Wavelength and Frequency
In this experiment, the frequencies are recorded at high certainty values. The increased certainty in these values is due to the high precision of the Amplitude knob. It takes only a few seconds to change the frequency before an effect is seen.
When the experiment is repeated for a standing wave with two wavelengths, we get different results. The two-segment waves vibrate with a node at each end and one note in the middle such that the wavelength is equal to the length of the string used in the experiment. The frequency of two segment wavelength is about twice the frequency of one segment wavelength.
v = f
Where is the wavelength
f, is the frequency
In a single segment vibration, L =0.5
In a two-segment vibration, L=
Since L remains the same, the frequency of the two segments will be given by 1/0.5 =2
Therefore, the frequency of two segment wavelength is twice the single segment wavelength. The ratio of single segment frequency to two-segment frequency is 1:2. I expected the 1:2 ratio since the length of the string has been reduced by half in two-segment vibrations. Therefore, the speed of vibrating wire is reduced and the excess energy generated helps to double the frequency of the vibration.
When the string vibrates in two segments, the wavelength becomes invisible with the naked eye due to the high speed up and down movement. However, the wavelength can be seen by the use of strobe light by adjusting its frequency to be near the frequency of the Sine Wave Generator. The strobe light provides a slow motion movement that can be used to assess the wavelength.
At the antinode, the displacement of the string is at the maximum. When the string is touched at the antinode, the velocity and the wavelength are affected since the displacement will be reduced. However, no observable changes can be seen when the string is touched at the central node since there is no displacement. It is possible to hold the strings at the node without significantly affecting vibration due to minimal displacement. However, this changes when the hand is moved towards the central node as displacement is greatly affected.
When the string vibrates in one segment, the wavelength will be half the length of the string.
v = f
Since the string is moving is vibrating in one segment, velocity can be simply be illustrated by the formula;
v = 0.5 l
The speed of a two segment wave is calculated by the formula v = f. However, the difference is that the length (L) equals wavelength ( for the two-segment wave.
The frequency can be adjusted such that the string vibrates in three segments. However, the velocity will change such that the string will move faster than the one segment and two segment waves. Therefore, it is evident that the speed of the wave depends on the wavelength and frequency.
When the length of the string is adjusted, the speed of the wave is affected. By reducing the length of the string, the speed of the waves is increased. Therefore, the speed of the wave depends on the length of the string.
King, G.C. (2009). Vibrations and Waves. Wiley; 1 edition