Saturday, March 17, 2012

Standing Wave

Purpose
      The purpose for this experiment is to be able to observe and analyze standing waves created using oscillator. We will also analyze the effect of tension on the string to the standing waves. In this lab, the wavelength, nodes and frequency will be recorded.

Experiment
      The setup for this experiment is as follow:
This show how we setup one end of the string

The other end of the string is attached to an oscillator

Once the setup is ready, experiment is conducted. The following is the observation seen in the experiment :
This shows one of the node in the string

Length between nodes are obtained to measure the wavelength
The data taken is as follow:
     
f(Hz)
#of node
L between node(cm)
wavelength (cm)
n
21 ± 1
2
61 ± 0.5
122 ± 0.5
1
43± 1
3
30.5 ± 0.5
61 ± 0.5
2
64± 1
4
20.313 ± 0.5
40.63 ± 0.5
3
85± 1
5
15.25 ± 0.5
30.5 ± 0.5
4
108± 1
6
12.2 ± 0.5
24.4 ± 0.5
5
129± 1
7
10.17 ± 0.5
20.34 ± 0.5
6
152± 1
8
8.714 ± 0.5
17.43 ± 0.5
7
174± 1
9
7.625 ± 0.5
15.25 ± 0.5
8
195± 1
10
6.778 ± 0.5
13.56 ± 0.5
9



This data is taken when we put the mass = 551 ± 1 g which gives
 Tension = 5.396 ± 1 N
 Length of string = 61 ± 0.5 cm
 v = 26.62 ± 0.75 m/s

The second run is also done by changing the tension of the string. We change the tension on the string by changing the hanging mass to  300 ± 1 g which will also change the tension:
Tension = 2.94 ± 1 N
 The data taken is as follow:
f(Hz)
#of node
L string(cm)
wavelength (cm)
n
16 ± 1
2
61 ± 0.5
122
1
32 ± 1
3
30.5
61
2
48 ± 1
4
20.313
40.626
3
64 ± 1
5
15.25
30.5
4
80 ± 1
6
12.2
24.4
5
96 ± 1
7
10.17
20.34
6
112 ± 1
8
8.714285714
17.42857143
7
128 ± 1
9
7.625
15.25
8
145 ± 1
10
6.777777778
13.55555556
9


v = 19.604 ± 0.75 m/s


Questions:
  1. The ratio for wave speed of case 1 compare to case 2 is :26.62 / 19.604 = 1.358
  2. By applying equation v = sqrt(T/density), the velocity is obtained and the ratio is calculated to be: 1.354.
  3. Based on the data obtained, the frequencies is indeed equal to the formula f = nf_1 where n is the number of the harmonic.
  4. The ratio for frequency in case 1 and case 2 is compiled below:
    case1
    case2
    ratio
    21 ± 1
    16 ± 1
    1.3125 ± 0.14
    43± 1
    32 ± 1
    1.34375 ±0.14
    64 ± 1
    48 ± 1
    1.333333±0.14
    85 ± 1
    64 ± 1
    1.328125±0.14
    108 ± 1
    80 ± 1
    1.35 ± 0.14
    129 ± 1
    96 ± 1
    1.34375±0.14
    152 ± 1
    112 ± 1
    1.357143±0.14
    174 ± 1
    128 ± 1
    1.359375±0.14
    195 ± 1
    145 ± 1
    1.344828±0.14
  5. Based on the data the ratio appears to be the same. There are a little difference for each which is caused by the uncertainty of the measurement and some rounding in the calculation.

Discussion
       Through this experiment, we know that the equation for wave speed = frequency * wavelength holds true. This is proven by the graph being linear with the slope being the wave speed. We also know that by reducing tension, the wave speed will also decrease. Some source of the error that could contribute to small difference in the value is the measurement uncertainty, rounding error, and also not all the frequency goes into the string since the string may not attached to the oscillator completely especially as frequency increase.


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