A friend in another city tells you that she has two organ pipes of different len
ID: 1282890 • Letter: A
Question
A friend in another city tells you that she has two organ pipes of different lengths, one open at both ends, the other open at one end only. In addition, she has determined that the beat frequency caused by the second-lowest frequency of each pipe is equal to the beat frequency caused by the seventh-lowest frequency of each pipe. Her challenge to you is to calculate the length of the organ pipe that is open at both ends, given that the length of the other pipe is 1.10 m. Note that there are two possible answers to this question. List them both, in the order indicated below.
Explanation / Answer
f2_beat = f7_beat
f2 - f2' = f7 - f7'
2*v/(2*L) - 3*v/(4*L') = 7*v/(2*L) - 13*v/(4*L')
1/(L) - 7/(2*L) = 3/(4*L') - 13/(4*L')
-2.5/L = -2.5/L'
L = L'
= 1.1 <<<<<<<<------------Answer
another possibility
f2' - f2 = f7 - f7'
3*v/(4*L) - 2*V/(2*L) = 7*v/(2*L) - 13*v/(4*L')
3*v/(4*L') - v/L = 7*v/(2*L) - 13*v/(4*L')
(3/4*L')+(13/4*L') = (7/2*L) + v/L
4/L' = 4.5/L
L = (4.5/4)*L'
= (4.5/4)*1.1
= 1.2375 m <<<<<<<<------------Answer