For a particular sound wave propagating in ai | vedclass

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Question

(B) The correct option is $B$.Concept: The relationship between path difference $(x)$ and phase difference $(\phi)$ is given by:$\phi = \frac{2 \pi x}

Vedclass · Accepted Answer

$550$

Vedclass · Answer

(B) The correct option is $B$.Concept: The relationship between path difference $(x)$ and phase difference $(\phi)$ is given by:$\phi = \frac{2 \pi x}{\lambda}$where $\lambda$ is the wavelength.From this, we can express the wavelength as: $\lambda = \frac{2 \pi x}{\phi}$.The velocity of a wave is given by $v = \lambda f$, where $f$ is the frequency.Substituting $\lambda$ into the velocity equation:$v = (\frac{2 \pi x}{\phi}) f$Rearranging to solve for frequency $f$:$f = \frac{v \phi}{2 \pi x}$Given values: $x = 0.54 \, m$, $\phi = 1.8 \pi$, and $v = 330 \, m/s$.Substituting these values:$f = \frac{330 	imes 1.8 \pi}{2 \pi 	imes 0.54}$$f = \frac{330 	imes 1.8}{2 	imes 0.54}$$f = \frac{594}{1.08} = 550 \, Hz$.

For a particular sound wave propagating in air, a path difference between two points is $0.54 \, m$ which is equivalent to a phase difference of $(1.8 \pi)$. If the velocity of the sound wave in air is $330 \, m/s$, the frequency of this wave is: (in $Hz$.)

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