Final answer:
To find the unknown frequency (f₁) when the beat frequency (16.73 Hz) and one known frequency (f₂ = 256 Hz) are given, use the formula fB = |f₁-f₂|.
Step-by-step explanation:
To calculate the frequency of the beat produced when two waves with close frequencies are played together, we use the beat frequency formula fB = |f₁-f₂|. In the given scenario, we already know the beat frequency is 16.73 Hz, and one of the frequencies (f₂) is 256 Hz. To solve for the other frequency (f₁), the piano's frequency, we simply rearrange the formula to f₁ = fB + f₂ or f₁ = fB - f₂, depending on whether f₁ is higher or lower than f₂.
Since beats occur when two waves of slightly different frequencies interfere with each other, the resulting sound fluctuates in loudness at the beat frequency. The combined wave effectively has an amplitude that varies at the beat frequency while the wave itself vibrates at the average frequency (fave) of the two original waves.