For the coiled spring in this experiment, the force-like property is the tension
ID: 3163190 • Letter: F
Question
For the coiled spring in this experiment, the force-like property is the tension in the coil and the mass like quantity is the mass per unit length: mass length p In alt cases, the speed of the wave is the square root on the force-like property divided by the mass like property For a spring (2) A standing wave pattern is the result of two or more waves of the same w avelength and frequency traveling in opposite directions and usually resulting from reflection off a barrier. Only specific wavelengths can result in standing waves; acceptable wavelengths are determined from the length of the medium supporting the standing wave, L and the nature of the reflecting surface. For standing waves in a spring with two fixed ends, the relationship is (3) 1, 2, 3 2LIn Since the speed, frequency and wavelength are related to each other by the wave equation (4) therefore, the allowed frequencies are n 1, 2, 3, fin n fo (5) whereExplanation / Answer
For the first data,
Length – 1.75 m
Tension, T =1.2 N
= m/L = 0.15/1.75 = 0.0857 kg/m
velocity = SQRT[T/] = 3.74 m/s
Wavelength for 1st harmonic
1 = 2L/1 = 3.5 m
For second harmonic, 2 = 2L/2 = 1.75 m
For third harmonic, 3 = 2L/3 = 1.167 m
Harmonic
Wavelength
Time for 20 vibrations (s)
Time for one vibration (s)
Frequency (Hz)
Velocity (m/s)
1
3.50
15.62
0.781
1.28
4.48
2
1.75
12.83
0.6415
1.56
2.72
3
1.167
11.65
0.5825
1.72
2.01
For the second data,
Length – 1.905 m
Tension, T =2.1 N
= m/L = 0.15/1.905 = 0.0787 kg/m
velocity = SQRT[T/] = 5.164 m/s
Wavelength for 1st harmonic
1 = 2L/1 = 3.81 m
For second harmonic, 2 = 2L/2 = 1.905 m
For third harmonic, 3 = 2L/3 = 1.27 m
Harmonic
Wavelength
Time for 20 vibrations (s)
Time for one vibration (s)
Frequency (Hz)
Velocity (m/s)
1
3.81
16.90
0.845
1.18
4.4958
2
1.905
14.93
0.7465
1.34
2.5527
3
1.27
11.03
0.5515
1.813
2.302
Harmonic
Wavelength
Time for 20 vibrations (s)
Time for one vibration (s)
Frequency (Hz)
Velocity (m/s)
1
3.50
15.62
0.781
1.28
4.48
2
1.75
12.83
0.6415
1.56
2.72
3
1.167
11.65
0.5825
1.72
2.01