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Hello, this lesson is about measuring waves in a ripple tank.

It's from the Physics unit "Measuring waves," and my name is Mr. Fairhurst.

By the end of this lesson, you should be able to accurately measure the wavelength, frequency, and wave speed of water waves in a ripple tank.

These are the keywords that you're going to come across during the lesson.

The ripple tank is the main piece of equipment that you're going to use to measure water waves accurately.

We're gonna film the water waves, and we're gonna play the film back in slow motion in order to make those measurements even more accurate.

The wave equation, which is wave speed equals frequency times wavelength, can be used to calculate values that we can't measure directly.

The uncertainty in the measurement is an estimate of how close to the real value we're able to get.

And we write this down using the correct number of significant figures to show how accurately we can take the measurement.

These are the definitions written down.

If at any point during the lesson you want to come back and have a look at these, just pause the video and come back to this slide.

The lesson's in two parts.

The main part of the lesson is about measuring wave speed with a ripple tank in two different ways.

And the final part of the lesson is looking at how we can write the measurements we've taken down and the calculations we make from those measurements to the correct number of significant figures to show how accurate they are.

Okay then, let's make a start with the first part.

The first thing to think about is the ripple tank, how it works and how we can set it up.

It's essentially a plastic tray with a clear bottom in which we can place a small amount of water.

It's got adjustable legs so that we can make the water an even depth throughout.

Now, to make the waves, we use a wobbly motor that's attached to a wooden beam that's hanging from two elastic threads.

Now, the motor's wobbly because it's got a weight that's set off-center so that as the motor spins round, the weight pulls the motor up and down, it makes the beam move up and down, and it dips in and out of the water, creating those water waves.

And we can control the speed of the motor to adjust the frequency of those waves to make them faster or slower.

Now, we can use a ripple tank in two different ways.

We can place it directly onto a tabletop, and we can hold rulers above the water waves to take measurements and so on.

Or we can put it upon legs and shine the light through the ripple tank to create a wave pattern in shadows underneath it.

Now, that means that we can take our measurements directly on the surface of the table rather than holding rulers and measuring equipment just above the water, and that makes it easier to take measurements.

The problem with that is that when we shine a light through, there may be a magnification effect.

That means that the distance between the shadows might be longer than the separation of the waves in the water.

So what we need to do is we need to make a careful adjustment.

And to do that, what you can do is you can place a 30-centimeter ruler in the ripple tank, you can place a 30-centimeter ruler on the table below, and then adjust the position of the lamp until the shadow of the ruler in the ripple tank exactly matches the ruler on the tabletop.

And once it does that, you know they're the same size.

And then we can take our measurements directly from the tabletop, and they are much more easy and straightforward to take.

And we're now going to show you a video clip that shows you how you can set up a ripple tank in real life.

This video shows how a ripple tank can be set up to observe water waves.

This part is called the ripple tank, and it's got a clear base that light can shine through.

A small amount of water is added to the ripple tank, and then the feet are adjusted to make sure that the water is completely level.

Once the water's level, we can turn on the electric motor.

The motor, as you can see here, is attached to a wooden beam, and the motor's designed so that it wobbles as it rotates round, making the beam wobble.

And the beam is dipped just into the surface of the water so that that causes ripples to move across the water.

Above the ripple tank, there's a very bright light called a strobe light that flashes very quickly.

The rate it flashes at can be controlled so that it makes the waves, the water waves, appear to freeze in time.

And very often, the strobe lamp is used to shine right through the ripple tank and to project an image of the waves onto a plain white surface beneath.

And if you get the setup just right, you can take accurate measurements of those waves on the hard surface beneath rather than trying to take the measurements on the water itself.

I'd now like you to have a go at this question.

Just pause the video whilst you have a go, and start it again once you've answered both parts.

Okay, so how did you get on? It is true that you can take accurate measurements of a water wave from its shadow projected onto a table.

But you can only do that if the lamp is adjusted so the shadows are the same size as the waves.

So well done if you got those right.

Now, once you've got your ripple tank set up and working, you'll probably notice that the water waves are moving far too quickly to measure accurately using a stopwatch, and the uncertainty in your measurements will be quite large.

To overcome this and to make the uncertainties much smaller, what we can do is we can film the water waves moving with a ruler and a stopwatch in the frame of the video.

And if we do that, we can freeze-frame the video when we play it back, and we can measure the exact position of a water wave and the time it's at that position.

