Question

A pipe 30 cm long, is open at both ends. Which harmonic mode of the pipe resonates a $1.1$ kHz source?

(speed of sound in air = 330 m s–1)

• A. First
• B. Second
• C. Third
• D. Fourth

Answer 1

Answer: (B)

Second

Answer 2

Here,

Speed of sound, v = $330ms^{- 1}$

Length of pipe,

$L = 30cm = 30 \times 10^{- 2}m$

In a open pipe (open at both ends), the frequency of its $n^{th}$harmonic is

$\upsilon_{n} = \frac{nv}{2L}$where n = 1,2,3,…….

$\therefore n = \frac{2L\upsilon_{n}}{v}$

Let $n^{th}$harmonic of open pipe resonate with

$1.1kHz$ Source.

$\therefore\upsilon_{n} = 1.1kHz = 1.1 \times 10^{3}Hz$

$\therefore n = \frac{2 \times 30 \times 10^{- 2} \times 1.1 \times 10^{3}}{330} = 2$