Apr 19, 2023

Chapter 21 Musical Instruments

Lecture 22

CR/NC Deadline Oct. 19

Apr 19, 2023 Physics 1 (Garcia) SJSU

Musical InstrumentsNow that we understand some of the physics of sound, let’s analyze how musical sound is produced by different types of musical instruments.

Apr 19, 2023

String InstrumentsStanding wave on the vibrating string causes forced oscillation of the sounding board.

Frequency for a string depends on:• Length of string• Thickness and composition• Tension in the string

Loudness depends on:• Amplitude of oscillation• Size of sounding board• Flexibility of sounding board

Modern piano has many long, massive steel strings under high tension (hundreds of pounds) on a large sounding board.

Standing Waves; ResonanceFrequencies of standing waves on a particular string are called resonant frequencies.

The lowest resonant frequency f1 is referred to as the fundamental and the higher resonant frequencies fn

= nf1 as the nth harmonics.

In order for different strings to have different fundamental frequencies, they must differ in length and/or mass/unit length.

A guitar has strings that are all the same length, but the mass/unit length varies.

We change the effective length of a string by pressing it against the fingerboard.

Standing Waves of Guitar StringsThin string

Thick string

Standing Waves - Piano

In a piano, the strings vary in both length and density. This gives the sound box of a grand piano its characteristic shape.

Once the length and material of the string is decided, individual strings may be tuned to the exact desired frequencies by changing the tension.

Apr 19, 2023 Physics 1 (Garcia) SJSU

Musical Pipe Instruments

Standing Waves: Open/Open PipeIf the tube is open at both ends, both ends are antinodes, and the sequence of harmonics is the same as that on a string. All harmonics appear.

Apr 19, 2023

Demo: Whirly Tube

Whirl a corrugated tube to produce a pure tone at the tube’s natural frequency.

Bernoulli principle creates low pressure at the moving end, drawing air through the tube.

A

L

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Playing Simple Horns

Standing waves of different frequencies (different notes) are produced, depending on how musician blows into the horn.

Simple bugle is just a long pipe wrapped in a coil so it’s compact.

Apr 19, 2023

Brass & Woodwind Vibrations

Vibrations in a pipe instrument created by:• Vibrating one’s lips (e.g., trumpet)• Blowing past an opening (e.g., flute)• Blowing & vibrating a reed (e.g., clarinet)

Apr 19, 2023 Physics 1 (Garcia) SJSU

Harmonic Series

Music for natural horns and bugles is limited by harmonic series, the frequencies of the fundamental and overtones.

Fundamental

Changing the Length

Finger-holes

Disadvantage: Reduced amplitude

Crooks

Disadvantage: Clumsy

To play notes beyond the harmonic series requires changing the frequency of the fundamental by changing the length of tube.

Apr 19, 2023 Physics 1 (Garcia) SJSU

Changing the Length

Trombone uses a continuous slide to vary its length

Cornett

Apr 19, 2023

Changing the Length

Valves used in trumpet, tuba, and French horn

Cornett

Similar to using a crook but easy to open & close

Woodwind InstrumentsResonant standing waves also produced in a pipe but the pipe length varied by air holes (finger-holes, keys, or pads).

Flute

Clarinet

Saxophone

Oboe

Bassoon

Meter stick

Cor anglais

Using air holes reduces amplitude of the sound

Apr 19, 2023

Percussion InstrumentsCreate oscillations by

striking an object, such as:

• Stretched drumhead

• Metal rod or disk

• Wooden object

Apr 19, 2023 Physics 1 (Garcia) SJSU

Drum Heads

Drum heads are stretched membranes that vibrate at different frequencies depending on the membrane’s oscillation pattern.

Note: These animations are not accurate because complex patterns should oscillate faster.

Key Points of Lecture 22Key Points of Lecture 22

Before Wednesday, read Hewitt Chap. 22 (first half).

Homework #16 due by 11:00 PM Friday Oct. 22.

• Musical Instruments