequency

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Answer qualitatively!

8.3 Modes of Vibration – Qualities of Sound

When a string, stretched between two fixed points, is plucked a standing wave pattern is produced. Nodes occur at both ends. Different frequencies of varying amplitudes may result depending on how many nodes and antinodes are produced. The resulting note is the sum of all of these different vibrations of the string.

In its simplest, or fundamental mode of vibration, the string vibrates in one segment. This produces its lowest frequency, called the fundamental frequency ( f0).

If the string vibrates in more than one segment, the resulting modes of vibration are called overtones. Since the string can only vibrate in certain patterns (always with nodes at each end) the frequencies of the overtones are simple to determine.

1st overtone (f1) f1 = 2fo

These vibrations are also referred to as harmonics.

Fundamental freq. fo First harmonic

First overtone f1 (2fo) Second harmonic

Second overtone f2 (3fo) Third harmonic

Third overtone f3 (4fo) Fourth harmonic

Stringed instruments vibrate in a complex mixture of overtones superimposed on the fundamental frequency. Very few vibrating sources can produce a note free of overtones. An exception is the tuning fork, but even it has overtones when first struck. However, because the overtones disappear quickly, the tuning fork is valuable in studying sound and tuning musical instruments.

The quality of a musical note depends on the number and relative intensity of the overtones it produces along with the fundamental frequency. The quality enables us to distinguish between notes of the same frequency and intensity coming from different sources; for example, we can easily distinguish between middle C on the piano, on the violin, and in the human voice.

8.4 Resonance in Air Columns

Closed Air ColumnsWhen a sound wave is sent down an air column (closed at one end) the end of the tube reflects the sound waves back. Certain frequencies produce standing wave patterns (through interference) that amplify the original sound. The closed end is fixed so a node is located there. The open end of the column is free to vibrate so an antinode is located there.

Resonance first occurs when the column is (1/4) λ in length. The next possible lengths are 3/4 λ, 5/4 λ, etc. check wooden box with tuning fork

1st Resonant length2nd Resonant Length

Sample Problem: The first resonant length of a closed air column occurs when the length is 16 cm.(a) What is the wavelength of the sound?(b) If the frequency of the source is 512 Hz, what is the speed of sound?(a) first resonant length = ¼ λ

¼ λ = 16 cm λ = 64cm

(b) v = f λ= 512 Hz (64cm)= 32 768 cm/s (327.7 m/s)

Open Air ColumnsResonance may also be produced in an open air column(open at both ends). Antinodes occur at free ends. This means the first length at which resonance occurs is 1/2 λ. Resonance will next occur at lengths of λ, 3/2 λ, 2 λ, etc.test air tubes

1st Resonant Length 2nd Resonant Length

Sample Problem: The third resonant length of an open air column occurs when the length is 50cm.(a) What is the wavelength of the sound?(b) If speed of the wave is 300 m/s, what is the source frequency?

(a) third resonant length = 3/2 λ 3/2 λ= 50 cm

λ = 0.33 m(b) f = v/ λ

= 300m/s / (0.33m)

= 9.0 x 102 Hz

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