A cylindrical tube closed at one end contains air. It produces the fundamental note of frequency 512 Hz. If the tube is opened at both ends, the fundamental frequency that can be excited is

Question

A cylindrical tube closed at one end contains air. It produces the fundamental note of frequency 512 Hz. If the tube is opened at both ends, the fundamental frequency that can be excited is (A) 256 Hz (B) 512 Hz (C) 1024 Hz (D) 128 Hz

Tardigrade Admin · Accepted Answer

Let l be the length of pipe, v the speed of sound, then the fundamental tone or first harmonic of closed tube <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/abaeb66baec7d1ce2d8fe3cbb733dc65-.png" /> n1=(v/4 l) For open tube n2=(v/2 l) ∴ n2=2 n1 Given, n1=512 Hz ∴ n2=2 × 512=1024 Hz

Q. A cylindrical tube closed at one end contains air. It produces the fundamental note of frequency $512 Hz$ . If the tube is opened at both ends, the fundamental frequency that can be excited is

256 Hz

512 Hz

1024 Hz

128 Hz

Let $l$ be the length of pipe, $v$ the speed of sound, then the fundamental tone or first harmonic of closed tube

$n_{1} = \frac{v}{4 l}$
For open tube
$n_{2} = \frac{v}{2 l}$
$∴ n_{2} = 2 n_{1}$
Given, $n_{1} = 512 Hz$
$∴ n_{2} = 2 \times 512 = 1024 Hz$

Q. A cylindrical tube closed at one end contains air. It produces the fundamental note of frequency 512Hz. If the tube is opened at both ends, the fundamental frequency that can be excited is