A special room contains a mixture of oxygen and helium that is breathable. Two musicians play a guitar and a flute in the room. Does each instrument sound different from when it is played in normal air? Why or why not?

In normal air, which primarily consists of nitrogen and oxygen, the speed of sound depends on temperature and the properties of these gases. In the given special room, the air is a mixture of oxygen and helium. Helium is lighter than both nitrogen and oxygen, so the gas mixture in the room has a lower overall density than the normal air.

The speed of sound (\(v\)) in a gas is determined by the square root of the ratio of the gas's adiabatic bulk modulus (\(B\)) to its density (\(\rho\)): \(v = \sqrt{\frac{B}{\rho}}\) The speed of sound increases when the density of the gas decreases if other factors remain constant. Since the density of the helium-oxygen mixture is lower than the normal air, the speed of sound in the special room will be higher.

The guitar is a string instrument, and its sound is produced by vibrating strings. The pitch of the sound depends on the tension, length, and mass per unit length of the strings. The speed of sound in the surrounding medium (in this case, the helium-oxygen mixture) doesn't affect the guitar's pitch. Therefore, a guitar will not sound different when played in the special room as compared to normal air. On the other hand, the flute is a wind instrument and relies on the vibration of the air column inside the instrument to produce sound. The pitch of the sound depends on the length of the air column and the speed of sound in the medium. Since the speed of sound is higher in the helium-oxygen mixture, the flute's sound will have a higher frequency and pitch in the special room compared to the normal air.

Each instrument will sound different when played in the special room compared to normal air. The guitar's sound will not change, as its pitch doesn't depend on the speed of sound in the surrounding medium. However, the flute will sound different, with a higher frequency and pitch, due to the increased speed of sound in the helium-oxygen mixture.