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 , p∼ 1 kg / m 3 and f ∼1000 Hz, then s will be the order of (take multiplicative constant to be 1 )

Question

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 , p∼ 1 kg / m 3 and f ∼1000 Hz, then s will be the order of (take multiplicative constant to be 1 ) (A) 10 mm (B) (3/100) mm (C) 1 mm (D) (1/10) mm

Tardigrade Admin · Accepted Answer

Δ p=B k S0 =ρ v2 × (ω/v) × S0 ⇒ S0=(Δ p/ρ v ω) ≈ (10/1 × 300 × 1000) m =(1/30) mm ≈ (3/100) mm

$10 mm$

$\frac{3}{100} mm$

$1 mm$

$\frac{1}{10} mm$

$Δ p = B k S_{0}$
$= ρ v^{2} \times \frac{ω}{v} \times S_{0}$
$\Rightarrow S_{0} = \frac{Δ p}{ρ v ω}$
$\approx \frac{10}{1 \times 300 \times 1000} m$
$= \frac{1}{30} mm \approx \frac{3}{100} mm$

10mm

1003​mm

1mm

101​mm

Δp=BkS0​ =ρv2×vω​×S0​ ⇒S0​=ρvωΔp​ ≈1×300×100010​m =301​mm≈1003​mm

$10 mm$

$\frac{3}{100} mm$

$1 mm$

$\frac{1}{10} mm$

$Δ p = B k S_{0}$
$= ρ v^{2} \times \frac{ω}{v} \times S_{0}$
$\Rightarrow S_{0} = \frac{Δ p}{ρ v ω}$
$\approx \frac{10}{1 \times 300 \times 1000} m$
$= \frac{1}{30} mm \approx \frac{3}{100} mm$