   Chapter 14, Problem 60P

Chapter
Section
Textbook Problem

The adjacent natural frequencies of an organ pipe are found to be 550. Hz and 650. Hz. (a) Calculate the fundamental frequency of the pipe. (b) Is the pipe open at both ends or open at only one end? (c) What is the length of the pipe?

(a)

To determine
To determine the fundamental frequency of the pipe.

Explanation

Given Info: The velocity of the sound in air is 343m/s, the harmonics produced at 1,2,3….upwards, and two adjacent natural frequencies of an organ pipe is 550 Hz and 650 Hz.

Formula to calculate the length of the pipe by using one of the natural frequencies is,

f1=vn2L

• f1 is the natural frequency.
• n is the integer.
• v is the speed of sound in air.
• L is the length of pipe.

Substitute 550Hz for f1 , 343m/s for v to find L.

(550Hz)=(343m/s)n2L (1)

Formula to calculate the length of the pipe by using other natural frequencies is,

f2=v(n+1)2L

• f2 is the natural frequency.
• n is the integer.
• v is the speed of sound in air.
• L is the length of pipe.

Substitute 650Hz for f2 , 343m/s for v to find L.

(650Hz)=(343m/s)(n+1)2L (2)

Subtracting the equation (2) from (1) we get the value of L

(b)

To determine
To determine the pipe ends.

(c)

To determine
The length of the pipe.

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