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

[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!

 

[berkeman]

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?

 

[KineticNRG]

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.