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Organ pipe A, with both ends open, has a fundamental frequency of300Hz. The third harmonic of organ piperole="math" localid="1661418890848" B, with one end open, has the same frequency as the second harmonic of pipeA. How long are (a) pipeAand (b) pipeB?

Short Answer

Expert verified
  1. The length of pipe A is0.572 m .
  2. The length of pipe B is0.429 m .

Step by step solution

01

Given data

  • Fundamental frequency ,f0=300Hz ( for pipe A)
  • Second harmonics of A = 3rd harmonics of B
02

Determining the concept

Apply the formula for harmonics for a closed and open organ pipe.

The expression for the frequency is given by,

f0=n2LAv

Here,f0 is frequency, L is length and vis the velocity.

03

(a) Determine the length of pipe A

Fundamental frequency is defined as,

f0=n2LAv

For fundamental frequency, n=1

f0=v2LA

LA=v2f0=(343 m/s)2×300Hz=0.572m

Hence,the length of pipe A is 0.572″¾.

04

(b) Determine the length of pipe B

Frequency of harmonics for one end open pipe is defined as,

fn=n−12v2LB

Forthirdharmonicsmeanssecondoverton,n=2

f3=2−12v2LB=3×343 m/s2×2×LB

f3=257.25LBHz

Now, second harmonic of A = third harmonic of B

2f0=f3

2(300Hz)=257.25LBHz-m

LB=257.25m600=0.429m

Hence,the length of pipe B is 0.429m.

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