Question

The human ear can detect sound in the frequency range of 20 Hz of 20000 Hz. Find the corresponding wavelength ( If the speed of the sound is 330ms⁻¹)

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Answer 1

Explanation:

Speed of sound in air v=330 m/s

Wavelength of sound wave λ=

ν

v

where ν is the frequency of sound wave.

Minimum frequency heard by human ear ν

min

=20 Hz

So, maximum wavelength of sound wave λ

max

=

ν

min

v

∴ λ

max

=

20

330

=16.5 m

Maximum frequency heard by human ear ν

max

=20 kHz=20000 Hz

So, minimum wavelength of sound wave λ

min

=

ν

max

v

∴ λ

min

=

20000

330

=16.5×10

−3

m=16.5 mm

Answer 2

Given:

V = 330ms⁻¹

$n_{min} = 20Hz,$

$n_{max} = 20 \: kHz$

Formula used : V = n λ

V = nλ

$λ \: = \frac{V}{n}$

$(i) \: for \: n_1 = 20Hz ;$

$λ = \frac{330}{20} \\ = 16.5 \: m$

$(ii) \: for \: n_2 = 20000 \: Hz$

$λ = \frac{330}{20000}$

λ = 16.5mm