Does the frequency of a vibrating substance like a string depend on its properties or simply depend on the agent which vibrates the string? We know that if someone vibrates a substance like a string, the string oscillates with its natural frequency. But I think the frequency depends on the rate the agent like a man's hand does vibration on the string. But my book says natural frequency only depends on the properties of the string. Please explain.
 A: The resonant frequency of the string only depends on its properties (tension, length, mass)
But in a real instrument the complex set of frequencies that produce the note depend on how it is plucked, the stop-start motion of a violin bow, the contact with the string, friction etc.
A: Generation of musical tones on a string: One's hand plucking a string is just an instantaneous pulse which is applied to the string causing two separate waves propagating in both directions. Those waves reflect from the sides (boundary conditions), and start a back-and-forth moving waves which interfere with each other. Then, each reflected wave contributes to the total summed waveform. This increases the total stored energy in the system which in return can produce enough mechanical vibrations that can hear. Those waves interfere perfectly only at certain frequencies, and when standing waves occur. This is when we hear the musical tones and their harmonics. 
The generation of harmonics: The critical resonant frequencies are generally very close to multiples of the fundamental frequency. Each harmonic has its own standing wave pattern, different locations for their peak and nulls. 
The weights of harmonics, the timbre: Generally all harmonics exist independently. This variance between the harmonics contribute to the timbre of the instrument. But on the other hand, the property of initial vibration energy source effects those coefficients. If one plucks a string at a point where some harmonics has a null, then this pluck will not generate that harmonic, thus changing the timbre. For examle, plucking at the center of a string will produce a strong fundamental harmonic whereas plucking close to the sides of the strings would increase the weighting coefficients of some of the higher harmonics.
So my answer to the question is, musical tone and the frequency values of all harmonics are determined by the instrument only. If one plucks the string or blows a flute differently this could directly affect the weights of the contributing harmonics, thus changing the timbre of the instrument.
