Question

The fundamental frequency of an open-open tube is 1500 Hz when the tube is filled with 0°C helium. What is its frequency when filled with 0°C air?

Short answer

The frequency of the tube when it is filled with air at$0°C$is$512Hz$.

Step-by-step solution

Given information

The fundamental frequency of the open-open tube is$f=1500Hz$.

Frequency of the tube when it is filled with air

For the open-open tube, the fundamental frequency of the standing wave is $1500Hz$ when the tube is filled with helium gas at$0°C$.

For the open-open tube, the fundamental frequency of the standing wave is $\lambda =\frac{2L}{m}$.

When the tube is filled with helium gas the fundamental frequency will be

role="math" localid="1650026727240" $f_{helium}=\frac{v_{helium}}{{\lambda }_1}=\frac{970m/s}{2L}\cdots \left(1\right)$

When the tube is filled with air the fundamental frequency will be

role="math" localid="1650026757106" $f_{air}=\frac{v_{air}}{{\lambda }_1}=\frac{331m/s}{2L}\cdots \left(2\right)$

From (1) and (2)

$$\begin{gathered} \frac{f_{air}}{f_{helium}}=\frac{331}{970} \\ {f}_{air}=\frac{331}{970}\times 1500 \\ =512Hz \end{gathered}$$

Therefore, the frequency of the tube when it is filled with air at$0°C$is$512Hz$.