stationary waves

What is a stationary wave?

A wave formed when two waves of the same amplitude travel at the same speed in opposite directions and interfere.

What are nodes in a stationary wave?

Points of destructive interference where the displacement is zero.

What are antinodes?

Points of constructive interference where the amplitude is maximum.

What is resonance?

The storing of energy in an oscillation of a stationary wave due to energy supplied by an external force.

How are stationary waves produced in musical instruments?

When a travelling wave and its reflection interfere inside the instrument, which acts as a resonator.

What type of wave occurs on strings vs in pipes?

On strings → transverse waves; in pipes → longitudinal waves.

What vibrates in string instruments?

The string itself.

What vibrates in pipes?

The air column.

What happens at the ends of a string?

Nodes form at both ends.

What happens in a closed pipe?

There is a node at one end and an antinode at the other.

What happens in an open pipe?

There is a node in the middle and antinodes at both ends.

What is the lowest frequency called, and what determines its wavelength?

The fundamental frequency — wavelength depends on the pipe/string length:
String: λ = 2l
Closed pipe: λ = 4l
Open pipe: λ = 2l

How can frequency be altered in a string instrument?

By changing the string’s length, tension, or mass per unit length.

How can frequency be altered in pipes?

By changing air pressure or the length of the air column (e.g., using a stop).

What are the similarities between waves on strings and in pipes?

Both use oscillations, produce stationary waves, and create sound due to resonance.

What is the equation linking tension, wave speed, and linear mass density?

𝑇=𝜇𝑣^2

What is linear mass density?

𝜇=𝑚/?