Music: Sound that follows a regular pattern; a mixture of frequencies which have a clear mathematical relationship between them.

Transcription

1 The Sound of Music

2 Music: Sound that follows a regular pattern; a mixture of frequencies which have a clear mathematical relationship between them.

3 How is music formed? By STANDING WAVES Formed due to interference and reflection Two identical waves travel in opposite directions and interfere, constructively or destructively

4 Standing Waves Created when periodic waves with equal amplitude and wavelength reflect and superimpose on one another. Standing waves appear to have parts that are not moving

5 STANDING WAVES

6 AN AN N N N N AN

7 Standing Waves and Frequency Only certain frequencies of vibration can produce standing wave patterns. WALTER

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10 Standing Waves The nodes and antinodes remain in a fixed position for a given frequency. There can be more than one frequency for standing waves depending on the type of boundary. Frequencies at which standing waves can be produced are called the natural (or resonant) frequencies.

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12 Ex. 2 If a vibrating string had 4 nodes how many wavelengths would be present? Ex. 3. If a vibrating string had 2 antinodes how many wavelengths would be present?

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14 SOURCES OF SOUND Sound comes from a vibrating object. If an object vibrates with frequency and intensity within the audible range, it produces sound we can hear. MUSICAL INSTRUMENTS A standing wave is produced when a guitar string is plucked or a flute is played. String Instruments: guitar, violin and piano Wind Instruments: Open Pipe: flute and some organ pipes Closed Pipe: clarinet, oboe and saxophone Percussion Instruments: Drums, bells, cymbals

15 INSTRUMENTS When an instrument produces sound, it forms standing waves and resonates at several related frequencies. Fundamental Frequency(1 st harmonic): the lowest frequency that an instrument vibrates at. Defines it s pitch

16 A guitar or piano string is fixed at both ends and when the string is plucked, standing waves can be produced in the string. Since the ends are fixed, they will be the nodes. 2-antinode Demo mini-wiggler

17 As a string vibrates, it sets surrounding air molecules into vibrational motion. (called forced vibrations) The frequency at which these air molecules vibrate is equal to the frequency of vibration of the guitar string. Forced vibrations: the vibration of an object caused by another vibrating object. AKA Resonance

18 Frequency in the string 1. Length changed by applying tension Decreasing the tension causes string to lengthen Longer string means wavelength is longer. Therefore the frequency is lower. DIRECTLY PROPORTIONAL 2. Diameter As the diameter of the string increases the frequency decreases (lower) INVERSELY PROPORTIONAL

19 The sounds produced by vibrating strings are not very loud. Many stringed instruments make use of a sounding board or box, sometimes called a resonator, to amplify the sounds produced. The strings on a piano are attached to a sounding board while for guitar strings a sound box is used. When the string is plucked and begins to vibrate, the sounding board or box begins to vibrate as well (forced vibrations). Since the board or box has a greater area in contact with the air, it tends to amplify the sounds. On a guitar or a violin, the length of the strings are the same, but their mass per length is different. That changes the velocity and so the frequency changes.

20 Possible Standing Waves on One String

21 The equation for strings is f frequency in hertz n number of harmonic L length of string in meters V velocity in medium in meters/sec λ - wavelength in meters - n can be any integer value greater than one.

22 A wave travels through a string at 220m/s. Find the fundamental frequency (1 st Harmonic) of the string if its length is 0.50m. v= 220 m/s L = 0.5 m n = 1 f = nv/2l f =(1)(220 m/s) /(2)(0.5m) f = 220 Hz

23 WIND INSTRUMENTS Wind instruments produce sound from the vibrations of standing waves that occur in of columns air inside a pipe OPEN PIPE: Pipes can have two openings (not fixed) CLOSED PIPE: one opening (closed pipe-fixed)

24 Open Pipes Ex. flute Walter again A standing wave in a pipe open at both ends must have an antinode at each end of the pipe. The figure below shows standing waves in a pipe that is open at both ends.

25 CLOSED PIPES In general, a standing wave in a bottle or pipe open at one end must have a node at the bottom and an antinode at the top. Only produce sounds in ODD HARMONICS Each sound you hear will occur when an antinode appears at the top of the pipe

26 Closed Pipes You get your first sound or encounter your first antinode when the length of the actual pipe is equal to a quarter of a wavelength. In a closed pipe, you have a NODE at the 2nd harmonic position, therefore NO SOUND is produced In a closed pipe you have an ANTINODE at the 3 rd harmonic position, therefore SOUND is produced. CONCLUSION: Sounds in CLOSED pipes are produced ONLY at ODD HARMONICS

27 How can you change the fundamental frequency of a wind instrument? Change the length of the air column: open and close valves As the length shortens, the wavelength gets shorter Which means the frequency gets higher and the pitch is higher