An organ pipe filled with a gas at 27° C resonates at 400 Hz in its fundamental mode. If it is filled with the same gas at 90° C, the resonance frequency at the same mode will be :-

Question

An organ pipe filled with a gas at 27° C resonates at 400 Hz in its fundamental mode. If it is filled with the same gas at 90° C, the resonance frequency at the same mode will be :- (A) 420 Hz (B) 440 Hz (C) 484 Hz (D) 512 Hz

Tardigrade Admin · Accepted Answer

( n 1/ n 2)=(( v 1/4 ℓ)/( v 2)4 ℓ) (400/ n 2)=( v 1/ v 2)[ from v propto √ T ] (400/ n 2)=√( T 1/ T 2) (400/ n 2)=√(300/363) ⇒ n 2=440 Hz

Q. An organ pipe filled with a gas at $2 7^{\circ} C$ resonates at $400 Hz$ in its fundamental mode. If it is filled with the same gas at $9 0^{\circ} C$ , the resonance frequency at the same mode will be :-

$420 Hz$

$440 Hz$

$484 Hz$

$512 Hz$

$\frac{n _{1}}{n _{2}} = \frac{\frac{v _{1}}{4 ℓ}}{\frac{v _{2}}{4 ℓ}}$
$\frac{400}{n _{2}} = \frac{v _{1}}{v _{2}} [$ from $v \propto T]$
$\frac{400}{n _{2}} = \frac{T _{1}}{T _{2}}$
$\frac{400}{n _{2}} = \frac{300}{363}$
$\Rightarrow n_{2} = 440 Hz$

Q. An organ pipe filled with a gas at 27∘C resonates at 400Hz in its fundamental mode. If it is filled with the same gas at 90∘C, the resonance frequency at the same mode will be :-

420Hz

440Hz

484Hz

512Hz