# Measuring the Speed of Sound in Water, Using Faraday's Law

• KTBMedia
In summary: It's a... situation. In summary, the speed of sound in water is slower than expected. The experiment is failing to measure the expected speed of sound due to a delay caused by a magnet moving on a sponge. The experiment can be improved by trying a shorter or longer tube, or by using transducers to measure the phase velocity of the sound.

#### KTBMedia

TL;DR Summary
I'd like some others to take a look at our approach here and see where we may be going wrong.
Hi! This project involves both mechanical and electrical elements, so I'm discussing it in this forum since I'm not sure which one it would fit better into.

I'm working on an experiment in which I'm trying to measure the speed of sound through water. The approach is simple: I have a long vertically-positioned PVC pipe filled with water, with two incredibly strong neodymium magnets positioned at either end. The magnet at the bottom is resting on a sponge, and the one at the top is connected to a thinner cylinder that is clamped into position separately from the primary tube. Two coils of wire are positioned outside of the PVC pipe, each one surrounding the places where either magnet is located. When I hit the top of the thinner cylinder with a mallet, in addition to sending a current through the coil that's measured on an oscilloscope, the motion will also send a mechanical shockwave through the water that disturbs the bottom magnet, generating a current through the bottom coil and creating a second signal on the oscilloscope. In theory, the oscilloscope signals can be used to determine how much time it's taken for the wave to travel through the length of the tube.

Anyways, setting this whole thing up, I keep finding speeds in the range of 500 to 700 m/s, usually on the lower end. The distance between the two coils is just under 2 meters, and the time difference between the two signals keeps showing up at about 4.0 ms (sometimes as low as 2.5 ms in certain trials, but rarely). This is interesting, because The Engineering ToolBox puts the speed of sound in room temperature water at around 1481 m/s, and I'm not even breaking half of that.

I decided to ask here because I'm not sure what could be causing this issue, or how to correct for it to improve the experiment. Could the walls of the tube be slowing down the wave through some sort of friction / shear stress effect? Is the vertical positioning of the PVC tube problematic? Is there a general flaw with the approach (e.g. Are we incorrect in thinking that the mechanical wave speed should be the same as the speed of sound)? How can we alter these things?

Thanks!

I would think something like a magnet moving on a sponge would introduce some delay. Have you tried with transducers?

gleem
A general rule when getting confusing results is to change something and try again. In this case, try a shorter or longer tube. If the measured velocity changes, look for a time delay error by plotting measured velocity against distance between sensors.

In your specific case, try searching water hammer or speed of water hammer. Water hammer is a shock wave in a water filled pipe typically caused by closing a valve too fast. From one hit: For water in very stiff pipes the sonic speed could be as high as 1480 m/s. But in some plastic pipe the wave speed can be lower than 200 m/s.

The pipe is a transmission line not a free space medium. So propagation is described by the various modes of vibration which are possible. In particular, notice that a transmission line having standing waves does not have a propagation time as such, because it is an energy store, not a transmission medium.

Further to my post #5, I would also like to mention that I have myself had problems demonstrating the speed of sound using air filled telescopic tubes. The effect is that the sound delay does not vary progressivly with increasing distance, due to the effect of standing waves. If we study standing waves on electrical transmission lines, we see that the phase shift along the line, rather than increasing progressively, tends to remain constant with distance and then suddenly undergoes 180 degree phase shift at the nodes.

I'd say it's even simpler - "the speed of sound" (or light, etc..) refers to plane waves. You want to measure the speed of plane waves, you're going to need plane waves.

Not sure about the requirement for plane waves. The energy from a point source will spread out spherically at the speed of sound until it reaches shell of a given radius. I can't see an error here.

Also this experiment measures the propagation speed of a pulse in a tube of water inside a tube of plastic. A wave pulse travels at the group velocity which may be quite different from the phase velocity of the sound.
Now you have a happy dilemma: you can either devise a better experiment to measure the "speed of sound" (phase velocity) or try to untangle what you are presently measuring (or both!) There is no wrong answer here: only unsupportable conclusions.

gleem
tech99 said:
requirement for plane wave
It's not a requirement so much as matching what you see to definition.

The spherical wave becomes arbitrarily close to a plane wave at far distances, but looks different at near distances. Up close you likely even have both waves and near field.

Since the "sound" is not well defined here, it's hard to tell, but your solutions are probably not anything like planes waves - more likely planes waves up and down and Bessel functions across.

I think there are a number of issues. Using a mallet to create the disturbance is probably not producing consistent waveforms. Something like dropping a weight from a certain height should be better. Using a sponge to support the bottom weight might not be good as suggested by @scottdave since it is not elastic and may introduce a response lag in the motion of that magnet. And then there is where on the source wave you trigger the scope and where on the two waveforms you make your determine your time measurement.

