How Can Two Stones and a Stopwatch Help Measure the Width of a Lake?

[veryc0nfused]

Homework Statement

The question asked is: Two students are given 2 stones and a waterproof stopwatch, along with swimwear. Using this material they are then required to estimate the distance across a lake. This question could obviously be answered using fairly simple process, however, it is posed in a fluid mechanics subject and therefore I assume must in some way involve the water in the lake. 2. The attempt at a solution
At this point in time my only attempt at solving this question would be to one person on either side of the lake. Have one person slam the rocks together underwater and to time the response. However, i don't think this is a very good solutions. Any help would be great, thanks!

 

[veryc0nfused]

The other thought I had would be to use the rocks to create a surface wave and time it to reach the other side?

 

[Chestermiller]

I like your sound wave idea.

 

[siddharth23]

Surface waves do not necessarily have a specific speed. Sound waves on the other hand, have a definite speed inside water. Sound wave is a good idea. But will the intensity of sound be enough that it'll be heard at the other end?

 

[sonnyfab]

So, I'm going to think through an answer that uses all of the pieces of equipment.

Since I have a stopwatch, I'm going to have to measure the time of something. I want to know a distance. It sounds to me like I'm going to try to estimate the velocity of something, have whatever that is move across the lake, and time it.

I have swimwear, so I could swim. So if I swim out for an unknown (somewhat large to be more accurate, but close enough to hear well) distance and leave me friend on the bank, I can watch him drop one rock onto the other. I start the watch when I see him drop and stop it when I hear them hit. Reaction time is going to make it messy, but I can repeat that as many times as I want and take an average.

I know sound goes about 343 m/s, so once I have a good estimate of how long it takes for me to hear the rocks hit, I multiple by 343m/s and get the distance I am from my friend. Then I swim in while timing myself, and I know my velocity swimming. Then I time myself swimming across a lake.

Lots of assumptions here: I swim at a constant velocity, my time measurements are somewhat accurate, no current.

If the watch was just some cheap non-waterproof model and and I didn't have swimwear I'd just have to walk around the lake and have him drop the rocks, time to hear the sound, and multiply by the speed of sound...

There's probably an easier way, but I think that method should work. Plus, it uses all your stuff, which in science class seems to be a plus (although in real life science, just like in well designed labs, you have bunches of equipment you don't use...)

Hope it helps.

Dr Peter Vaughan
BASIS Peoria Physics

 

[siddharth23]

Nice idea Doc..coming in the hearing range and then measuring the swimming speed. Cheers!

Only problem is, I just checked, the speed of sound in water in 1484 m/s. That's a bit too fast.

Problem with ripple speend is you'll have to know it's wavelength and frequency and ripple speed varies with wind speed.

Seem to be in a pickle..

 

[sonnyfab]

Speed of Sound

I agree that if we performed the experiment under water, so that the waves traveled through water, it would be much more difficult (or at least there would be a lot more error). But the speed of a pressure wave depends on which medium the wave travels in. As long as my friend drops the one rock onto the other rock on the bank and not actually in the water, and I keep my head above the water, then the sound will travel from him to me through the air between us, and we can use the speed of sound in air (343m/s).

Dr Peter Vaughan