# JEE Class main Answered

**Plz sove my query as soon as possible shown below**

Asked by sarveshvibrantacademy | 16 Mar, 2019, 13:13: PM

Expert Answer

when a stretched string under tension is fixed at both ends, standing waves are setup.

if y is displacment at any point x, then standing wave equation is given by, y = 2a sin(kx) cos(ωt) ...........................(1)

for fundamental mode k = 2π/λ = 2π/(2L) = π/L where λ is wavelength and L is length of string.

ω = 2πf = 2π(v/λ) = πv/L , where f is frequency = v/λ and v is velocity of wave in the string.

velocity at a given point x is given by, .............................(2)

for a small mass of string dm at a point x, maximum kinetic energy dk is given by,

................................(3)

where μ is the linear mass density (mass /unit length).

we have used the relations and T = mg , to get the simplified eqn.(3)

Maximum Kinetic energy K

_{max }for full string of length L =( integration limits : when x = 0, kx = 0 ; when x = L, kx = kL = π )

maximum kinetic energy K

_{max}is obtained from eqn.(4) ,----------------------------------------

for first ovetone, maximum kinetic energy is calculated in similar manner by using k = (2π) / λ = (2π) / L

Answered by Thiyagarajan K | 17 Mar, 2019, 11:55: AM

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