Question

A pipe closed at one end produces a fundamental note of 412 Hz. It is cut into two pieces of equal length. The fundamental notes produced by the two pieces are ____________

Options

• 206 Hz, 412 Hz

• 412 Hz, 824 Hz

• 206 Hz, 824 Hz

• 824 Hz, 1648 Hz

Answer 1

A pipe closed at one end produces a fundamental note of 412 Hz. It is cut into two pieces of equal length. The fundamental notes produced by the two pieces are 824 Hz, 1648 Hz.

Expalnation:

`"n" =v/4"L" = 412 "Hz" `

Let it cut into two parts: One is closed and other is an open pipe.

Each pipe has a length equal to half the length of original pipe.

`"n"_"c" = "v"/(4"L'") = "v"/(4(4//2)) = (2"v")/(4"L")`

` = 2 xx 412`

` = 824  "Hz"`

`"n"_"o" = "v"/(2"L'") = "v"/(2("L"/2)) = (4"v")/(4"L") = 4("v"/(4"L"))`

`= 4 xx 412`

` = 1648 "Hz"`