Describe what will happen to the fundamental frequency of the tubes if thetemperature of the air changes to a higher temperature. Will the fundamental frequenciesof the two tubes still be identical at the higher temperature? Give a clear mathematicaljustification for your answer.

The speed of sound in air is directly proportional to the square root of the absolute temperature. This means that as the temperature increases, the speed of sound also increases.

The fundamental frequency of a tube is given by the equation f = v/2L, where f is the frequency, v is the speed of sound, and L is the length of the tube.

If the temperature increases, the speed of sound v increases. Therefore, the fundamental frequency f of the tube also increases, because f is directly proportional to v.

If the two tubes are identical in length and the temperature of the air inside them is the same, then their fundamental frequencies will still be identical at the higher temperature. This is because the speed of sound will increase by the same factor in both tubes, and since their lengths are the same, the increase in speed of sound will result in the same increase in fundamental frequency for both tubes.

Mathematically, if v1 is the speed of sound at the initial temperature and v2 is the speed of sound at the higher temperature, then the ratio of the fundamental frequencies at the two temperatures is f2/f1 = v2/v1. Since v2/v1 is the same for both tubes, f2/f1 will also be the same for both tubes, meaning that their fundamental frequencies will still be identical at the higher temperature.