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A wave traveling from the left encounters a junction between the heavy string in which it moves and a lighter one. The incoming wave divides equally into a transmitted and reflected component. What is the ratio of densities of the string?
Asked by anaghaagarwal15 | 15 Mar, 2022, 05:15: PM
Amplitudes of reflected waves and transmitted waves are given as

............................(1)
..........................(2)
Where A denotes Amplitude of waves , subscript i denotes incident wave,
subscript r denotes reflected wave  and subscript t denotes transmitted wave.

v1 and v2 are velocities in string-1 and string-2 respectively.

If the incoming wave is divided equally into reflected and transmitted component means
intensities of reflected and transmitted components are equal.

Since intensity of wave is proportional square of amplitude , we get

Ar2  = At2

Using eqn.(1) and (2) in above expression , we get after simplification as

we get the following quadratic equation in v1 from above expression

we get v2 = 3 v1 as acceptable solution from above expression

velocity of wave in the string is given as

where T is tension in the string and d is linear mass density ( mass per unit length )

hence , v2 ( 1 / d)
Answered by Thiyagarajan K | 15 Mar, 2022, 11:07: PM
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