3. resonance occurs when a medium vibrates at the same frequency as the external vibrating force causing the vibration. If the forcing frequency equals its natural frequency, the amplitude of the oscillations within the object will increase dramatically and the maximum possible energy will be transferred from the source into the object In musical instruments and loudspeakers, resonance is a desirable phenomenon, amplifying the sound. In a musical instrument, the resonator vibrates at the same frequency as the principal vibrator, making the sound much louder. RESONANCE

4. STRINGED INSTRUMENTS When a string vibrates, the transverse waves travel along the string and then reflect off the fixed ends of the string. The superposition of the incident and reflected transverse waves create standing wave patterns in the string. All the standing wave patterns have nodes at the fixed ends of the string.

5. HARMONICS The frequencies that cause the complex vibrations of standing waves are called harmonics. The harmonics represent the resonant frequencies of the string. All harmonics are produced in a string simultaneously creating a complex mixture of frequencies in the air we know as the note the instrument has produced (the timbre of the sound) The simplest standing wave in a string fixed at both ends has a node at each end and an antinode between them. The simplest standing wave produced in a string fixed at both ends is called the first harmonic or fundamental.

6. H ARMONICS ON A STRING