PHY12L - E303 - TRANSVERSE WAVE: FREQUENCY OF VIBRATION

ANALYSIS ON TRANSVERSE WAVE: FREQUENCY OF VIBRATION

 

          A transverse wave is a moving wave that consists of oscillations occurring perpendicular (or right angled) to the direction of energy transfer. If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions that lie in the y–z plane, as defined by the Wikipedia.

 

          In the experiment we have conducted, we will see the relationship of velocity, frequency and wavelength. But since transverse wave is difficult to see, what the experiment shows is a standing wave where a standing wave pattern is a vibrational pattern created within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source. 

         

          So setting up the experiment, the materials used were 1piece of string vibrator, 1 piece of sine wave generator, 2 pieces of iron stand with clamp, 1 piece of pulley, 1 set of weights, 1 mass hanger, 1 piece extension cord, 1 piece meter stick and 5 pieces of guitar string.

 

          For the first part of the experiment, we set up the apparatus by connecting the sine wave generator to the string vibrator and then attached a guitar string that will be used for the five trials here in part one. A constant frequency was set by adjusting the amplitude and the frequency of the sine wave generator. We then attained a constant frequency of 116 Hz.

          For the second part, a constant diameter of guitar string of 0.010 inches was used having a linear mass density of 0.0039 g/cm. The changing factor or the variable factor here is the mass at the end of the string that is pulling it to have clearer vision of the wave, also known as the tension. At first, we placed a 50g weight on the mass hanger and turned on the sine wave generator. We adjusted the amplitude to see the waves better and count the segment created. There are a variety of patterns by which the guitar string could naturally vibrate; each pattern is associated with one of the natural frequencies of the guitar strings. We counted 4 segments and length of 63cm.  Using the formula shown below, we computed for the experimental value of frequency of the first trial in the experiment t and did the same thing for the remaining trials.

 

Where: n= number of segments

L= length of the total number of segments

T= tension or the weight pulling the string

u= linear mass density of the string

 

The data gathered were:

TRIAL	T(dynes)	N	L(cm)	f(Hz)
1	53, 900	4	63.0	118.02
2	73, 500	3	56.5	115.25
3	83, 300	3	59.2	117.10
4	93,100	3	61.5	119.17
5	102, 900	3	64.0	120.39

 

          From the data, we got an average frequency of 117.99 Hz. And using the formula of percentage error,

We attained 1.71% error in the experiment. And as observed, as the tension increases, the number of segments decreases and frequency increases. This is because tension is inversely proportional to the number of segments but directly proportional to the frequency.

 

          For the part three of the experiment, the constant factor is the weight or the tension that will be used and still, the frequency which is 116 Hz. We used the mass of 110g + 5g of the mass hanger and that will have a tension of 107, 800 g/cm. The changing factor here or the variable is the guitar string. The relationship of the number of segment, the length of the string with the total segments, linear mass density, and frequency were being examined. The data gathered were:

 

TRIAL	DIAMETER(in)	u	n	L(cm)	f(Hz)
1	0.010	0.0039	2	44	119.49
2	0.014	0.0078	3	50	111.53
3	0.017	0.0112	3	41	113.50
4	0.020	0.0150	5	59	113.59
5	0.022	0.0184	6	64	113.46

 

          The measured length of the total number of segments is not close to the stylus or not even on the start of it. We measure it by starting on the whole part of the segment to be more accurate of the result. In this part, we attained an average of 114.31 Hz and got 1.45% error.

 

          As seen on the table, the results show that as the diameter of the guitar strings increases, the number of segment also increases but the frequency decreases.

 

          Since the outcome of the experiment wasn't exact with the actual value of the frequency, Errors may have arisen from the measurement of the segments. Someone with a keen-eye and someone with a stable hand to hold the measuring device to have a precise and accurate measurement is need in this experiment. Wrong measurement and the wave produce near the stylus. The stylus can be the source of error because the clip that connects the stylus to string vibrator affect the wave of the segment produce in the first segment. The sources of error that can affect the experiment are the amplitude, The amplitude is also a source of error because we must allocate better amplitude to see the wave; increase in altitude will make a different wave and uneasy to measure the length. Measurement of the length is a source of error in the experiment. We must able to measure the length accurate to have less error. Also, the string used by the device should be completely leveled and free to vibrate without obstructions.

 

         

 

 

CONCLUSION ON TRANSVERSE WAVE: FREQUENCY OF VIBRATION

          A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction that the wave moves. Transverse waves are always characterized by particle motion being perpendicular to wave motion.

 

          Based on the results achieved in table1, it clearly shows that the tension is directly proportional to the frequency and inversely proportional to the number of segments. As tension increases, frequency also increases and also as tension increases, number of segments decreases. On the other hand, table 2 shows the relationship of the diameter of the string, its linear mass density to the number of segments and frequency. As linear mass density increases, number of segments increases and frequency decreases. Therefore, linear mass density is directly proportional to number of segments and inversely proportional to frequency. The formula in the manual was the same to the data gathered.

 

          Sources of error were wrong measurement of the length of the total number of segments since you cannot place the meter stick near the string for it will affect the movement of the wave. In addition, we must count the number of segment after it passes the stylus because the stylus is affected by the clip that connects the string vibrator to the stylus. Two, we must also consider the measurement of the length of string with complete number of segment. Last, we must check the different relationship of frequency to the segment, tension, linear mass density and length.