derive the velocity of transverse wave in stretched string
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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.
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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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