Question

A progressive sound wave of frequency $500$ Hz is traveling through air with a speed of $350$ m/s. A compression maximum appears at a place at a given instant. The minimum time interval after which the rarefaction maximum occurs at the same point is?

• A. $200$ s
• B. $1/250$ s
• C. $1/500$ s
• D. $1/1000$ s

Answer 1

The correct option is D $1/1000$ s

We know that the time between two consecutive compression or rarefaction is $T$.

But the time between two consecutive compression and rarefaction is $\frac{T}{2}$.

Since, $T=\frac{\lambda }{v}$

And here, $t=\frac{x}{v}=\frac{\lambda /2}{v}=\frac{T}{2}$

Now, $t=\frac{T}{2}=\frac{1}{2f}$

$⟹t=\frac{1}{1000}s$

Answer-(D)