# Displacement relation for a progressive waves and Speed of a travelling wave

• When a string is stretched between two ends is plucked at right angles to its and released a transverse wave travels along the length of string and velocity is given \tt V = \sqrt{\frac{T}{\mu}} where "T" is tension and "μ" is linear density.
• A uniform rope of length 'L' and mass 'm' hangs vertically from a rigid support. A block of mass 'M' is attached to the free end of rope A transverse wave pulse of wavelength λB is produced at the lower end of rope the wavelength of the pulse when it reaches the top of rope (λT) them \frac{\lambda_{T}}{\lambda_{B}} = \sqrt{\frac{M+m}{M}}
• If the particle vibration is parallel to the wave propagation then the waves produced are longitudinal waves. In longitudinal waves compressions and rare factions are formed.
• Displacement relation for a progressive wave is given by y = A sin (wt ± Kx) where 'y' is the instant displacement, "A" is the amplitude "w" is angular frequency 'K' is the wave number and "x" is position of particle at time 't'
• The distance travelled by the wave is one second is called wave velocity and is given by Vwave = w/k and is related with particle velocity as Vparticle = Vwave × slope of wave.

### Speed of transverse,longitudinal waves View the Topic in this video From 0:19 To 12:08

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