Question

A pop gun consists of a tube 25 cm long closed at one end by a cork and at the other end by a tightly fitted piston as shown. The piston is pushed slowly in. When the pressure rises to one and half times the atmospheric pressure, the cork is violently blown out. The frequency of the pop caused by its ejection is (V=340 m/s)

• A. 510 Hz
• B. 1020 Hz
• C. 205 Hz
• D. 740 Hz

Answer 1

The correct option is A 510 Hz

From Boyles law:

$P\times 25\times A=1.5\times P\times L\times A$

$\Rightarrow L=\frac{50}{3}cm$

After ejection of cork, for oscillating air:

$\frac{\lambda }{4}=L$ and use $V$$=$$n\lambda$

$\Rightarrow \lambda$$=$$4\times \frac{50}{3}$ $=$$\frac{200}{3}cm$ $=$ $\frac{2}{3}m$

Using equation: $V$$=$$n$$\lambda$

$n$ $=$ $340\times \frac{3}{2}$ $=$ $510Hz$