How does the piece of an organ pipe change with temperature?

The pitch of an organ pipe changes directly with temperature: as the temperature rises, the pitch increases, and as it falls, the pitch decreases.

The Direct Relationship Between Temperature and Organ Pipe Pitch

The sound produced by an organ pipe is fundamentally influenced by the ambient temperature. As explicitly stated, "The pitch of organ pipes rises and falls with the temperature in a direct relation, i.e a rise in temperature is accompanied by a rise in pitch; when the temperature falls, the pitch falls as well." This means that warmer air makes the organ sound sharper, while colder air makes it sound flatter.

Why Temperature Affects Pitch

The primary reason for this phenomenon lies in how temperature affects the speed of sound in the air inside and around the pipe.

• Speed of Sound: Sound waves travel faster through warmer air than through colder air. This is because air molecules move more rapidly and collide more frequently at higher temperatures, allowing vibrations to propagate more quickly.
• Wavelength and Frequency: The pitch of a sound is determined by its frequency. For an organ pipe of a fixed length, the fundamental wavelength of the sound it produces is largely determined by the physical dimensions of the pipe itself. While the pipe material expands or contracts slightly with temperature, this effect is negligible compared to the change in the speed of sound in the air.
• The Formula: The relationship is expressed by the formula $v = f \lambda$, where:
  • $v$ is the speed of sound.
  • $f$ is the frequency (pitch).
  • $\lambda$ is the wavelength.
    Since the wavelength ($\lambda$) remains relatively constant for a given pipe, if the speed of sound ($v$) increases due to higher temperature, the frequency ($f$) must also increase, resulting in a higher pitch. Conversely, if the speed of sound decreases, the frequency decreases, leading to a lower pitch.

Practical Implications for Organ Tuning

This temperature dependency has significant practical implications for organ builders, tuners, and musicians.

• Tuning Challenges: Organs are typically tuned at a specific, stable room temperature. If the venue's temperature fluctuates, the entire instrument's pitch will shift. This can lead to the organ sounding out of tune, especially when played with other instruments that might not be as susceptible to temperature changes (like stringed instruments or pianos).
• Concert Conditions: For professional performances, efforts are often made to maintain a consistent temperature within the concert hall to ensure the organ remains in tune and at the desired pitch standard.
• Material Effects: While the primary effect is on the air inside the pipe, the pipe material (wood or metal) also expands and contracts with temperature. However, the change in the pipe's physical length (and thus its effective wavelength) is minor compared to the change in the speed of sound in the air.
• Regular Adjustments: Organ tuners must account for environmental conditions, and large, complex instruments often require retuning or pitch adjustments if the ambient temperature deviates significantly from the tuning standard.

Summary of Temperature's Effect on Pitch

The table below summarizes the direct relationship between temperature and the pitch of an organ pipe:

Understanding this direct relationship is crucial for maintaining the musical integrity and performance quality of an organ.