Question

A pipe $17cm$ long is closed at one end. Which harmonic mode of the pipe resonates with $1.5kHz$ ?
(Speed of sound in air $=340m{s}^{-1}$)

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

Answer 1

Answer: (B)

Third

Here, speed of sound, $\nu =340m{s}^{-1}$

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

${\upsilon }_n=\frac{n\nu }{4L}$ where $n=1,3,4,7,.....$

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

$\therefore {\upsilon }_n=1.5\times {10}^{3}Hz$

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

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