A hollow metallic tube of length L and closed at one end produce resonance with a tuning fork of frequency n. The entire tube is then heated carefully so that at equilbrium temperature its length changes by ℓ. If the change in velocity V of sound is v, the resonance will now be produced by tuning fork of frequency.

Question

A hollow metallic tube of length L and closed at one end produce resonance with a tuning fork of frequency n. The entire tube is then heated carefully so that at equilbrium temperature its length changes by ℓ. If the change in velocity V of sound is v, the resonance will now be produced by tuning fork of frequency. (A) ( V + v ) /[4( L +ℓ)] (B) ( V + v ) /[4( L -ℓ)] (C) ( V - v ) /[4( L +ℓ)] (D) ( V - v ) /[4( L -ℓ)]

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/4042da1f192a095f38e3bf8db004be4e-.png" /> n =( v /4 ℓ) By increasing temperature, velocity of sound length both increases, so n=(V+v/4(L+ℓ))

$(V + v) / [4 (L + ℓ)]$

$(V + v) / [4 (L - ℓ)]$

$(V - v) / [4 (L + ℓ)]$

$(V - v) / [4 (L - ℓ)]$

$n = \frac{v}{4 ℓ}$
By increasing temperature, velocity of sound $&$ length both increases, so
$n = \frac{V + v}{4 ( L + ℓ )}$

(V+v)/[4(L+ℓ)]

(V+v)/[4(L−ℓ)]

(V−v)/[4(L+ℓ)]

(V−v)/[4(L−ℓ)]

n=4ℓv​ By increasing temperature, velocity of sound & length both increases, so n=4(L+ℓ)V+v​

$(V + v) / [4 (L + ℓ)]$

$(V + v) / [4 (L - ℓ)]$

$(V - v) / [4 (L + ℓ)]$

$(V - v) / [4 (L - ℓ)]$

$n = \frac{v}{4 ℓ}$
By increasing temperature, velocity of sound $&$ length both increases, so
$n = \frac{V + v}{4 ( L + ℓ )}$