Question 122: Waves

Question

Assume that the displacement(s) of air is
proportional to the pressure difference ($\Delta $p)
created by a sound wave. Displacement (s)
further depends on the speed of sound (v),
density of air ($\rho $) and the frequency (f). If
$\Delta $p ~ 10 Pa, v ~ 300 m/s, $\rho $ ~ 1 kg/m
3
and f ~ 1000 Hz,
then s will be of the order of (take the
multiplicative constant to be 1) :

Accepted Answer

Given, S $ \propto $ $\Delta $p
and Proportionally constant = 1
We know,
$\Delta $p = S$\beta $k
= $ho $v
2
$ 	imes $ ${\omega  \over v} 	imes S$
= ${ho v\omega S}$
$ 	herefore $ S = ${{\Delta p} \over {ho v\omega }}$
= ${{\Delta p} \over {ho v2\pi f}}$
= ${{\Delta p} \over {ho vf}}$
[As Proportionally constant = 1 so assume 2$\pi $ = 1]
$ = {{10} \over {1 	imes 300 	imes 1000}}$
$ = {1 \over {30}}mm$
$ \approx {3 \over {100}}mm$

Answer

1 mm

Answer

${3 \over {100}}$ mm

Answer

10 mm

Answer

${1 \over {10}}$ mm

Waves

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