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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 :

Explanation:

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

[tex]f=\dfrac{nv}{2l}[/tex]

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

For fundamental frequency, n = 1

[tex]f=\dfrac{1\times 343}{2\times 0.26}\\\\f=659.61\ Hz[/tex]

First overtone frequency,

[tex]f_1=2f\\\\f_1=2\times 659.61\\\\f_1=1319.22\ Hz[/tex]

Second overtone frequency,

[tex]f_2=3f\\\\f_2=3\times 659.61\\\\f_2=1978.83\ Hz[/tex]

Third overtone frequency

[tex]f_3=4f\\\\f_3=4\times 659.61\\\\f_3=2638.44\ Hz[/tex]

Hence, this is the required solution.

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