We measure the meas and length of string
We tie the string both of strings to clamps and connect the wave driver with string, and we add 200 g to the end of string placed over pulley. We connect function generator and wave driver through wires, and we turn on the function generator.
We observe the pattern of standing wave on string. We increase the frequency of generator slowly until there is one loop of standing wave, and we record the oscillation frequency and calculate the wavelength. We repeat this this step by increasing frequency. We have the frequency and wavelength with different number of nodes.
The data and graphs of frequency and wavelength:
Case 1: The string is 1.45m, mass is 0.250 kg.
| Frequency (Hz) | Number of nodes | Wavelength (m) |
| 15 | 1 | 2.9 |
| 30 | 2 | 1.45 |
| 45 | 3 | 0.967 |
| 62 | 4 | 0.725 |
| 77 | 5 | 0.58 |
Slope = Velocity = 45.24 ms^-1
Theoretical value of speed = ((m1g)/(m2/L))^1/2 = 34.4 ± 2.87 ms^-1
| Experiment wave speed (ms^-1) | Predicated wave speed (ms^-1) | Ratio |
| 45.24 | 34.4 ± 2.87 | 1.32 ± 0.110 |
Case 2: The string is 1.45m, mass is 0.450 kg.
| Frequency (Hz) | Number of nodes | Wavelength (m) |
| 21 | 1 | 2.9 |
| 43 | 2 | 1.45 |
| 64 | 3 | 0.967 |
| 85 | 4 | 0.725 |
| 107 | 5 | 0.58 |
Slope = Velocity = 62.06 ms^-1
Theoretical value of speed = ((m1g)/(m2/L))^1/2 = 46.2 ± 3.85 ms^-1
| Experiment wave speed (ms^-1) | Predicated wave speed (ms^-1) | Ratio |
| 62.06 | 46.2 ± 3.85 | 1.34 ± 0.112 |
Case 3: The string is 1m, mass is 0.450 kg.
| Frequency (Hz) | Number of nodes | Wavelength (m) |
| 31 | 1 | 2 |
| 62 | 2 | 1 |
| 93 | 3 | 0.67 |
| 123 | 4 | 0.5 |
Slope = Velocity = 61.48 ms^-1
Theoretical value of speed = ((m1g)/(m2/L))^1/2 = 38.4 ± 3.20ms^-1
| Experiment wave speed (ms^-1) | Predicated wave speed (ms^-1) | Ratio |
| 61.48 | 38.4 ± 3.20 | 1.60 ± 0.133 |
Ratio of wave speeds:
| Wave speed of Case 1 (ms^-1) | Wave speed of Case 2 (ms^-1) | Ratio of Wave speed for Case 1 to 2 |
| 45.24 | 62.06 | 0.729 |
| Predicted Wave speed of Case 1 ( ms^-1) | Predicted Wave speed of Case 2 (ms^-1) | Ratio of Predicted Wave speed for Case 1 to 2 |
| 34.4 ± 2.87 | 46.2 ± 3.85 | 0.745 which is closed to 0.729 |
We have the experimental wave speed ratios almost closed to predicted wave speeds for both wave speeds.
| Frequency (Hz) | Number of nodes | Theoretical value of freqency (Hz) |
| 15 | 1 | 15 x 1 = 15 |
| 30 | 2 | 15 x 2 = 30 |
| 45 | 3 | 15 x 3 = 45 |
| 62 | 4 | 15 x 4 = 60 closed to 62 |
| 77 | 5 | 15 x 5 = 75 closed to 77 |
Relationship of frequency harmonics for case 1 compared to case 2:
| Frequency of case1 (Hz) | Frequency of case2 (Hz) | Ratio |
| 15 | 21 | 0.71428571 |
| 30 | 43 | 0.69767442 |
| 45 | 64 | 0.703125 |
| 62 | 85 | 0.72941176 |
| 77 | 107 | 0.71962617 |
We have the ratio of frequency for each harmonic for case 1 and 2 closed to 0.7, and we have the graph of frequency for each harmonic for case 1 and 2 almost a straight line, so there is a pattern for the ratio of frequency for case 1 and 2.
Conclusion:
We successfully observe the pattern of standing wave on the string. We successfully record the wavelength and frequency of different hanging mass, and different length of string used for several nodes. However, we fail to find the wave speed as the experimental wave speed is significantly different from the predicated wave speed. There are errors which makes the experimental wave speed significantly different from predicated value. Firstly, we measure the length of the string inaccurately as we cannot determine the reading the end of string over the pulley accurately. Secondly, the hanging mass is not stable and always oscillating, which makes part of energy lost to the hanging mass and affect the standing wave pattern. Thirdly, there is also standing wave pattern on the string connected from pulley and hanging mass, which means there is energy from vibrator lost to this part of string, and it will increases one more nodes of the whole standing wave pattern. These three errors affect the experiment value of wave speed significantly, and makes it different from predicated values of wave speed.
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