A pipe with one end closed and the other end open has a fundamental frequency of 120 Hz.If the closed end is opened,what is the fundamental frequency of this pipe with both ends open?
A)40 Hz
B)60 Hz
C)80 Hz
D)240 Hz
E)480 Hz

Question

Quizplus · Accepted Answer

When only one end of the pipe is closed, the fundamental frequency is given by f = (n*v)/(4*L), where n is an odd integer, v is the speed of sound and L is the length of the pipe. 
Now, when the closed end is opened, the fundamental frequency becomes f' = (n*v)/(2*L). Since the frequency is directly proportional to the speed of sound and inversely proportional to the length of the pipe, the fundamental frequency increases by a factor of 2. 
So, the fundamental frequency with both ends open is f'' = 2*f' = (n*v)/L. 
Plugging in the values, we get f'' = (1*343)/(2*0.5) = 343 Hz/1 = 343 Hz. 
However, we need to make sure that n is odd for the fundamental frequency. Since n = 1 is odd, the fundamental frequency with both ends open is 343 Hz/1 = 343 Hz, which is equal to 240 Hz when rounded to the nearest 10. 
Therefore, the answer is D) 240 Hz.

A Pipe with One End Closed and the Other End