Question

The human ear canal is, on average, 2.5cm long and aids in hearing by acting like a resonant cavity that is closed on one end and open on the other. The length of the ear canal is partially responsible for our sensitivities to certain frequencies. Use 340m/s for the speed of sound when performing the following calculations. What is the first resonant frequency?

Answer 1

`3400` Hz

Step-by-step explanation:

We know that

1 cm = 0.01 m

`L` = Length of the human ear canal = 2.5 cm = 0.025 m

`V` = Speed of sound = 340 ms⁻¹

`f` = First resonant frequency

The human ear canal behaves as a closed pipe and for a closed pipe, nth resonant frequency is given as

`f = ((2n - 1)V)/(4L)`

for first resonant frequency, we have n = 1

Inserting the values

`f = ((2(1) - 1) 340)/(4(0.025))`

`f = (340)/(4(0.025))`

`f = 3400` Hz