# What exactly are sympathetic vibrations?

On every source and in every example, it seems that sympathetic vibrations are quite directly linked to or are the same as resonance.

The classic example of sympathetic vibrations is of two similar tuning forks (same frequency). When one of these tuning forks is set into vibration and brought close to the other at rest, the latter starts to vibrate. Here, air is forced into vibration at the same frequency as itself by the first tuning fork, and these vibrations carry to the second tuning fork which vibrates readily (resonance).

My textbook, however, defines sympathetic vibrations as -

The amplitude of forced vibrations of a body does not remain constant due to the presence of damping forces of the surrounding medium. However, it is possible to keep the amplitude of vibrations constant by applying an external periodic force such that the external periodic force compensates for the loss of energy in each vibration due to the damping forces. The vibrations of the body are then called sympathetic vibrations.

I am aware that resonance means that bodies having natural frequencies or higher harmonics similar to the frequency of external periodic forces acting on them will vibrate readily with heightened amplitude.

If I'm understanding correctly:

Vibrations can carry from an external periodic force to a body even if the body does not resonate with the external force, the amplitude in such a case is small(compared to resonance) and the body vibrates with the frequency of the driving force and not its natural frequency.

Even in such a case - It is possible to keep the amplitude of vibrations of the body constant by applying an external periodic force which does not resonate with the body such that the external periodic force compensates for the loss of energy in each vibration due to the damping forces.

So if that can be done without resonance being involved, why are sympathetic vibrations referred to with examples of resonance everywhere? Is it that the textbook I'm referring to is entirely wrong or not specific? An intuitive answer would be highly appreciated.

• Related: physics.stackexchange.com/a/684915/226902. Wiki: en.wikipedia.org/wiki/Sympathetic_resonance "Sympathetic resonance is an example of injection locking occurring between coupled oscillators". Injection locking: en.wikipedia.org/wiki/Injection_locking . More links on resonance here: physics.stackexchange.com/a/750711/226902 About " sympathetic vibrations/resonance", see also: physics.stackexchange.com/q/366371/226902 Commented Feb 20, 2023 at 14:33
• @Quillo thanks for your response. It seems as though all of these links are implying that sympathetic vibrations occur when there’s a harmonic likeliness between a body and an external force i.e. resonance. So is it that the circumstance mentioned in textbook of an external periodic force compensating for loss of energy due to damping while maintaining same amplitude is possible only in an injection locking or resonance related scenario? Or is it that the book is entirely wrong in mentioning all that in reference to sympathetic vibrations? Commented Feb 20, 2023 at 15:31
• I have the same feeling. The links do not really contain a full answer, but, at least, narrow down the question to exactly what you describe in your comment. I have no clear answer now, but if I'll find something interesting I'll let you know! Commented Feb 20, 2023 at 16:47