Interactive Activity Wave on a String

Wave on a String

Data Table 1

Frequency Setting	Measured Wavelength in (cm)
1.00 Hz	5cm
2.00 Hz	3cm
3.00 Hz	2cm

Data Table 2

Damping Setting	Tension Setting	Amplitude (cm) of first wave crest from the left	Wavelength (cm) of first full wave from the Left
None	Low	1cm	0.2cm
Lots	Low	0.4cm	1cm
None	High	1cm	6.1cm
Lots	High	0.6cm	4.6cm

Data Table 3

Frequency Setting	Time Interval	Number of waves Counted in 10 seconds	Average Number of waves counted in 10 seconds	Number of waves passing in 1 second
0.50 Hz	10 seconds	5	5	5	5	0.5
1.00 Hz	10 seconds	11	11	11	11	1.1
2.00 Hz	10 seconds	20	20	20	20	2

Experiment 1: Manipulating a Wave on a String

Based on the definitions of transverse and longitudinal waves (chapter 6), longitudinal wave – is being generated along the string. In Longitudinal waves, the medium is displacing parallel to direction of the wave.

When wrench is wiggled faster, more energy is given to string. 

Energy = (Planck's constant) (frequency) More the energy, more is frequency. Therefore, frequency increases. Now, frequency = speed of wave / wavelength. Wavelength is inversely proportional to frequency. Therefore, when frequency increases the wavelength decreases. 

As wrench is wiggled further UP and DOWN the wave amplitude increases. This can be easily observed in simulation or on any physical apparatus. It happens because 

wave′s energy(E)∝amplitude(A2). So, by wiggling wrench UP and DOWN we impart some energy which is manifested as increase in amplitude. When the end of the string is loose or fixed, we observe amplification taking place. Whether the medium is fixed in space or free to move at its end, waves are amplified when they are entirely in phase and interfere constructively, and they cancel out when they are fully out of phase and interfere destructively. As the waves continue to pass each other and are reflected from the opposite end, they interact in both directions, resulting in a standing wave. 

For the experiments with different end settings: With the end fixed or loose, multiple waves interact along the string and with no end, a single wave is produced. Energy is only conserved when there is no end because during the reflection from fixed or free end there will be some amount of energy loss due to collisions of particles with the boundary.

Experiment 2: The Effects of Damping and Tension

In comparison of the measured amplitudes and wavelengths as per data table 2, I observed that as the damping increases, the amplitude of oscillation decreases but, the wavelength remains same because it depends on medium. I observed that as the tension increases, the amplitude decreases and the wavelength goes about 4cm, so greater the tension, the greater the wavelength. Adding damping causes the energy travelling along the wave to be dissipated. Increasing the frequency decreases the wavelength. This is because the frequency of a wave is inversely proportional to the wavelength. Increasing the damping decreases the amplitude as the wave moved forward. This is because damping makes the wave lose more and more energy as it propagates, thus decreasing its amplitude.

Experiment 3: Measuring Wavelength

Comparing the measured wavelength for each of the frequencies as per data table 1, the data shows us that as frequency increases, the wavelength decreases. Wave speed is the product of frequency and wavelength: Wave speed (cm/s) = Wavelength (cm) X Frequency (Hz). As per the data collected, the calculated wave speed is close to 6cm/s.

Experiment 4: Calculating Wave Period

Based on the definition of frequency and in reflecting on experiment the frequency unit’s hertz (hz) represents the number waves passing a given point per second. Based on the definition of the wave period (the time it takes one complete wave to pass a given point) and in reflection of experiment the wave period would be determined by diving 1 by the frequency