A cylinder pipe of length 28 cm closed on one end is to be in resonance when a tuning fork is sounded near the open end at 100Hz. Determine the value of end - correction of the pipe. Take the velocity of sound in air as 340m /second
To determine the value of the end correction of the pipe, we first need to understand the concept of resonance in a closed pipe.
In a closed pipe, such as the cylinder pipe described in the question, resonance occurs when the length of the pipe is equal to a specific fraction of the wavelength of the sound wave produced by the tuning fork. The closed end of the pipe acts as a node, which is a point of no displacement, while the open end acts as an antinode, which is a point of maximum displacement.
The formula to calculate the resonant frequencies of a closed pipe is given by:
f = (2n - 1) * (v / 4L)
Where:
f is the frequency of the tuning fork (100Hz in this case)
n is the harmonic number (1 for the fundamental frequency, 2 for the second harmonic, 3 for the third harmonic, and so on)
v is the velocity of sound in air (340m/s)
L is the length of the pipe (28cm or 0.28m since the length is given in centimeters)
We can rearrange the formula to solve for L:
L = (2n - 1) * (v / 4f)
Now, let's substitute the given values and calculate the length of the pipe for the fundamental frequency (n = 1):
L = (2 * 1 - 1) * (340 / (4 * 100))
L = (2 - 1) * (340 / 400)
L = 1 * (0.85)
L = 0.85m
The end correction of the pipe is the difference between the actual length of the closed pipe and the calculated length for resonance. In this case, the actual length is 0.28m, and the calculated length for resonance is 0.85m.
End correction = Actual length - Calculated length
End correction = 0.28m - 0.85m
End correction = -0.57m
Therefore, the value of the end correction of the pipe is -0.57m (negative indicating that the open end is lower than expected).