Standing Waves
Name
Instructor
Course
Date of Submission
Waves on a String
Abstract
The principal objective of this lab was to study the conditions required for the creation of standing waves. The experiment was based on the principal of superposition, where a second wave exerted on a tight, stretched string and combined with the reflected wave.
Results
Table 1: Data from the Experiment
Loops λ (m) Mass (kg) Tension, T (N) √T
(N) Fcalc. FStroboscope (Hz) V (ms-1) µ
2 1.50 0.250 2.45 1.565 57.443 179.96 86.164 0.00033
3 1.13 0.150 1.4715 1.213 59.03 179.95 66.78 0.00033
4 0.84 0.080 0.76 0.8717 57.9 108 47.98 0.00033
5 0.66 0.050 0.49 0.7 58.4 108 38.53 0.00033
Figure 1: A graph of Wavelength, λ, (m) versus square root of tension, T1/2
Sample Calculations: …show more content…
The slope, m, of the graph corresponds to 1/(fõ).
Consistent with theoretical predictions, the graph of wavelength (λ) versus the square root of tension (T1/2) was linear. Indeed, the correlation, R2, was 0.998 (≈1) as shown in Figure 1, suggesting that there was high compliance with expectations.
Question 2b:
From Figure 1 above, the value of slope is 0.9566 = 1/ fõ).
Slope = 0.9566 〖Hz〗^(-1) 〖(µ) 〗^(-0.5)
Increasing the tension, T, increases the velocity of waves on the string and vice versa, according to the relation, v= √(T/µ). The same trend was observed in Table 1. When the tension, T, decreased from 2.45 N to 0.49 N, the velocity decreased from 86.164 to 38.53 ms-1. Since the wavelength, λ, varies proportionately with the speed, v, of the wave according to the relation, v = fλ, it then follows that an increase in tension would increase the wavelength of the waves and vice versa. …show more content…
An electrically driven vibrator was used to maintain a constant frequency. The string was not changed during the trials and thus, the mass per unit length, µ, remained constant. The frequency of the stroboscope was decreased from 179.96 Hz to 108 Hz in order to obtain the highest frequency at which the vibrator was gripped in position. The correct frequency of the vibration was 59.03 Hz. It was observed that the wavelength varies linearly with the square root of tension. The correlation was close to + 1 (0.998 ≈1), suggesting that the two variables were closely related. In addition, the percentage error was negligible at
Instructor
Course
Date of Submission
Waves on a String
Abstract
The principal objective of this lab was to study the conditions required for the creation of standing waves. The experiment was based on the principal of superposition, where a second wave exerted on a tight, stretched string and combined with the reflected wave.
Results
Table 1: Data from the Experiment
Loops λ (m) Mass (kg) Tension, T (N) √T
(N) Fcalc. FStroboscope (Hz) V (ms-1) µ
2 1.50 0.250 2.45 1.565 57.443 179.96 86.164 0.00033
3 1.13 0.150 1.4715 1.213 59.03 179.95 66.78 0.00033
4 0.84 0.080 0.76 0.8717 57.9 108 47.98 0.00033
5 0.66 0.050 0.49 0.7 58.4 108 38.53 0.00033
Figure 1: A graph of Wavelength, λ, (m) versus square root of tension, T1/2
Sample Calculations: …show more content…
The slope, m, of the graph corresponds to 1/(fõ).
Consistent with theoretical predictions, the graph of wavelength (λ) versus the square root of tension (T1/2) was linear. Indeed, the correlation, R2, was 0.998 (≈1) as shown in Figure 1, suggesting that there was high compliance with expectations.
Question 2b:
From Figure 1 above, the value of slope is 0.9566 = 1/ fõ).
Slope = 0.9566 〖Hz〗^(-1) 〖(µ) 〗^(-0.5)
Increasing the tension, T, increases the velocity of waves on the string and vice versa, according to the relation, v= √(T/µ). The same trend was observed in Table 1. When the tension, T, decreased from 2.45 N to 0.49 N, the velocity decreased from 86.164 to 38.53 ms-1. Since the wavelength, λ, varies proportionately with the speed, v, of the wave according to the relation, v = fλ, it then follows that an increase in tension would increase the wavelength of the waves and vice versa. …show more content…
An electrically driven vibrator was used to maintain a constant frequency. The string was not changed during the trials and thus, the mass per unit length, µ, remained constant. The frequency of the stroboscope was decreased from 179.96 Hz to 108 Hz in order to obtain the highest frequency at which the vibrator was gripped in position. The correct frequency of the vibration was 59.03 Hz. It was observed that the wavelength varies linearly with the square root of tension. The correlation was close to + 1 (0.998 ≈1), suggesting that the two variables were closely related. In addition, the percentage error was negligible at