An open organ pipe emits E (330 Hz ) when the temperature is 26 ∘C. The speed of sound in air is v≈(331+0.60T)m/s, where T is the temperature in ∘C. Determine the length of the pipe.
Question
Question
An open organ pipe emits E (330 Hz ) when the temperature is 26 ∘C. The speed of sound in air is v≈(331+0.60T)m/s, where T is the temperature in ∘C. Determine the length of the pipe.
Answer:
0.525 m
Explanation:
From the question,
In an open pipe,
v = λf………………. Equation 1
Where v = speed of sound in the pipe, f = frequency, λ = wave length.
But,
λ = 2l……………. Equation 2
Where l = length of the pipe
Substitute equation 2 into equation 1
v = 2lf………….. Equation 3
make l the subject of the equation
l = v/2f…………. Equation 4
Given:
v ≈ (331+0.60T) m/s at T = 26°C
v ≈ (331+0.60×26) ≈ 346.6 m/s
f = 330 Hz.
Substitute these values into equation 4
l = 346.6/(2×330)
l = 346.6/660
l = 0.525 m
Hence the length of the pipe is 0.525 m