Question

derive the velocity of transverse wave in stretched string​

Answer 1

Explanation:

1)Transverse wave speed determined by:

Mass per unit length- As mass gives rise to Kinetic energy. If no mass then no kinetic energy. Then there will be no velocity. ...

2)Tension-Tension is the key factor which makes the disturbance propagates along the string. Because of tension the disturbance travels throughout the wave.

Answer 2

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Speed of a transverse wave in a stretched string

• Consider a stretched string and if given transverse disturbance on one end then the disturbance travels throughout the string.
• Thereby giving rise to transverse waves.
• The particles move up and down and the waves travel perpendicular to the oscillation of the particles.
• Transverse wave speed determined by:
• Mass per unit length- As mass gives rise to Kinetic energy.If no mass then no kinetic energy.Then there will be no velocity.
• It is denoted by μ.
• Tension-Tension is the key factor which makes the disturbance propagates along the string.
• Because of tension the disturbance travels throughout the wave.
• It is denoted by T.

• Dimensional Analysis to show how the speed is related to mass per unit length and Tension

μ = [M]/[L] = [ML-1] (i)

T=F=ma =[M][LT-2] = [MLT-2] (ii)

Dividing equation (i) by (ii) :- [ML-1]/[MLT-2] = L-2T-2 =[T/L]2 =[TL-1]2 =1/v2

Therefore μ/T = 1/v2

v=C√T/ μ where C=dimensionless constant

Conclusion: v depends on properties of the medium and not on frequency of the wave.

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