And then we can play the video forwards in slow motion, keep track of where that wave is, freeze the frame at a later point, and measure its exact position and time again.

And using that method, we can measure the timers at each position to the nearest hundredth of a second.

Now, when we're measuring to the nearest hundredth of a second, it can sometimes be very accurate and sometimes not very accurate.

If we measure a short time period, for example, like 0.

02 seconds, it's not a very accurate measurement.

And that's because 0.

02 seconds is measured to just one significant figure.

This number of significant figures, we start counting from the first non-zero number from left to right.

So in this case, we've just got the two.

So we've got one significant figure.

And the reason this is not very accurate is because if we're measuring to the nearest hundredth of a second, then that 0.

01 second uncertainty means that that's about half of the whole value of the measurement.

So that makes a big difference.

If, by contrast, we measured a longer time period, let's say 1.

02 seconds, we're now measuring still to the nearest hundredth of a second, but now to three significant figures.

So a difference of plus or minus 0.

1 second makes a much smaller difference because it's a much smaller fraction of the whole measurement.

So we can reduce the size of any uncertainties in our measurements if we measure times over a longer period where there's more significant figures in the measurement.

Have a look at this question and see how many significant figures you think there are in 0.

45 seconds.

Pause the video, and start again once you've made your decision.

Okay, how did you get on? The correct answer is two significant figures, the four and the five.

We start counting significant figures from the first non-zero number, which in this case is the four.

Well done if you got that right.

Now, we've just looked at how we can measure the uncertainty in measurements of time.

What about for measurements with a ruler? It's the smallest division on the scale of a ruler that gives the minimum uncertainty in the measurements made.

And when we're talking about uncertainty in a measurement, it's the amount of doubt in that result.

And we often write those, we're using the plus or minus symbol.

For example, this.

So this would be a distance of 2.

5 centimetres plus or minus 0.

1 centimetres.

So our uncertainty would be about.

1 of a centimetre.

It might be slightly more than 2.

5, it might be a little bit less.

The smaller the uncertainty is, the less doubt and the more certainty we have that our result is accurate.

Now, this ruler measures to the nearest millimetre, plus or minus 0.

1 centimetres.

And if we measure a distance of, say, 27.

2 centimetres to the nearest.

1 centimetre, it's got less uncertainty than the short measurements of.

2 centimetres, plus or minus.

1.

They're both measured to the nearest millimetre, but if you add.

1 centimetres to.

2, it makes it half as big again.

And if you add the same.

1 centimetre to 27.

2 centimetres, it makes it only a tiny fraction bigger.

So small uncertainties make less of a difference if we're measuring longer lengths.

So when we're taking our measurements, it's better to make the measurement as long as we sensibly can.

Which of these measurements do you think will be affected least by an error of plus or minus 0.

1 centimetres? Pause the video whilst you think about it, and start again once you're ready.

Okay, how did you get on? The correct answer is 25.

3 centimetres because that's the longest measurement and 0.

1 centimetres is a smaller fraction of that measurement than it is of the other two.

So well done if you got that right.

So far, we've thought about how we can measure distance and time more accurately in a ripple tank.

Once we've got those measurements for a wave, we can calculate its speed by using this equation, wave speed equals distance divided by time.

There is a different method we could use to calculate its speed too.

If we measured its frequency and its wavelength, we could use the wave equation, wave speed equals frequency times wavelength.

To measure the frequency of a water wave in a ripple tank, we need to film the wave with a timer in the shot, and then we can play back the video in slow motion and work out the frequency of the wave in one of two ways.

We could count the number of waves passing a particular point and the time it takes them to pass and then use the equation of frequency equals the number of waves divided by the time taken.

Alternatively, we could film the wobbly motor and count the number of turns it makes in a set amount of time.

And then the frequency's the number of turns of the motor divided by the time taken.

The more turns that are counted, the less difference any small errors are going to make to the measurement, so it's a good idea to count as many turns as we sensibly can.

To measure the wavelength of a water wave in a ripple tank, we again need to film the wave, but this time with a ruler in shot.

And then we can use freeze-frame to measure the wavelength directly against the ruler.

However, if we were to measure the length of, say, 10 waves and then divide the answer by 10, we would still get a measurement for the wavelength, but as well as dividing the total length measurement by 10, we also divide the uncertainty in that measurement by 10 so we get a much more accurate value.

So in other words, the more wavelengths that we measure the length of together, the more accurate the measurement of a single wavelength will be.

