In a closed organ pipe of length 105 cm, standing waves are set up corresponding to third overtone. What distance from the closed end, a pressure node is formed?

Question

In a closed organ pipe of length 105 cm, standing waves are set up corresponding to third overtone. What distance from the closed end, a pressure node is formed? (A) 5 cm (B) 15 cm (C) 25 cm (D) 30 cm

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/5790a662043a4b0cc9556170a800f468-.png" /> In a closed pipe f=((2 P+1)/4 l) v For third overtone (f)=(7 v/4 l) λ=(v/f)=(v/7 v) × 4 l λ=(4 l/7) λ=(4 × 105/7) λ=60 cm First pressure node will be formed (λ/4)

Q. In a closed organ pipe of length $105 c m$ , standing waves are set up corresponding to third overtone. What distance from the closed end, a pressure node is formed?

5 cm

15 cm

25 cm

30 cm

In a closed pipe $f = \frac{( 2 P + 1 )}{4 l} v$
For third overtone $(f) = \frac{7 v}{4 l}$
$λ = \frac{v}{f} = \frac{v}{7 v} \times 4 l$
$λ = \frac{4 l}{7}$
$λ = \frac{4 \times 105}{7}$
$λ = 60 c m$
First pressure node will be formed $\frac{λ}{4}$

Q. In a closed organ pipe of length 105cm, standing waves are set up corresponding to third overtone. What distance from the closed end, a pressure node is formed?