12.5 Harmonics

Question 1

How do stringed instruments produce musical notes?

Answer 1

• Stringed instruments produce musical notes by vibrating strings, which create standing waves with nodes at fixed ends and antinodes in between.
• The pitch of the note depends on the string length, tension, and mass per unit length, with shorter, tighter, or lighter strings producing higher frequencies.
• The instrument body amplifies the sound through resonance, and harmonics add richness by generating higher-frequency overtones.

Question 2

What does each string have?

Answer 2

• A fundamental mode of vibration (also called the first harmonic) which is the simplest vibration pattern in which a system oscillates. It has the lowest possible frequency for that system. In a vibrating string, the fundamental mode has one antinode in the middle and nodes at both ends. In an open pipe, it has a single half-wavelength fitting in the pipe length.
• A fundamental frequency: the lowest frequency at which a system naturally vibrates in its fundamental mode. All higher harmonics (overtones) are integer multiples of this fundamental frequency.

Question 3

How do you produce stationary waves on strings?

Answer 3

Stretch the string between two fixed points, these points act as nodes. When the string is plucked a progressive wave travels along the string and reflects of its ends. This creates two progressive waves travelling in opposite directions that then form a stationary wave.

• When the string is plucked, it vibrates in its fundamental mode of vibration.

Question 4

Describe how different harmonics on a string might be observed in a classroom.

Answer 4

A stretched string fixed at one end with a vibration generator (connected to a signal generator) at the other end.

Adjust the frequency of the signal generator and produce strings with different frequencies.

Question 5

What is a harmonic?

Answer 5

A harmonic is a specific vibration pattern that an object (like a string or air column) can naturally produce.

Each harmonic has a:

Specific wavelength

Specific frequency

Specific shape (number of nodes and antinodes)

They’re like musical “layers” stacked on top of the base sound.