Why do pianos not produce beats? Beats occur when two sounds that are close in frequency interfere with each other and produce periodic variation in amplitude - called beats.
Piano keys that are next to each other seem to satisfy this. They only differ from each other by 4Hz or so.

If I played two keys that are next to each other - would I not be producing beats since they are similar frequencies interfering? Yet pianos do not produce beats -why?
 A: Different pairs of notes on the piano (or any other instrument) will produce more, or less, of a noticeable beat effect depending on

*

*the musical interval

*the register (low or high)

*the timbre (sound quality) of the instrument

*the intonation used (fine-tuning of notes relative to each other - it's not always exactly matching the theory)

Each note on a piano will be made up of many frequencies - the fundamental (the frequency shown in your graphic above), and overtones. The overtones are (ideally) integer multiples of the fundamental, known in this case also as harmonics.
So that low A on your piano has a fundamental of 27.50 Hz, but also harmonics at 55Hz, 82.5Hz, 110Hz, 137.5Hz, etc.
The B just above it (skipping over the Bb even) will have a fundamental of 30.5Hz and harmonics of 61Hz, 91.5Hz, 122Hz, etc.
So if you play them both together, you've got some combination of all those frequencies and more going on. There will be beat frequencies between all of the combinations.
Additionally, depending on the piano (size of the strings, etc), the fundamental will almost always not be the loudest frequency for any of those low notes. So 27.5Hz and 30.5Hz will be subdued compared to the many higher harmonics.
So, there's a lot more going on than just comparing the fundamental frequencies. However, this points to a reason that the exam answer is incorrect (even assuming their limit of 7Hz for what we hear as 'beats' is true). There can easily be beats between two notes on a piano that have fundamental frequencies much more than 7Hz apart.
Let's begin with a higher A, up at 110Hz. Its fifth harmonic will be 5x110Hz, or 550 Hz.
Next, play the C# above it at 139Hz. Its fourth harmonic will be 4x139 Hz, or 556 Hz.
If you play those two together, there will be a noticeable beat frequency of 6 Hz (among others). This is a well-known issue with what's called "equal temperament", and that's another story. Suffice to say, the piano tuner will frequently "adjust" some notes on the piano so as to reduce the effect. It is a tricky process to hide some offensive beat frequencies by introducing other, less-noticeable, inaccuracies.
