A long composite string is made up by joining two strings of different mass per unit length μ and $$4$$μ respectively. The composite string is under the same tension. A transverse wave pulse $$Y=6$$ $$mmsin5t+40x$$, where ‘t’ is in seconds and ‘x’ is in metres, is sent along the lighter string towards the joint. The joint is at $$x=0$$ . The equation of the wave pulse reflected from the joint is

Question

A long composite string is made up by joining two strings of different mass per unit length  μ  and $$4$$μ respectively. The composite string is under the same tension. A transverse wave pulse $$Y=6$$ $$mmsin5t+40x$$, where ‘t’ is in seconds and ‘x’ is in metres, is sent along the lighter string towards the joint. The joint is at $$x=0$$ . The equation of the wave pulse reflected from the joint is

Infinity Learn · Accepted Answer

Given wave pulse  $$Y=6$$ $$mmsin5t+40x$$.....$$.1We$$ know speed of wave $$v=T$$μ...$$.2Assume$$  $$v1=Speed$$ in string $$1$$ $$(of$$ density μ$$1$$ $$)v2=Speed$$ in string $$2$$ $$(of$$ density  μ$$2)v1=T$$μ;$$v2=T4$$μ⇒$$v1v2=2$$∴$$v2$$

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