QJEEM20Phb759: JEE Main 2020 Physics - Class 11 JEEM20Phb759 Solution: Assume that the displacement(s) of air is proportional to the…

Question

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Assume that the displacement(s) of air is proportional to the pressure difference (

Δ

p) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air (

ρ

) and the frequency (f). If

Δ

p ~ 10 Pa, v ~ 300 m/s,

ρ

~ 1 kg/m³ and f ~ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1) :

Accepted Answer

Given, S

\propto

Δ

p

and Proportionally constant = 1

We know,

Δ

p = S

β

k

=

ρ

v²

\times

\frac{ω}{v} \times S

=

ρ v ω S

∴

S =

\frac{Δ p}{ρ v ω}

=

\frac{Δ p}{ρ v 2 π f}

=

\frac{Δ p}{ρ v f}

[As Proportionally constant = 1 so assume 2

π

= 1]

= \frac{10}{1 \times 300 \times 1000}

= \frac{1}{30} m m

\approx \frac{3}{100} m m

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