What is the exact frequency of musical note G#4?

When G#4 is played on a piano or acoustic instrument, vibrating strings or air columns compress adjacent atmospheric molecules at a fundamental frequency of 415.3 cycles per second (Hz). In standard air at 20°C, each compression wavefront is separated by 82.64 cm.

12-Tone Equal Temperament (12-TET)

In modern Western music, the octave is divided into 12 equal logarithmic intervals. The frequency ratio between every adjacent semitone is the twelfth root of two (¹²√2 = 2^1/12 ≈ 1.059463).

f=440·2^{(k − 49) / 12}

Acoustic Standing Waves & Resonators

To produce G#4, open cylindrical organ pipes require an acoustic length of λ / 2 ≈ 41.3 cm, while closed resonators resonate at a quarter-wavelength λ / 4 ≈ 20.7 cm.

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Traian AnghelAuthor & Reviewer

Physics Teacher & Educational Technologist • Brăila, Romania

Last Reviewed: August 2026

Wave Lab calculators are constructed using rigorous peer-reviewed physics formulas from verified metrological repositories. Every equation, spectral conversion, and acoustic property is tested against NIST, CIE, and ISO datasets.

Verified Sources:NIST CODATACIE 1931 2° ObserverNASA Glenn Research