Question

A child has an ear canal that is 1.3 cm long. Assume the speed of sound is v = 344 m/s.

At what sound frequencies in the audible range will the child have increased hearing sensitivity?

Express your answer using two significant figures. Enter your answers numerically separated by commas.

Answer 1

The frequencies are
`(f, f_1) = (6615.4 \ Hz , 19846.2\ Hz)`

Step-by-step explanation:

From the question we are told that

The length of the ear canal is
`l = 1.3 \ cm =(1.3)/(100) = 0.013 \ m`

The speed of sound is assumed to be
`v_s = 344 \ m/s`

Now taking look at a typical ear canal we see that we assume it is a closed pipe

Now the fundamental harmonics for the pipe(ear canal) is mathematically represented as

`f = (v_s)/(4 * l )`

substituting values

`f = (344)/(4 * 0.013 )`

`f = 6615.4 \ Hz`

Also the the second harmonic for the pipe (ear canal) is mathematically represented as

`f_1 = (3v_s)/(4 * l)`

substituting values

`f_1 = (3 * 344)/(4 * 0.013)`

`f_1 = 19846.2 \ Hz`

Given that sound would be loudest in the pipe at the frequency, it implies that the child will have an increased audible sensitivity at this frequencies