Prelim Practice: Standing Waves in Sound Tubes

There will be no problem set next week as we have an exam coming. To help prepare you, this and the following are some problems from the first prelim given in the fall of 2001.

Four tubes, each with two closed ends, are filled with different noble gases at atmospheric pressure and room temperature; therefore, they have the same bulk modulus $B$ but different mass densities $\rho_o$, $2\rho_o$, etc. (See Figure 2). The tubes also have different lengths, as shown on Figure 2. Which two of these (A & B or B & D, etc.) tubes will have the same lowest resonant frequency?

Figure 2: Closed tubes filled with noble gases.