When a string is vibrated with a tuning fork, the amplitude of the string's vibration depends on several factors, including the properties of the string, the tuning fork, and the way they interact.
The amplitude of the string's vibration can be influenced by the frequency of the tuning fork and its resonance with the natural frequency of the string. If the tuning fork's frequency matches the natural frequency of the string, a phenomenon called resonance occurs. In this case, the string absorbs energy from the tuning fork more efficiently, resulting in a larger amplitude of vibration.
However, if the tuning fork's frequency does not match the natural frequency of the string, the amplitude of the string's vibration will be smaller. The energy transfer between the tuning fork and the string will be less efficient, leading to a reduced amplitude.
In summary, if the tuning fork's frequency matches the natural frequency of the string, the amplitude of the string's vibration can be larger than that of the tuning fork. Otherwise, if there is no resonance, the amplitude will be smaller.