Wind Instrument Frequency

Standing longitudinal waves in a tube result from interference between waves traveling in ______ directions.

Answer: opposite

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Explanation: Standing waves form when incoming and reflected waves (traveling in opposite directions) interfere.

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Example: Organ pipes create sound via standing waves from waves moving back and forth.

The relationship between incident and reflected waves depends on whether the tube end is open or ______.

Answer: closed

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Explanation: Open ends reflect waves without phase change; closed ends invert the phase.

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Example: A flute (open end) vs. a clarinet (closed end) produce different harmonics.

Standing longitudinal waves in a tube result from interference between waves traveling in ______ directions.

Answer: opposite

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Explanation: Standing waves form when incoming and reflected waves (traveling in opposite directions) interfere.

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Example: Organ pipes create sound via standing waves from waves moving back and forth.

The relationship between incident and reflected waves depends on whether the tube end is open or ______.

Answer: closed

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Explanation: Open ends reflect waves without phase change; closed ends invert the phase.

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Example: A flute (open end) vs. a clarinet (closed end) produce different harmonics.

If one end is closed, a ______ exists at that end.

Answer: node

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Explanation: Air cannot move at a closed end, creating a node (zero displacement).

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Example: Covering one end of a tube creates a node at that end.

If the end is open, the air has freedom of motion, forming an ______.

Answer: antinode

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Explanation: Open ends allow maximum air displacement (antinode).

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Example: Blowing across a bottle’s open top creates an antinode.

Wavelength equation for first harmonic (open-open pipe):

Answer: λ₁=2L

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Explanation: First harmonic spans half a wavelength, fitting one node between two antinodes.

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Example: A 1m open-open pipe has λ1=2 m

In a pipe closed at one end, the open end is an antinode, and the closed end is a ______.

Answer: node

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Explanation: Closed end restricts air motion (node); open end allows maximum motion (antinode).

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Example: A clarinet’s reed end is a node, open end is an antinode.

Wavelength equation for first harmonic (closed-open pipe):

Answer: λ₁=4L

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Explanation: First harmonic spans a quarter-wavelength.

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Example: A 1m closed-open pipe resonates at λ=4 m

Wave speed equation:

Answer: v=fλ

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v: Wave speed (scalar, SI unit: m/s)

f: Frequency (scalar, SI unit: Hz)

λ: Wavelength (scalar, SI unit: m)

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Example: A 440 Hz wave with λ=0.78 m has v=343 m/s