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Post date: Jun 14, 2016 3:22:29 PM
As part of the new Edexcel GCSE specification, one of the core practicals looks at measuring the speed of sound in a solid. The idea is to strike a long metal bar and by measuring the pitch and knowing the wavelength, we can calculate the speed. While this is familiar territory at A-level, standing waves are not part of the GCSE specification. With that in mind here's my attempt at a simple explanation for how the science behind the experiment.
1. Measuring the Frequency
We start by hitting the end of a long metal bar. This causes sound waves travel to backwards and forwards through the bar at the speed of sound.
This causes the bar to vibrate at a specific frequency shown in the animation below. This vibration also creates sound waves in air that we hear with that same frequency as the sound waves in the metal bar.
We can measure the frequency of the bar (which is the same as the air) using a smart phone app.
2. Finding the Wavelength
For each atom in the bar, we can track its displacement from where the atom would be if we hadn't hit the bar. This looks the graph below where the y-axis shows movement away from its normal position. When it is positive, the atoms have shifted to the right side of the bar, when it's negative they've shifted to the left.
From the graph above, we notice a few things:
Atoms in the middle don’t move much.
Atoms near the edge move the most and both ends move in opposite directions (when one is to the left, the other is to the right and vice versa)
Just by looking at the displacement graph we see that the bar length is half one wavelength (L=λ/2)
We can then say one wavelength = 2 x bar length (or λ=2L)
3. Calculating Speed
We can put the frequency (from part 1) and the wavelength (from part 2) to find the speed.
speed = frequency x wavelength
speed = frequency x 2 x bar length
*The reason the bar vibrates in this way is all to do with standing waves which is beyond the scope at GCSE
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