Chapter 17, Problem 104A

(a)

To determine

To identify:Whether the instrument should be designed to have open pipes or closed pipes.

Answer to Problem 104A

The instrument should be designed to have open pipes that will fit into a small space.

Explanation of Solution

Given:

Pipe organs are designed to fit into small spaces.

Consider the wavelength of the filter is denoted by $\lambda$ .Consider the length of the pipe is denoted by $L$ .

In case of open pipes, the resonation of pipe takes place only when the length of the pipe is even number of quarter wavelength.

  ${\lambda }_{\text{open}}=2L$

In case of closed pipes, the resonation of pipe takes place only when the length of the pipe is odd number of quarter wavelength.

  ${\lambda }_{\text{closed}}=4L$

In order to have same wavelength of the resonance sound, the length of closed pipe is twice that of the length of the open pipe.

The closed pipe needs more large space (double the space) in comparison the open pipe. So, the person will design open pipe as the space is small.

Conclusion:

Thus, the person will design open pipe.

(b)

To determine

To identify:Whether an organ constructed with open pipes will sound same as one constructed with closed pipes.

Answer to Problem 104A

No, an organ constructed with open pipes will not sound same as with closed pipes.

Explanation of Solution

Given:

Pipe organs are designed to fit into small spaces.

Refer Part (a).

Consider open pipe and closed pipe of equal length.

The wavelength of the resonance sound of closed pipe is twice that of the wavelength of the resonance sound of open pipe.

The wavelength and frequency of sound are inversely proportional to each other.

The frequency of the resonance sound of closed pipe is half that of the frequency of the resonance sound of open pipe.

Hence, the sound produced by the organ using open pipe will be different from the sound of the organ produced by the closed pipe of same length.

Conclusion:

Thus, an organ constructed with open pipes will not sound the same as one constructed with closed pipes.