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### 4.Discussion

4.1 Analysis of results+4.2 Key findings

we did 3 tests, each inputting the expected frequencies and tuned it around, noting down the decibel measured at these frequencies.The precision of both the decibel meter and the frequency generator is both 2 decimal place, because the first decimal place for both the frequency and the decibel keeps flickering, we rounded the frequency and decibel off to the nearest whole number.

As we tuned the frequencies to the values near the expected frequencies, there were some frequencies at which we observed a steep increase of the decibel reading, meaning that there was a sharp increase in the volume. The frequencies noted with a steep increase in decibel reading are the average readings: 142Hz, 320Hz, 492Hz, 666Hz, 821Hz and 984Hz

from our research we know that these frequencies were the resonant frequencies due to the increased strength of the waves.we tested out each of the expected frequencies and noted down the corresponding strengths of each. as shown in the graph below

Figure 3: Graph of frequency (Hz)(x axis) against intensity (dB)(y axis)

The resonant frequencies were not what we calculated them to be , some were off by a few hertz. about 10 hertz. this was expected though, as we used the length of the tube as the length between the two sound sources , but in reality the distance is the distance between the two diaphragms of the speakers, but we had no way of measuring that as trying to measure it would require a change in the speakers positions and would then affect the length between the 2 speakers’ diaphragms and in turn affect the frequencies at which the standing wave form.

we concluded that the decibel increase of the resonant frequencies compared to non resonant frequencies was always 5dB louder, meaning that the sound was 1.5 times as loud as normal, from that data, we deduced that increase in strength caused by resonance is not affected by frequency, but the occurrence of resonance itself is .
we also found out that the dB increases the closer it gets to resonant frequencies.

we also concluded that material also played a part in resonance as noticed by an anomaly of an sharp increase in the decibel measured. the decibel measured around that resonant frequency was 10 decibels higher than other resonant frequencies.

4.3 Explanation of key findings

From our research we know that these frequencies were the resonant frequencies due to the increased strength of the waves.we tested out each of the expected frequencies and noted down the corresponding strengths of each. as shown in the graph below

we concluded that the increase in strength remains constant for any. we deduced this from the results that show a constant increase in of 5dB for every resonant frequency. meaning that the sound was 1.5 times as loud as normal, from that data, we deduced that increase in strength caused by resonance is not affected by frequency, but the occurrence of resonance itself is .

There was an anomaly in the third resonant frequency, the decibel measured during that resonance was much higher than other resonance, this could be due to equipment error or that this frequency was the acrylic tube’s resonant frequency. if it was the acrylic tube’s resonant frequency, it would oscillate along with the sound waves further increasing the strength of the wave, explaining the abnormally high readings. From that  anomaly , we know that "material also plays a part in resonance" (Lab In A Lorry, 2012), so where we want resonance to be stronger, materials could be accounted in designing to boost resonance and where resonance is not wanted, materials also could be put into play to reduce resonance.

4.4 Evaluation of Hypothesis

Our hypothesis was proven correct by the results of the experiment

we hypothesised that the loudness of the sound will increase when certain frequencies calculated by the formula is played. This was shown by our results and confirmed that these frequencies were indeed resonant frequencies

in our experiment we played the frequencies on two speakers and compared the decibel that was produced against a non resonant frequency. we measured that the decibel during resonant frequency was 1.5 times louder than non resonant frequencies. the frequency that turned out to be resonant was slightly different from the predicted frequencies was slightly different but this was expected as mentioned earlier.Another observation that we observed was that some of the foam balls we put inside the tube started forming wave shapes when the resonant frequency forms, further confirming a stronger wave when resonant forms.

4.5 Areas for improvement

in our experiment, we took the length of our tube to be that of the distance between the two sound sources , but this is not true. the sound source comes from the diaphragm of our speaker , which is deep inside the speaker and hence the actual distance is the length of the tube plus the distance the diaphragm is from the tube, but we have no way of measuring that, perhaps if we had more time, that distance could be calculated for a more accurate experiment.

Also, the frequency was imputed by hand using a dial causing the frequency to jump around by 0.1 hertz , this would be less accurate compared to typing in the frequency . a way to improve this would be to use our macbook to input the frequency, this way the inputted frequency would always be constant.

As the room we tested in was not completely soundproof, background noises can affect the decibels measured. we measured the background noise to be 62 decibels, many magnitudes smaller than our tested results, however small the background interference, our test would be more precise