Question

What will be the fundamental frequency and first three overtones for a 26cm long organ at 20°C if it is open ( at 20°C, the speed of sound in air is 343m/s)

Answer 1

Explanation:

The frequency of an organ pipe if it is open is given by :

$f=\dfrac{nv}{2l}$

v is speed of sound in air is 343 m/s at 20°C

For fundamental frequency, n = 1

$f=\dfrac{1\times 343}{2\times 0.26}\\\\f=659.61\ Hz$

First overtone frequency,

$f_1=2f\\\\f_1=2\times 659.61\\\\f_1=1319.22\ Hz$

Second overtone frequency,

$f_2=3f\\\\f_2=3\times 659.61\\\\f_2=1978.83\ Hz$

Third overtone frequency

$f_3=4f\\\\f_3=4\times 659.61\\\\f_3=2638.44\ Hz$

Hence, this is the required solution.