Have a look at this question.

Which of these measurements do you think gives the most accurate wavelength? Pause the video whilst you think about this, and then start again once you're ready.

Okay, so how did you get on? The correct answer is the 25 wavelengths at 28 centimetres because we're dividing the length, the 28.

0 centimetres, by 25.

We're also dividing the plus or minus 0.

1 centimetre uncertainty by 25 as well.

So that's the most accurate answer, so well done if you got that right.

What I'd like you to do now is to use those ideas and a ripple tank to measure the speed of a water wave using two different methods.

First of all, film in slow motion to measure a time and a distance.

Give each measurement to the correct number of significant figures, and use them to calculate wave speed using distance divided by time.

Once you've got some measurements doing it that way, then you can try filming in slow motion to measure the frequency and the wavelength.

And again, give each measurement to the correct number of significant figures, and calculate the wave speed this time using frequency times wavelength.

Pause the video whilst you collect your results, and start it again once you're ready.

This next part of the video shows how a set of sample results were collected.

This video shows you how to measure the speed of a water wave using two different methods and a ripple tank.

The first method is the standard way using the speed equation, speed equals distance divided by time.

What we've done is to film a water wave moving along a ruler with a stopwatch in view so we can see the time, and then we've recorded that with a video and playing it back in slow motion.

If we identify one wave, we can follow that going forward in slow motion and then pause the video again a little bit later to see how far it's gone and how long it's taken to get there.

And then keeping track of where that wave is as it moves along, we can stop the timer when it reaches that point there and take the measurement.

And then we can use the difference in the distances, which is 28 centimetres, as the distance travelled, the difference in the times, which is half a second, 0.

50 seconds, as the time taken, and use those values to measure the speed of the wave using distance divided by time.

And that gives us a wave speed of 56 centimetres per second.

Now, although that's an easy way to calculate speed, it's really tricky to measure using the ripple tank.

So instead, we're going to use the wave equation, which is speed equals frequency times wavelength.

And to do that, first of all, we're going to measure the frequency of the wave.

To do that, I'm going to replay the video, and we're going to count the number of turns of the motor in the half second that we're going to time.

So if you're ready.

So did you get 14? That's 14 rotations in half a second, or 28 rotations, that's twice 14, in one second.

So we've got a frequency of 28 hertz.

Next, we need to measure the wavelength of the wave.

And to do this, we can simply use this image, this frozen image, to count the number of wavelengths between the mark here and the mark at the start.

And if you pause the video and count very carefully, you'll find that between 1 and 29 centimetres, there are 15 wavelengths.

So we've got 15 wavelengths in 28 centimetres.

So one wavelength is 28 centimetres divided by 15, which is equal to 1.

9 centimetres.

So that gives us a wave speed of 28 hertz times 1.

9 centimetres, which is 53.

2 centimetres per second.

Here's a set of sample results for the first part of the investigation, and hopefully your results look something similar to these ones.

And for the second part of the investigation, these are a sample set of results, and again, yours should look something similar to these, although if you got a different depth of water, then you might find that the answers are slightly different.

So well done if you got something like this.

We're now moving on to the final part of the lesson in which we're going to look a little bit more thoroughly at the importance of significant figures in calculations and how we can work out what the number of significant figures is in our answers.

Let's have a look at this example first of all.

From measurements of distance and time, we can calculate the wave speed using this equation.

So for example, a wave travelling 16.

2 centimetres in 1.

12 seconds, we can calculate its wave speed as equal to 16.

2 divided by 1.

12, and that gives us an answer of 14.

4642857 centimetres per second.

Now, clearly we haven't measured it to that high degree of accuracy, and we can't actually give our answers in a calculation any more accurately than we took our measurements.

So in this case, our measurements were both to three significant figures, so we give the wave speed here to three significant figures too, which is 14.

5 centimetres per second.

In this example, a wave is travelling 6.

2 centimetres in 1.

12 seconds.

So the wave speed we can calculate as being equal to 6.

2 centimetres divided by 1.

12, which gives us 5.

53571429 centimetres per second, which is clearly far more accurate than we took our measurements to.

The distance we measured to two significant figures, and the time to three significant figures.

And that means that the wave speed can only be calculated to two significant figures.

So we give the wave speed as 5.

5 centimetres per second, and then put in brackets after it, we've measured that to two significant figures.

