The fundamental frequency of a pipe open at both ends is 512 Hz. If it is closed at one end, its fundamental frequency will be

Concept:

• The sound-producing device which resonates at a particular pitch is called an Organ pipe.
• When one end of an organ pipe is closed and the other end is open then it is called a closed organ pipe.
• When both the ends of the organ pipe are open then it is called an open organ pipe.

\(Fundamental~frequency~of~an~open~organ~pipe~\left( {{f}_{o}} \right)=\frac{v}{2l}\)

\(Frequency~of~a~closed~organ~pipe~\left( {{f}_{c}} \right)=\frac{nv}{4l}\)

Where n = positive integer, v = velocity of sound, and l = length of the organ pipe.

Calculations:

Given that, f_o = 512 Hz

\(Frequency~of~a~closed~organ~pipe~\left( {{f}_{c}} \right)=\frac{nv}{4l}\)

\(Fundamental~frequency~of~an~open~organ~pipe~\left( {{f}_{o}} \right)=\frac{v}{2l}\) = 2 f_c

i.e f_c = f_o/2 = 512/2 = 256 Hz.

The fundamental frequency will be 256 Hz.