Question

An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends vibrating in third harmonic. The ratio of lengths of the two pipes is ____________.

Options

• 1 : 2

• 3 : 8

• 8 : 3

• 4 : 1

Answer 1

An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends vibrating in third harmonic. The ratio of lengths of the two pipes is 1 : 2.

Explanation:

In first overtone of organ pipe open at one end,

`"n"_"e" = (3"v")/(4l_"c")`     ......(i)

In third harmonic or second overtone of organ pipe open at both ends,

`"n"_0 = (3"v")/(2l_"c")`     .......(ii)

`"Given, n"_"c" = "n"_"o" Rightarrow (3"v")/(4l_"c") = (3"v"_0)/(2l_0) Rightarrow l_"c"/l_0 = 1/2`