Speed of sound

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Stony Brook University *

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Physics

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Apr 3, 2024

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Paige Smith Phys 121 12/3/23 Yue Chen
Intro: One way of determining the speed of sound is through the use of instruments such as wind instruments. Although sound is all around us, we can determine the speed of sound of a “wind instrument” in this lab. By taking 2 pieces of paper and creating a tube, we can calculate the frequency of sound and learn how sound moves through the tube. One thing that we do know is that wind instruments are essentially tubes of air where sound waves have the ability to vibrate as they travel. This vibration creates the sounds that we hear. Procedure: 1. Using 2 pieces of paper, create a tube by sliding one tube into the other. 2. Measure the length of the created tube 3. Set up the sweep generator by setting the frequency to 100 Hz, the frequency to 5000 Hz and the duration to 60 seconds 4. Plug in the earbuds to the headphone jack 5. Tape the earbuds together and place them into one end of the tube 6. Place the other end of the tube at the microphone that is built into the iOLab device 7. Press play on the sweeping generator and record on the iOLab application 8. Using the FFT function, choose 3 peaks and find the frequency of said peaks 9. Calculate the fundamental frequency to find the speed of sound Results After recording the sweeping generator sound, we find that there are different frequencies as it continues sweeping through. The first peak showed a frequency of v=412.112 Hz. Figure 1: frequency of first peak from sweeping generator *we take the v value to determine the speed of sound We can solve for v using the equation f n = n v 4 L f n ( 4 L ) n = v *n=1 Using a system of these 2 equations, we will solve for fn and then for v f n = n f 1 and f n + 2 =( n + 2 ) f 1
Fig 1: the figure shows the frequency at the first point Fig 2: the figure shows the frequency at the second point Peak 1: 84.296-51.514= 32.782
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32.782/-2 = -16.391 = f n v = f n ( 4 L ) n = -16.391(4(.40)) = -26.88 m/s Fig 3: the figure shows the frequency at the first point Fig 4: the figure shows the frequency at the second point Peak 2: 295.035-369.963 = −74.928
−74.928/-2 = 37.46 v = f n ( 4 L ) n = 37.46(4(.40)) = 59.9 Fig 5:the figure shows the frequency at the first point
Fig 6: the figure shows the frequency at the second point Peak 3: 711.83-753.978 = -42.2 42.2/-2 = 21.1 21.1(4)(.4) = 33.7 Freq 1 (Hz) Freq 2 (Hz) Speed of sound (m/s) 84.296 51.514 -26.88 295.035 369.963 59.9 711.83 753.978 33.7 Table1: The table shows a list of the frequencies and speed of sound Phone frequency Frequency 1 Frequency 2 2 696.818 1061.595
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8 851.146 1061.565 9 851.146 921.296 0 696.818 921.298 Table 2: List of frequencies based on their number We can see that for the most part, the frequency is fairly similar for the first peak, however the second peak was off. Fig1: the figure shows the first peak of the number 2 Fig 2: the figure shows the second peak of the number 2
Fig 3: the figure shows the first peak of the number 8 Fig4: the figure shows the second peak of the number 8
Fig 5:the figure shows the first peak of the number 9 Fig 6: the figure shows the second peak of the number 9
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Fig 8: the figure shows the first peak of the number 0 Fig 8: the figure shows the second peak of the number 0 Error analysis: Frequency 1: (696.818-697)/697 = 0.0% 851.146 - 852)/852 = 0.0% 851.146 -852/852 = 0.0% (696.818-941)/941 = 26% Frequency 2: (1061.595 - 1209)/1209 = 12% 1061.565 - 1336)/1336 = 20% 921.296 - 1477)/1477 = 38% 921.298 -1336)/1336 = 31%
Discussion: We were able to find the values of the speed of sound through the equation v = f n ( 4 L ) n . The value was vastly different than the V values on the FFT, however, we were looking at different variables as well. During the second part of the experiment, we found the first frequency of the beep was very close to its given value however the second frequency peak did not have the same result. This could be partly due to the volume. Although, the volume was at max, its possible background noise could have contributed to these results. Conclusion : In conclusion, our results showed that we can find the speed of sound using the equation v = f n ( 4 L ) n . we also can confirm that the iOLab device accurately measured the frequency of sound correctly because we found the frequency of the ring tone to be accurate to its given value.
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