Speed of a Travelling Wave & Equation of Progressive Wave

Speed of Transverse Motion

On a stretched string v = √(T/m)

where, T = tension in the string and m = mass per unit length of the string.

Speed of transverse wave in a solid v = √(η/ρ)

where, η is modulus of rigidity and ρ is density of solid.

Plane Progressive Simple Harmonic Wave

Equation of a plane progressive simple harmonic wave

or   

where,

• y = displacement,
• a = amplitude of vibration
• λ = wavelength of wave, of particle,
• T = time period of wave,
• x = distance of particle from the origin and
• u = velocity of wave.

 Important Relation Related to Equation of Progressive Wave

where.   ts culled propagation constant of wave motion.
Wavelength, 
Time period. 
Frequency, 

Phase of the vibration is the angle of sine m equation, to plan progressive wave. It is denoted by φ.

Relation between phase difference and path difference and time difference