9/8 Experiment 4: Standing Waves

Introduction:
In this experiment, a string is attached to a mechanism which give certain frequency that can generate

waves on the string. The velocity of the wave will be determine by the tension of the string and the mass

per unit length of the string. v=(T/u)^(1/2). The frequency of the mechanism will be adjust by a function generator that we can adjust the nob into the desire frequency

Analyze:

Constants u 0.001165kg/m Case 1 (w/ 123cm and 200.2g) 1 loop 2 loops 3 loops 4 loops 5 loops 6 loops 7 loops 8 loops 9 loops node 2 3 4 5 6 7 8 9 10 antinode 1 2 3 4 5 6 7 8 9 frequency(Hz) 17 36 51 71 86 104 122 140 158 wave length(m) 2.460 1.230 0.820 0.615 0.492 0.410 0.351 0.308 0.273 velocity(m/s) 41.82 44.28 41.82 43.665 42.312 42.64 42.87429 43.05 43.18667 avg velocity 42.84977 1.060431375 2.045551 1.060431 0.664596 0.289199 0.044004 0.000601 0.040091 0.113498 uncertainty 2.306166 Case 2 (w/ 131cm and 100g) 1 loop 2 loops 3 loops 4 loops 5 loops 6 loops 7 loops 8 loops 9 loops node 2 3 4 5 6 7 8 9 10 antinode 1 2 3 4 5 6 7 8 9 frequency(Hz) 11 ? 34 46 56 63 77 93 102 wave length(m) 2.620 1.310 0.873 0.655 0.524 0.437 0.374 0.328 0.291 velocity 28.82 #VALUE! 29.69333 30.13 29.344 27.51 28.82 30.4575 29.69333 avg velocity 29.30852 0.238652605 0.148081 0.674828 0.001259 3.234677 0.238653 1.320153 0.148081 2.450384

case 1
Theoretical velocity: 41.04m/s +- 0.17m/s


experiment velocity:43.07m/s +- 2.3 m/s

Both values are within their uncertainty, which they are consistent to each others

Case 2:
Theoretical velocity: 29.02 +-  0.23 m/s

Experimental Velocity :29.70+- 2.45m/s

Both values are within their uncertainties, which mean they agree with themselves


The ratio of velocities between case 1 and case 2 is about 1.38, which is close to radical 2 as we expected

Both cases' frequencies followed the patter of f = vn/2L  where v is the wave velocity, n is the number of antinode, and L is the length of the string. As we expected, when the wave lengths are the same, the lower velocity requires lover frequency inorder to reach certain resonance frequency. On the other hand, the higher the velocity requires higher frequency to reach the resonance frequency.

In case 1, the ration between first and second harmonic frequency is 2.11, and between second and thrid is 1.4, between third and fourth is 1.39. As we can see, the ratio decreases as the number of harmonic frequency increases. In case 2, it also has the same pattern occured.