JEE Advanced 2024 Paper 2 · Physics · Waves and Sound · medium

A pipe of length 0.85 m is closed at one end and open at the other. Take the speed of sound in air as 340 m s^-1 and ignore end corrections.

One or more options correct

A pipe of length

0.85\ \mathrm{m}

is closed at one end and open at the other. Take the speed of sound in air as

340\ \mathrm{m\,s^{-1}}

and ignore end corrections. Which of the following statements is/are correct?

A. A tuning fork of frequency $500\ \mathrm{Hz}$ sets the air column in resonance.
B. A tuning fork of frequency $600\ \mathrm{Hz}$ sets the air column in resonance.
C. If the pipe were closed at both ends, its fundamental frequency would be $100\ \mathrm{Hz}$ .
D. If the absolute temperature of the air rises by $4\%$ , the fundamental frequency becomes approximately $102\ \mathrm{Hz}$ .

Show answer and solution

Answer: A, D

For a pipe closed at one end,

f_n=(2n-1)\dfrac{v}{4L}=(2n-1)\times100\ \mathrm{Hz}

, giving

100, 300, 500, 700,\dots\ \mathrm{Hz}

(odd multiples only). (A)

500\ \mathrm{Hz}=5\times100

is the third allowed mode, so it is correct. (B)

600\ \mathrm{Hz}

is an even multiple and is not allowed, so it is incorrect. (C) With both ends closed there is a displacement node at each end, so

L=\lambda/2

and

f_1=v/2L=200\ \mathrm{Hz}

, not

100\ \mathrm{Hz}

; incorrect. (D)

v\propto\sqrt{T}

, so

f_1

becomes

100\sqrt{1.04}=101.98\approx102\ \mathrm{Hz}

(neglecting the tiny change of

L

); correct. Hence (A) and (D).

Original question written in the JEE Advanced 2024 Paper 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake