Chelsea is tuning a piano when She discovers that G above middle C is vibrating with a higher frequency than her G tuning fork, which vibrates at 392 Hz. She plays the piano key and tuning fork at the same time and hears a beat frequency of 2.0 Hz. What is the frequency of the G on the piano.
F = 392 + 2 = 394 Hz
Piano strings have Inharmonicity. It means you need to tune the notes a bit sharper than a tuning fork as you go higher than the middle octave. If you don`t do that , when you play the octave on a piano , it will sound horrible .The opposite effect happens below the middle octave.You need to tune them progressively lower compared to tuning forks.
Also , each piano has it`s own personal amounts of inharmonicity. Smaller pianos have more inharmonicity than large Grand Pianos . It`s all caused by the stiffness of the strings .(Mainly the end bits).
To find the frequency of the G on the piano, we can use the concept of beats.
1. The beat frequency is the difference between the frequencies of the two oscillating sources. In this case, the tuning fork oscillates at a frequency of 392 Hz, and the G above middle C on the piano has a higher frequency.
2. Let's assume the frequency of the G on the piano as 'x' Hz.
3. The beat frequency is given as 2.0 Hz, which means the difference in frequencies between the piano and the tuning fork is 2.0 Hz.
4. Mathematically, this can be expressed as: x - 392 = 2.0
5. To find the value of 'x', we need to solve this equation. By adding 392 to both sides, we get: x = 394.0 Hz
Therefore, the frequency of the G above middle C on the piano is 394.0 Hz.