Question

If the maximum tolerable pressure variation in sound is undefined at

1000 Hz

. Find the amplitude of density and displacement. Given: Bulk modulus of medium

B = 1.4 \times 10^{5} Pa

, density of the medium

ρ = 1.20 kg / m^{3}

and speed of sound

= 341 m / s

Accepted Answer

Given that,

Speed of sound= $341 m / s$

$ρ = 1.20 k g / m^{3}$

$B = 1.4 \times 10^{5} P a$

Now, the density amplitude is given by,
$Δ ρ_{m} = \frac{ρ}{B} Δ p_{m}$

$\Rightarrow \frac{1.20}{1.4 \times 10^{5}} \times 28$

$\Rightarrow 2.4 \times 10^{- 4} kg / m^{3}$

Then, the displacement amplitude is given by,

$A = \frac{Δ p_{m}}{K B}$

where $K = \frac{2 π}{λ} = \frac{2 π f}{v}$
This implies, $A = \frac{v}{2 π f} \cdot \frac{Δ p_{m}}{B}$

$= \frac{341}{2 \times (22 / 7) \times 1000} \times \frac{28}{1.4 \times 10^{5}}$

$= 1.1 \times 10^{- 5} m$

Hence, the amplitude of density is $2.4 \times 10^{- 4} kg / m^{3}$ and the amplitude of displacement is $1.1 \times 10^{- 5} m .$

B M Sharma Solutions for Chapter: Sound Waves and Doppler Effect, Exercise 1: ILLUSTRATIONS

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Sound Waves and Doppler Effect, Exercise 1: ILLUSTRATIONS

Questions from B M Sharma Solutions for Chapter: Sound Waves and Doppler Effect, Exercise 1: ILLUSTRATIONS with Hints & Solutions

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