Physics · Sound Waves

JEE Main 2024 — 8 April, Shift 1 — Question 54

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right)$ then the value of $a$ is $\qquad$ .

Answer: 16

Numerical answer — enter this value.

Step-by-step solution

For closed organ pipe

$\mathrm{f}_{\mathrm{c}}=(2 \mathrm{n}+1) \frac{\mathrm{v}}{4 \ell}=\frac{15 \mathrm{v}}{4 \ell}$

For open organ pipe

$\mathrm{f}_{\mathrm{o}}=(\mathrm{n}+1) \frac{\mathrm{v}}{2 \ell}=\frac{8 \mathrm{v}}{2 \ell}$

$\frac{\mathrm{f}_{\mathrm{c}}}{\mathrm{f}_{\mathrm{o}}}=\frac{15}{16}=\frac{\mathrm{a}-1}{\mathrm{a}}$

$\Rightarrow \mathrm{a}=16$

Answer key and solution verified before publishing.

Practise Sound Waves

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2024
Paper: 8 April, Shift 1
Subject: Physics
Chapter: Sound Waves
Topic: Vibrations in rod and Air Columns - Organ pipes