Verified Solution • 2025–26 Session moderate

QJEEAdv19Pha33e: JEE Advanced 2019 Physics - Class 11 JEEAdv19Pha33e Solution: A musical instrument is made using four different metal…

A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length

μ

, 2

μ

, 3

μ

and 4

μ

respectively. The instrument is played by vibrating the strings by varying the free length in between the range L₀ and 2L₀. It is found that in string-1

μ

at free length L₀ and tension T₀ the fundamental mode frequency is f₀.

List-I gives the above four strings while list-II lists the magnitude of some quantity.

JEE Advanced 2019 Paper 2 Offline Physics - Waves Question 26 English

If the tension in each string is T₀, the correct match for the highest fundamental frequency in f₀ units will be

Multiple Choice Options

A I → P, II → Q, III → T, IV → S
B I → P, II → R, III → S, IV → Q
C I → Q, II → S, III → R, IV → P
D I → Q, II → P, III → R, IV → T

Step-by-Step Verified Solution

Fundamental frequency is maximum when length is minimum i.e. L₀,

Case 1.

L = L_{0}, T = T_{0}, f = f_{0}

;

f_{1} = \frac{1}{2 L_{0}} \sqrt{\frac{T_{0}}{μ}}

Case 2.

f_{2} = \frac{1}{L_{0}} \sqrt{\frac{T_{2}}{2 μ}} = \frac{f_{0}}{\sqrt{2}}

Case 3.

f_{3} = \frac{1}{L_{0}} \sqrt{\frac{T_{2}}{3 μ}} = \frac{f_{0}}{\sqrt{3}}

Case 4.

f_{4} = \frac{1}{L_{0}} \sqrt{\frac{T_{2}}{4 μ}} = \frac{f_{0}}{2}

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