Lecture on Progressive and Standing Waves

Progressive Waves

• Move along in a medium
• Transfer energy as they progress
• Called progressive because of their energy transfer

Standing or Stationary Waves

• Do not transfer energy, they store it
• Appear not to move

Formation of Standing Waves

• Occur when a progressive wave reflects off a boundary or endpoint
• Reflected wave has the same amplitude and phase difference
• Superposition of these waves results in standing waves

Characteristics of Standing Waves

• Node: Point with no displacement
• Antinode: Point with maximum displacement

Examples on a String

• Fixed ends at both sides
• Waves cannot move at the ends (nodes present)

First Standing Wave

• Nodes at the ends
• Antinode in the middle
• Represents the fundamental mode of vibration

Second Standing Wave

• Contains one complete wavelength
• Has nodes at both ends and a node in the middle
• Antinodes between nodes
• Wavelength from node to antinode equals wavelength/2

Fundamental Frequency and Harmonics

• Fundamental Frequency (F0): First harmonic, length equals wavelength/2
• Wavelength then equals 2L

Second Harmonic

• Wavelength equals the length of the string
• Twice the frequency of the first harmonic

Higher Harmonics

• Third and fourth harmonics follow
• Multiple modes of vibration
• As frequency increases, wavelength decreases

Application

• Many musical instruments utilize these harmonics
• Multiple modes of vibration contribute to sound

Standing waves form an essential part of understanding musical instruments and wave physics, providing insight into how energy storage and frequency manipulation occur through various harmonics.