Question 472: Waves

Question

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is

Accepted Answer

The fundamental frequency of an open pipe,
n
oop
, is given by
V / (2L)
, where
V
is the speed of sound and
L
is the length of the pipe.
For a closed pipe of the same length, the fundamental frequency,
n
cop
, is
V / (4L)
since only half as many wavelengths fit into the same length due to the closed end.
Therefore, the ratio of frequencies of an open pipe to a closed pipe is:
$$\frac{n_{	ext{oop}}}{n_{	ext{cop}}} = \frac{V / (2L)}{V / (4L)} = \frac{4L}{2L} = 2:1$$
This shows that the fundamental frequency of an open pipe is twice that of a closed pipe of the same length.

Answer

$$2: 1$$

Answer

$$1: 3$$

Answer

$$3: 1$$

Answer

$$1: 2$$

Waves

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is

Choose the correct answer: