Question

For an organ pipe, resonance frequencies are observed at $425Hz\text{and}765Hz$. The speed of sound in air is $340m/s$.Find a resonance frequency between these two frequencies

• A. $595Hz$
• B. $575Hz$
• C. $535Hz$
• D. $605Hz$

Answer 1

The correct option is A $595Hz$

Given:

Speed of sound= 340m/sec

Let us assume that the organ pipe is closed. Then the consecutive frequencies can be written as

$n{f}_o,(n+2)f_o,(n+4)f_o$

Where, $f_o$ is the fundamental frequency

The first consecutive frequency can be written as,$f_1$ $\Rightarrow 425=n{f}_o$ …(1)

The second consecutive frequency can be written as, $f_2=(n+2)f_o$ ….(2)

The third consecutive frequency can be written as,$f_3$ $\Rightarrow 765=(n+4)f_o$ …(3)

Taking ratio of equation (1), (2) and (3), we get, $n=5$

Putting this value in equation (1), we get,$f_o=85$

Hence, fundamental frequency is 85Hz

Putting this value in equation (2)

$f_2=(5+2)85$

$f_2=595$

Therefore, the frequency between the two frequency is 595 Hz

Correct answer (a)