Question

A pipe 17 cm long is closed at one end. Which harmonic mode of the pipe resonates a 1.5 kHz source?

(speed of sound in air = 340 m s–1)

• A. First
• B. Third
• C. Fifth
• D. Seventh

Answer 1

Answer: (B)

Third

Answer 2

Here, speed of sound,

$v = 340ms^{- 1}$

Length of pipe,

$L = 17cm = 17 \times 10^{- 2}m$

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

$\upsilon_{n} = \frac{nv}{4L}wheren = 1,3,5,7,.......$

Let $n^{th}$harmonic of closed pipe resonates with $1.5kHz$source.

$\therefore\upsilon_{n} = 1.5 \times 10^{3}Hz$

$\therefore 1.5 \times 10^{3} = \frac{nv}{4L}$

$n = \frac{1.5 \times 10^{3} \times 4 \times 17 \times 10^{- 2}}{340}$

N = 3