A pipe closed at one end produces a fundamental note of frequency 412 Hz. If it is cut into two pieces of equal lengths , then the fundamental frequencies produced by the two pieces would be

Options

A. 206 Hz, 412 Hz
B. 824 Hz, 1648 Hz
C. 412 Hz, 824 Hz
D. 206 Hz, 824 Hz

Answer

C

Explanation

The fundamental frequency of closed pipe at one end `=(v)/(4L)=412Hz`
When cut into two equal pieces, fundamental frequency of closed pipe of half the length
`=(v)/(4(L//2))=(2v)/(4L)=2xx412Hz=824Hz`
Fundamental frequency of open pipe of half the length
`=(v)/(2(L//2))=(v)/(L)=4xx(v)/(4L)=4xx412Hz=1648Hz`