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Chapter 6: Problem 29

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?

Short Answer

Expert verified
Answer: Yes, the sound produced by a guitar and a flute will be slightly different in a room filled with a mixture of oxygen and helium compared to normal air. This is due to the varying speed of sound in the oxygen-helium mixture, which can affect the perceived pitch of the instruments. However, the difference may not be significant if the mixture's composition is very similar to normal air.

Step by step solution

01

Understanding the properties of sound

Sound is a mechanical wave that travels through a medium, such as a gas, liquid, or solid. The speed of sound depends on the properties of the medium, including its density and elasticity. In general, the speed of sound increases with decreasing density and increasing elasticity of the medium.
02

Properties of Oxygen, Helium, and Normal Air

Oxygen (O2) and helium (He) are both gases, but they have different properties. In general, helium is less dense and has a higher speed of sound compared to oxygen. Normal air is composed mainly of nitrogen (N2, approximately 78%) and oxygen (O2, approximately 21%), with trace amounts of other gases. The speed of sound in air is intermediate between those of oxygen and helium.
03

Difference in the speed of sound in different mediums

The speed of sound is different in different mediums. In normal air, the speed of sound is approximately 343 meters per second at room temperature (20 degrees Celsius). In oxygen, the speed of sound is slightly lower, while in helium, the speed of sound is higher, at around 965 meters per second.
04

The effect of the medium on the frequency and pitch of musical instruments

The frequency of the sound produced by a musical instrument is determined by its design and construction, while the pitch perceived by the listener depends on the frequency as well as the speed of sound in the medium. Since the speed of sound in the room with the oxygen-helium mixture is different from the speed of sound in normal air, the pitch of the instruments will be altered. However, the change in pitch may not be significant, depending on how the mixture's composition compares to normal air.
05

Conclusion

In a room with a mixture of oxygen and helium, the guitar and flute will sound slightly different from when they are played in normal air. This is because the speed of sound in the oxygen-helium mixture is different from that in normal air, which can affect the perceived pitch of the instruments. However, it may be difficult to notice the difference if the mixture's composition is very similar to normal air.

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