Now, in this example, the uncertainty in distance had a much bigger effect than the uncertainty in time.

So if we're going to improve our investigation, we'd want to take more accurate measurements of distance before we start worrying about the time measurements.

Okay, so how many significant figures do you think that speed can be calculated to using a distance of 223.

5 centimetres and a time of 2.

34 seconds? Pause the video whilst you work it out, and start it again once you're ready.

Okay, what do you think? The correct answer was three significant figures, so B, and that's because the time was only measured to three significant figures, even though the distance was measured to four.

So well done if you got that right.

Let's have a look at this question.

Calculate the speed of a water wave of frequency 23 hertz and a wavelength of 1.

47 centimetres, and give your answer to the correct number of significant figures.

Well, we need to start with the wave equation, speed equals frequency times wavelength.

And we can substitute the values from the question into the equation.

And we get 23 hertz times 1.

47 centimetres, which gives us a speed of 33.

81 centimetres per second.

Now, to work out how accurately we can give the answer, we need to look back at the measurements in the question.

We've got the frequency measured to two significant figures and the wavelength to three.

That means that we can only give our answer to two significant figures.

So we need to round the speed up to 34 centimetres per second.

And it's good practise to put in brackets after it two significant figures.

What I'd like you to do is to have a go at this question.

Pause the video whilst you do so, and start it again once you're ready to look at your answer.

Okay, so how did you get on? Again, we need to start with the wave equation and substitute the values we're given in the question.

And we can multiply 26.

5 hertz by 1.

23 centimetres, and we get a speed of 32.

595 centimetres per second.

Now, looking back at the question, we can find that our measurements were both to three significant figures, which means we can only give the speed to three significant figures.

And in this instance, that rounds up to 32.

6 centimetres per second.

So well done if you got that answer.

I'd now I'd like you to have a go at these questions, giving all of your answers to the correct number of significant figures.

Pause the video whilst you do so, and start again once you're ready.

Okay, so how did you get on? Let's have a look at your answers.

Question one was calculate the speed of a water wave of frequency 8.

3 hertz and a wavelength of 7.

02 centimetres.

Well, we start with the wave equation, and we substitute in the values from the question, and we use those to calculate the speed as being equal to 58.

266 centimetres per second.

To work out the right number of significant figures, we need to go back to the measurements in the question.

Frequency was measured to two significant figures and the wavelength to three significant figures.

That means that we can only give the answer of speed to the nearest two significant figures.

So speed is equal to 58 centimetres per second to two significant figures.

Well done if you got that right.

Question two asks you to calculate the speed of a water wave that has a wavelength of 0.

7 metres and a frequency of 12.

0 hertz.

So again, we start with the wave equation, substitute in the values, and calculate the speed.

This time, 8.

4 metres per second.

Now, going back to the question this time, we find that the frequency was measured to three significant figures, but the wavelength was only measured to one.

We can ignore that initial zero.

That means the speed we need to give to as eight metres per second to one significant figure.

So well done if you got that right.

And then question three, calculate the frequency of a wave in a ripple tank that has a wavelength of 1.

28 centimetres and a speed of 32.

0 centimetres per second.

We use the wave speed equation again, and substitute in our values.

And this time, we're going to need to rearrange the equation to find frequency, and that is equal to 32.

0 centimetres per second divided by 1.

28 centimetres, which is equal to 25 hertz.

Now, when we go back to the measurements in the question, we notice that they're both measured to three significant figures, and that means we need to give our answer to three significant figures as well.

Writing 25.

0 hertz to three significant figures shows anybody looking at the answer that we're measuring it to the nearest plus or minus 0.

1 hertz.

So the three significant figures we've added into the answer describe the accuracy of that calculation.

So very well done if you got that right, and very well done indeed if you got all three of them right.

Well done for getting to the end of the lesson.

This is a short summary slide that covers the main points that we went through during the lesson.

And what we found out was that the speed of water waves in a ripple tank can be calculated in two different ways, speed equals distance divided by time or speed equals frequency times wavelength.

The wavelength we can measure by taking a still photograph or a freeze-frame of the waves shown with a ruler.

And frequency and time can be measured by filming the wave with a timer and playing it back in slow motion to record the different times.

Frequency is equal to the number of waves passing a point divided by the time taken, and it's measured in the number of waves per second.

The number of significant figures for each measurement shows how accurately it was measured.

So well done again for reaching the end of the lesson.

I do hope to see you next time.

Goodbye.