Final answer:
The natural frequency of a string is the frequency at which it vibrates freely. It will resonate at frequencies that are integer multiples of this fundamental frequency, known as harmonics or overtones. Resonance is a phenomenon where a system vibrating at its natural or harmonic frequency can exhibit amplified oscillations.
Step-by-step explanation:
The question deals with the concept of resonance and harmonic frequencies of a vibrating string which are an integral part of wave physics. The natural frequency of a string refers to the frequency at which it vibrates when disturbed. A string will also resonate at frequencies that are integer multiples of this fundamental frequency. These multiples are known as the harmonics or overtones of the string. For example, if a string has a natural frequency of 30.0 Hz, it will also resonate at 60 Hz, 90 Hz, 120 Hz, and so on, which are the second harmonic (2 times the fundamental frequency), third harmonic (3 times the fundamental frequency), fourth harmonic, etc.
Whenever an external periodic force is applied to a system at its natural frequency or one of its harmonic frequencies, the system will resonate. This can cause the amplitude of oscillations to dramatically increase, leading to larger vibrations. This property is taken advantage of in musical instruments, allowing the strings to produce loud and clear musical notes.