Abstract: There is a complex physical mechanism behind the sounding of piano. The purpose of this paper is to explain the phenomenon of piano sounding using theoretical physic knowledge, and to measure frequency and amplitude by using a software called Phyphox on smart phones as an experimental tool, so as to explore the accuracy, harmony and the causes of its unique tones, and analyze the phenomenon of beat frequency during playing. The experiment is mainly divided into three parts: (1) Using Mason's law and the strike point theory, the vibration frequency of the string is qualitatively studied by changing the effective length of the string and the relative position of the strike point; (2) The Phyphox software on a smart phone is used to measure the vibration frequency of different strings and verify the existence of twelve equal temperament and overtone series; (3) The beat frequency phenomenon under different intervals and pitch combinations is measured. The experimental results show that there is an integer ratio relationship between the fundamental frequency and the double frequency of the piano, which accords with the theory of overtone series. The frequency ratio between adjacent sounds is close to the theoretical value, which verifies the twelve-average law. The phenomenon of beat frequency is observed in harmony, and the amplitude shows periodic changes. The experimental results support the application of Mason's law and twelve equal law in piano sound. In addition, the existence of beat frequency provides a theoretical basis for piano tuning. Future research could explore higher precision measurement devices and software to improve the automation of piano tuning and extend the study to other instruments.

Key words: piano, vibration, physical mechanism, beat frequency phenomenon