What is the speed of sound waves?

Speed = Distance (m)

         Time (s)

In the case of the experiments and the graph it becomes:

Speed (gradient) = Change in distance (m)

                        Change in time (s)

Therefore the speed I calculated, stated on the graph, was 324m/s (correct to 3 significant figures), which in actual fact is very close to the actual speed of sound waves in the air which is 330m/s.

When the plate was hit it caused the longitudinal sound waves to travel in circles until it was picked up by the first microphone. Therefore this suggests that from the middle of the circular waves (the contact point between the hammer and the metal plate) the radius must be 10cm, seeing as the plate was held 10cm above the first microphone. Now, because the waves were circular the 10cm radius must also account diagonally, where the sound wave had to pass to reach the second microphone.  

        The diagram on the next page shows what happened in diagrammatical terms of the experiment, especially when the plate was hit.

        

        The right angled triangle shows the points A (the contact point between hammer and the plate), B (the first microphone) and C (the second microphone). The triangle is created because after the sound waves wad travelled vertically down to B, it then had to travel diagonally to C, which for the waves is the easiest route.

        Therefore instead of using the distance between B and C to plot, I have to use the “actual” distance the sound wave travelled through the air. However, because the radius reached out to 10cm when using Pythagoras’s theorem to find the distance the sound wave travelled to reach C, I have to minus 10cm from the total value. Due to the fact that the “actual” distance travelled lies between the outer most part of the circular waves and C.

        The following equation shows how the distance was calculated when the distance between points B and C was 1m.

Hypotenuse = 1 m² + 0.1 m²

Hypotenuse = 1.01 m²

Hypotenuse = 1.01 m²

                     = 1.004987562 m

X = 0.1m = 1.004987562 m

X = 0.90487562 m

   = 0.91 m (correct to 2 decimal places)

This system was used to calculate the distance for the rest of the distances when the distance was moved between the microphones.

The following table shows the distance between the microphones and then the actual distance that was plotted on the graph on page 2.

 

        This gave us more accurate results because if we plotted the distance between the microphones, this would not be telling us the distance the sound had to travel. On account of, that the sound did not travel to the start microphone and then through the wires and the fast timer to the stop microphone. Rather the sound waves travelled to the start microphone, which in turn started the fast timer and then when the sound had reached to stop microphone the faster was then stopped, and that time was recorded.

        To refer back to my graph, we found out the distance the sound waves had travelled to get to the second microphone. Also I had to multiply the microseconds into seconds because to be able to find the speed of the sound wave the time has to be in seconds.

        

Evaluation

        The prediction that I made was that sound would travel through the air at 330m/s. The result that I got from my graph was that the sound travelled through the air at 324m/s from my experiment. This is very close to my prediction and the actual speed of sound through the air, which is actually 330m/s. The results that I got from doing the experiment were reliable to the extent that I got a speed close to my prediction, which in turn backs up my prediction well. Also the line goes through the origin which is correct, because if the plate was struck 10cm above the two microphones which had no distance between them, they would both pick up the sound at the same time. Therefore the fast timer would not have recorded any time.

  Although my results were reliable and the gradient was reliable, I do not consider the results I got to be 100% accurate. This is because when you look at the graph there are two anomalies. The reason for these anomalies which do not lie close to the line of best fit, but do not lie exactly very far way and do follow the pattern, could have been as follows:

• The metal plate was held – This could have meant that the distance between the plate and the start microphone could alter by a mm or even a cm, which would make a great difference to the time it would take for the sound to travel. For example, if the person’s hand had moved to 9cm instead of 10cm then the speed of the sound waves, when there was a 1m distance between the microphones, would have been 149 m/s (3 significant figures). Whereas when the person was holding the plate at 10cm the speed of sound was 301 m/s. The difference being 152 m/s, which would make a great difference to the end result.
•  The ruler was not stuck down – This could have made a difference to the distance between the microphones if it were to have moved. For example if the start microphone was moved to 90cm but was actually placed at 87 cm because the ruler moved, but the plate was still at 10cm. Then the speed of sound would have been at that point, 271 m/s (3 significant figures). Whereas if the distance was 90cm between the two microphones then the sound would have been, 317 m/s. This result is closer to the 330 m/s which is the speed of sound, rather than 271 m/s. As you can see the slightest change in distance between the plate and the microphone, or even between the microphones would have made a large difference for the gradient, thus having an effect on the speed.
• The equipment could have been faulty or old – This would have meant that the sound may have been picked up slower than it should have done by either microphones, and so although the fast timer was accurate, it would record the time slower than it actually was.  This again would have made a difference on the gradient.
• No repeats - This should have been done as a precaution just in case any of the problems stated above could have occurred. This way you could get a larger average, which would have a smaller error on the gradient or any calculations made.
• The reasons above could have accounted for the anomalies that were made.
• Also, however hard I hit the plate did not affect the amplitude of the sound wave and so could not have caused any anomalies.

If I were to concoct the experiment again then I would make a few changes. For example:

• Clamp the plate down at a height of 10cm, so the distance would be reduced.
• Use better microphones so the sound is picked up quickly and more accurately.
• After doing the experiments I would do it again maybe 3 or 4 times, and find an overall average.
• I would stick the ruler down to the table.

I could further this investigation in a number of ways:

• Conduct the experiment in a bell jar to prove that sound needs a medium, like air, to travel.
• Use different materials for the plate to see if that affects the sound through the air. It could make it travel slower or even faster.
• Concoct the experiment in different mediums, to see if the speed of sound through the air is the same as the speed of sound through water.
•  I could also use different distances between the microphones, and the height the plate is held at. This would allow me to plot more points and draw different graphs and work out the speed. In turn proving that sound through air is 330 m/s.