A student in her physics lab measures the standing-wave modes of a tube. The lowest frequency that makes a resonance is 30 Hz. As the frequency is increased, the next resonance is at 90 Hz. What will be the next resonance after this?

The next resonance will be 150 Hz.

Explanation:

The frequency of the sound produced by a tube, both open and closed, is directly proportional to the speed of propagation. Hence, to produce the different harmonics of a tube, the wave propagation speed must be increased.

The frequency of the sound produced by a tube, both open and closed, is inversely proportional to the length of the tube. The greater the length of the tube, the frequency is lower.

Frecuency of the standing sound wave modes in a open-closed tube is:

fₙ=n*f₁ where m is an integer and f₁ is the first frecuency (30 Hz)

The next resonance is at 90 Hz. This means that it occurs when n = 3:

f₃=3*30 Hz= 90 Hz

This means that the next resonance occurs when n = 5:

f₅=5*30 Hz= 150 Hz

The next resonance will be 150 Hz.