Question

When open pipe is closed from one end third overtone of closed pipe is higher in frequency by 150 Hz, then second overtone of open pipe. The fundamental frequency of open end pipe will be ____________.

Options

• 400 Hz

• 200 Hz

• 500 Hz

• 300 Hz

Answer 1

When open pipe is closed from one end third overtone of closed pipe is higher in frequency by 150 Hz, then second overtone of open pipe. The fundamental frequency of open end pipe will be 300 Hz.

Explanation:

The frequency of third overtone of closed pipe is

f₃ = (2(3) + 1)f₁ = 7f₁

where, f₁ = fundamental frequency of closed pipe = `"v"/(4"l")`

The frequency of second overtone of open pipe is 

f₂ = (2 + 1)f₁ = 3f₁

where, f₁ = fundamental frequency of open pipe = `"v"/(2"l")` = 2f₁

Given, f₃ − f₂ = 150

7f₁ − 3f₁ = 150

7f₁ − 3(2f₁) = 150

f₁ = 150 Hz

∴ f₁ = 2f₁ = 300 Hz