Question

A person hears sound wave beast at 3000Hz at the temperature of 30 °C. What is the person's ear canal length? Please explain

Answer 1

Answer:

The person's ear canal length is 2.91 cm.

Explanation:

Given that,

Frequency = 3000 Hz

Temperature = 30°C

We need to calculate the speed

Using equation of sound wave with temperature

[texs]v(t)=331+0.6\times T[/tex]

Put the value of T

$v(t)=331+0.6\times30^{\circ}\ C$

$v(t)=349\ m/s$

We need to calculate the length

Using formula of closed organ pipe

$f=\dfrac{v}{4L}$

$L=\dfrac{v}{4f}$

Where, L = length

v = velocity

f = frequency

Put the value into the formula

$L=\dfrac{349}{4\times3000}$

$L=0.0291\ m$

$L=2.91\times10^{-2}\ m$

$L=2.91\ cm$

Hence, The person's ear canal length is 2.91 cm.