An open pipe is in resonance in 2nd harmonic with frequency . Now one end of the tube is closed and frequency is increased to such that the resonance again occurs in th harmonic. Choose the correct option. [2005]

Question

An open pipe is in resonance in 2nd harmonic with frequency $f_{1}$ . Now one end of the tube is closed and frequency is increased to $f_{2}$ such that the resonance again occurs in $n$ th harmonic. Choose the correct option. [2005]

Smart Achievers · Accepted Answer

(4)

$Frequency of 2nd harmonic of open pipe,$

$f_{1} = \frac{v}{λ} = \frac{v}{l} \dots (i)$

$Frequency of n^{th} harmonic of closed pipe,$

$f_{2} = \frac{v}{λ} = \frac{n v}{4 l} \dots (i i)$

$Here n is an odd number. From eq. (i) and (ii)$

$f_{2} = \frac{n}{4} f_{1},$ $For first resonance, n = 5$ $∴ f_{2} = \frac{5}{4} f_{1}$

Solution

Q.
An open pipe is in resonance in 2nd harmonic with frequency $f_{1}$ . Now one end of the tube is closed and frequency is increased to $f_{2}$ such that the resonance again occurs in $n$ th harmonic. Choose the correct option. [2005]

1 $n = 3, f_{2} = \frac{3}{4} f_{1}$

2 $n = 3, f_{2} = \frac{5}{4} f_{1}$

3 $n = 5, f_{2} = \frac{3}{4} f_{1}$

4 $n = 5, f_{2} = \frac{5}{4} f_{1}$

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Solution

Q. An open pipe is in resonance in 2nd harmonic with frequency f1. Now one end of the tube is closed and frequency is increased to f2 such that the resonance again occurs in nth harmonic. Choose the correct option. [2005]

1 n=3, f2=34f1

2 n=3, f2=54f1

3 n=5, f2=34f1

4 n=5, f2=54f1