Waves

Transverse and Longitudinal Waves

In transverse waves, particles oscillate perpendicular to the wave propagation direction (like waves on a string), while in longitudinal waves, particles oscillate parallel to it (like sound waves in air).

Speed of a Transverse Wave on a Stretched String

The speed of a wave on a string depends directly on the tension in the string and inversely on its linear mass density, given by v = sqrt(T/μ).

Principle of Superposition

When two or more waves overlap in space, the net displacement at any point is the algebraic sum of the displacements due to individual waves, leading to phenomena like interference and beats.

Standing Waves and Normal Modes

When two identical waves traveling in opposite directions interfere, they form standing waves with alternating nodes (zero displacement) and antinodes (maximum displacement).

Beats

The periodic rise and fall in the intensity of sound produced when two slightly different frequencies interfere is known as beats, with the beat frequency equal to the difference of the two component frequencies.