For a pipe closed at one end, the fundamental frequency is given by:
f1=‌where:
f1 is the fundamental frequency
v is the speed of sound
L is the length of the pipe
The possible frequencies for a pipe closed at one end are odd multiples of the fundamental frequency:
fn=(2n−1)f1=(2n−1)‌where
n is an integer
(1,2,3,...).
We need to find the number of possible frequencies below 1250 Hz . Let's plug in the given values and solve for
n :
1250‌Hz≥(2n−1)‌Simplifying the inequality:
‌1250‌Hz≥(2n−1)100‌Hz‌12.5≥2n−1‌13.5≥2n‌n≤6.75 Since
n must be an integer, the maximum value of
n is 6 . This means there are 6 possible frequencies below 1250 Hz .
Therefore, the correct answer is Option A: 6.