The ear canal acts as a cylindrical pipe closed at one end - Leaving Cert Physics - Question e - 2016
Question e
The ear canal acts as a cylindrical pipe closed at one end. It is of average length 2.3 cm. The speed of sound in air is 340 m s⁻¹.
What is the fundamental frequency... show full transcript
Worked Solution & Example Answer:The ear canal acts as a cylindrical pipe closed at one end - Leaving Cert Physics - Question e - 2016
Step 1
Calculate the Wavelength
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Answer
To find the wavelength (
\lambda
), we use the formula adapted for a pipe closed at one end:
λ=n4L
where:
L is the length of the ear canal (2.3 cm = 0.023 m)
n is the harmonic number, which is 1 for the fundamental frequency.
Thus,
λ=4×0.023m=0.092m
Step 2
Calculate the Fundamental Frequency
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Answer
Now, we can calculate the fundamental frequency (f) using the wave speed equation:
f=λc
Substituting the values:
Speed of sound (c) = 340 m s⁻¹
Wavelength (\n \lambda
) = 0.092 m
Therefore,
f=0.092m340m/s≈3696Hz
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