# 350 Hz sound travels through air and metal pipe at different speeds.

• KineticNRG
In summary, the sound in the metal pipe travels a different path than the sound in the air. This causes the sound in the pipe to be heard twice at a different time, and the radius of the fence is 81.9 meters.
KineticNRG
I stumbled on this question while studying sound waves today, and it has got me stumped. I've been thinking this through for hours, to no avail. It goes: A park has a circular fence with a metal pipe as the top rail. If the fence is hit with a hammer it produces a sound of 350 Hz. At a point directly opposite the sound is heard twice at 0.30 seconds apart. If the speed of sound in air is 330 m/s and 1310 m/s in the metal pipe, then what is the radius of the fence?

I have used the formula Velocity = Frequency/Wavelength to determine the Wavelength of the sound in air (0.94 m) and in the pipe (3.74 m), but after that I'm stuck. My book gives the answer as 82 m, but no working is shown to help me understand why. I know that the sound will reach the other side via the air first, and can work out how far the sound will travel through the pipe in 0.3 seconds, but don't know how to calculate the total distance (circumference) or the diameter of the circular fence. Arrrgh, my brain hurts!

KineticNRG said:
I stumbled on this question while studying sound waves today, and it has got me stumped. I've been thinking this through for hours, to no avail. It goes: A park has a circular fence with a metal pipe as the top rail. If the fence is hit with a hammer it produces a sound of 350 Hz. At a point directly opposite the sound is heard twice at 0.30 seconds apart. If the speed of sound in air is 330 m/s and 1310 m/s in the metal pipe, then what is the radius of the fence?

I have used the formula Velocity = Frequency/Wavelength to determine the Wavelength of the sound in air (0.94 m) and in the pipe (3.74 m), but after that I'm stuck. My book gives the answer as 82 m, but no working is shown to help me understand why. I know that the sound will reach the other side via the air first, and can work out how far the sound will travel through the pipe in 0.3 seconds, but don't know how to calculate the total distance (circumference) or the diameter of the circular fence. Arrrgh, my brain hurts!

I believe the wavelength is irrelevant. The relevant piece that you may be missing is that the sound in the pipe travels to the observer by a different path than the sound in the air... Can you identify the two paths? What things are different about the two paths?

Yes, the wavelength was irrelevant. It was in the question just to trick us! It turned out that this is a velocity = displacement/time problem. I used that formula for the metal pipe, using pi*Radius as displacement. So the rearranged formula is Time = pi*Radius/Velocity. Due to time and radius being unknowns, I used the same formula with the displacement for the sound in air as 2*Radius. ie: Velocity = 2*Radius/Time+0.3 .By solving these simultaneously I got the correct answer of 81.9m. Thanks for the reply, otherwise I'd probably still be trying to figure out the relevance of the sound being 350 Hz.

## 1. How does sound travel through air and metal pipes at different speeds?

Sound travels through air and metal pipes at different speeds due to differences in their physical properties. In air, sound waves travel as compressions and rarefactions of air molecules, which are relatively far apart. In metal pipes, sound waves travel as vibrations of the solid material, which are much closer together. This difference in molecular density causes sound to travel faster through metal pipes than through air.

## 2. What is the speed of sound at 350 Hz in air and in a metal pipe?

At 350 Hz, the speed of sound in air is approximately 343 meters per second. In a metal pipe, the speed of sound is typically faster, depending on the type of metal and its thickness. For example, in a steel pipe, the speed of sound at 350 Hz can range from 500 to 600 meters per second.

## 3. Why does sound travel faster through a metal pipe than through air?

Sound travels faster through a metal pipe than through air because the molecules in a solid material are closer together, allowing sound waves to propagate more quickly. In contrast, air molecules are further apart, creating more resistance and slowing down the speed of sound.

## 4. Does temperature affect the speed of sound at 350 Hz in air and in a metal pipe?

Yes, temperature can affect the speed of sound in both air and metal pipes. In general, sound travels faster in warmer temperatures and slower in colder temperatures. However, the effect of temperature on sound speed is more significant in air than in metal pipes.

## 5. How does the diameter of a metal pipe impact the speed of sound at 350 Hz?

The diameter of a metal pipe can affect the speed of sound at 350 Hz, but the impact is not as significant as other factors such as the type of metal and temperature. Generally, a larger diameter pipe will allow for slightly faster sound propagation compared to a smaller diameter pipe.

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