Could you show us a picture of the scope screen?

scottdave
Thanks for the informative posts, everyone! You've all brought up some very interesting points and ideas.

Fortunately, however, I'm pleased to say that the solution was much simpler than having to devise a whole new setup; it turns out, I made the silly mistake of failing to do adequate research prior to making this thread. After doing some further reading online -- you guys are right, the sonic speed in a fluid in a pipe is well-known to be very different from the sonic speed in that same fluid in free space.

After a bit of searching, I found a handy formula for the sonic speed within a pipe in terms of the thickness of the pipe and the Young's modulus of the material, so I simply determined those values for the pipe I'm using and voilà! The new "expected" speed given by that formula is basically exactly what we've been measuring. So it turns out, I don't really need to do or change anything at all; our measurements agree with the theory. We were just using the wrong theory. :PThat said, there are a few other comments some have made here that I'd like to respond to.

First, I'm not sure what @scottdave and @gleem mean in saying that the sponge would "introduce some delay" or that it's "not elastic". The whole reason we used the sponge in the first place is because it's very elastic, and it's the material we have on-hand that seemed like it would allow for the fastest response of the lower magnet. And @scottdave, I'd like some more information about your "transducer" suggestion, because I'm not really sure what you mean by that. How could we incorporate transducers into our setup currently? I don't see how we could bring them into the picture without drastically changing our setup, or just doing something entirely different.

To respond more thoroughly to @gleem: Yeah, you make a good point about the mallet's consistency. It's something I was a bit concerned about as well, but so far our measurements have actually been pretty similar. At least, to the degree that we care about -- we aren't looking for perfection or anything, this is just something we're doing for fun with simple college lab equipment. And I don't have any images of the scope data on hand right now, but I can have some by tomorrow evening if you're still interested in seeing them. The time difference we've been measuring is just between the two points where the waveforms start to rise from the axis.

DrClaude, Tom.G, jrmichler and 2 others
Since the time you measured is typically twice the time expected what is the chance that the second signal is from the top coil due to the reflection off the bottom magnet? Is the bottom magnet big enough to reflect the sound? I would expect it is a disk.

KTBMedia said:
The whole reason we used the sponge in the first place is because it's very elastic,
But filled with water?

gleem said:
Since the time you measured is typically twice the time expected what is the chance that the second signal is from the top coil due to the reflection off the bottom magnet? Is the bottom magnet big enough to reflect the sound? I would expect it is a disk.
Clever suggestion, but no, that can't be it. The second signal I was referring to certainly isn't from the top coil; the oscilloscope we're using takes multiple (color-coded) inputs, and the coils are plugged into them separately. Therefore, simply looking at the graphs we've generated makes it clear that a current is induced in both coils.

gleem said:
But filled with water?
Yes.

I'm not sure what you're trying to say here. If you're suggesting that the sponge will stiffen in the presence of the water, sure, but it's still a sponge. Is there a softer, even more elastic material you'd recommend instead?

The inconsistency of the times that you measure seems to me to be a problem. I would go back to the use of something other than a mallet to create the wave or try to find a way to get consistent reading first.

KTBMedia said:
Could the walls of the tube be slowing down the wave through some sort of friction / shear stress effect?

What are the diameters of the PVC tubes?
KTBMedia said:
The second signal I was referring to certainly isn't from the top coil; the oscilloscope we're using takes multiple (color-coded) inputs, and the coils are plugged into them separately. Therefore, simply looking at the graphs we've generated makes it clear that a current is induced in both coils.
Have you verified that signals applied to the two inputs simultaneously are shown to start at the same time?
I know we should expect them to but you never know.

KTBMedia said:
I'm not sure what you're trying to say here. If you're suggesting that the sponge will stiffen in the presence of the water, sure, but it's still a sponge. Is there a softer, even more elastic material you'd recommend instead?
Basically yes. Sponges are open cell allowing water to fill the void. When compressed, the sponge must expel some water or deform the cell walls in some way which seems to me to be a nonlinear process with more of a damping characteristic. How heavy is the magnet? Heavier objects respond more slowly to a force.

Typically a sound transducer as a microphone has a very light element to respond quickly and linearly to varying sound pressure.

Do the two waveforms have the same leading edge slope? I might expect the initial pulse to have a nearly vertical slope and the received pulse's leading edge being somewhat less so.

Add my vote to using transducers. Let me also suggest ultrasound, because you want the wavelength to be small compared to your apparatus. I's also think about a recognizable pulse shape and a scope - say 5 full cycles, wait a second, and repeat.

I'd also look at see if it's easy to change the length of the pipe. That will help sorting out anything unexpected.

gleem

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