# Essay about Frequency, Wave Lenght and Wave Velocity

2116 Words
Nov 25th, 2012
9 Pages

Abstract: The purpose of this experiment was to verify the relationship between frequencies, wave length and wave velocity of a transverse wave on a string, as well as the relationship between the spring tension and the number of standing waves formed. Two different strings used in this experiment are white and black in colour; the µ1 value calculated for the white string is 2.73 x 10-3 ±0.00055kg/m with an uncertainty of ±8.2932 x 10-5 kg/m while the µ2 value calculated for the black string is 1.38 x 10-3 kg/m with an uncertainty of ±8.6492 x 10-5 kg/m. However, the actual linear mass density µ0 of the white spring calculated is 2.87x10-3kg/m; compared to the experimental linear mass density µ1, the difference in error was

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Also, the greater the tension on a string the greater the pulling force from one particle to the other; therefore ability of the particle on a string to pull the particle next to it is directly proportional to the tension on the string. The speed of a wave is inversely proportional to its linear density, µ, because the mass of the end particle of the string will affect how fast it will respond to the pull from another particle. The maximum amplitude of a cord can only be achieved if the vibration of the frequency f, length of the cord L, and the speed of the wave on the cord v, is related such that a resonance and a stationary/standing wave are set up. Therefore, the natural frequencies fn, of the oscillation that produced the wave can be determined using the equation fn = {n/2L (√F/µ)} where n is the number of loops (segments between nodes).

Procedure:

The experiment was performed as written in the lab manual “refer to manual”.

Data and Analysis:

Fig 1: showing the graph of experimental frequencies vs. the natural frequencies of vibration of the white string.

The above graph represents the measured frequency vs. the natural frequency. From the graph, we can see that the slope is 19.137 ±0.00055 and the regression on the graph is 0.973, therefore demonstrating a straight line. The µ value for this graph was calculated to be 2.73 x 10-3 ±8.2932 x 10-5kg/m

The above graph represents the measured frequency vs. the natural frequency. From the

Procedure:

The experiment was performed as written in the lab manual “refer to manual”.

Data and Analysis:

Fig 1: showing the graph of experimental frequencies vs. the natural frequencies of vibration of the white string.

The above graph represents the measured frequency vs. the natural frequency. From the graph, we can see that the slope is 19.137 ±0.00055 and the regression on the graph is 0.973, therefore demonstrating a straight line. The µ value for this graph was calculated to be 2.73 x 10-3 ±8.2932 x 10-5kg/m

The above graph represents the measured frequency vs. the natural frequency. From the