James Grad, Dean Kieserman Science 8-2 1/7/12
Frequency and Amplitude in Mechanical Waves 1. Purpose: Research Question: If the frequency of a transverse wave is changed, does wavelength, wave speed, or both wavelength and wave speed change? How do changes in amplitude affect wavelength and wave speed? Variables: (for experiment I) Independent Variable: The frequency of each mechanical wave. Dependent Variable: The wave speed and wavelength of each mechanical wave. Variables: (for experiment II) Independent Variable: The amplitude of each mechanical wave. Dependent Variable: The wave speed and wavelength of each mechanical wave.
2. Hypothesis: If the frequency of a transverse wave is increased, the wavelength will decrease and wave speed will remain constant. If the amplitude of a transverse wave is increased, neither wavelength nor wave speed will change.
3. Procedure: Materials: 1 long spring 1 stopwatch 1 meter stick
Procedure: 1. Hold down one end of the long spring to the ground, and leave the other end loose. 2. Measure the time it takes to shake the long spring from side to side at a somewhat fast rate ten times, using the loose end. Repeat this two more times. This side to side distance should be 20 centimeters (amplitude = 10 centimeters.) 3. Measure the displacement of the long spring from the taped to free end. 4. Measure the time it takes for a single wave crest to travel from one end of the long spring to the other, three times. 5. Use the measurements from steps 2-4 to calculate wavelength, frequency and wave speed. 6. Repeat steps 2-5, except increase the amount of times the long spring is shaken in the time given in step 2 (try to double the amount of times the long spring is shaken.) 7. Repeat steps 2-5, except further increase (from step 6.) the amount of times the long spring is shaken in the time given in step 2 (try to triple the amount of times the long spring is shaken.) 8. Repeat step 2., attempting to measure the same amount of waves, except increase amplitude to 20 centimeters. 9. Repeat step 2., attempting measure the same amount of waves, except increase amplitude to 30 centimeters.
4. Data Tables: Affect of Frequency on Wavelength and Wave Speed (Experiment I) Frequency (Hz) Time for crest to travel length of Wavelength (m) (Over the time of 10 seconds) spring (seconds) Trial 1 Trial 2 Trial 3 Average Trial 1 Trial 2 Trial 3 Average
Wave Speed (m/s)
Trial 1 Trial 2 Trial 3
11Hz 18Hz 34Hz
10Hz 17Hz 34Hz
Amplitude Trial 1 (same as
9Hz 19Hz 34Hz
10=1Hz 18=1.8Hz 34=3.4Hz
1.18s 1.13s 1.03s
1.06s 1.16s .97s
1.1633s 1.1266s 1.02s
1.848m 1.06m .62m
Affect of Amplitude on Wavelength and Wave Speed (Experiment B) Frequency (Hz) Time for crest to travel length of spring Wavelength (m)
(cm) 10 cm
(s) 1 Hz
trial 1 in table above) Trial 2 Trial 3
1.25s 1.09s 1.06s
20 cm 30 cm
1 Hz I Hz
Trial 1
Trial 2
Trial 3
Average
1.25s
1.18s
1.06s
1.1633s
1.00s 1.13s
1.25s 1.37s
1.07s 1.28s
1.1066s 1.26s
Wave Speed
1.848m
(m/s) 1.848 m/s
1.943m 1.706m
1.943m/s 1.706m/s
5. Calculations:
1.848m/s 1.908m/s 2.108m/s
Frequency: To get the frequency of the wave, we timed how many waves were in 10 seconds. Wave speed: to get the wave speed, we measured how long the distance of the spring was, then divided that length by the time it took for one wave crest to reach the other side. Wavelength: Using, v = f * λ, (λ = v/f), the time divided by the frequency would equal the wavelength. So, if you had a frequency of 2, the distance of the spring would be 3 meters, the time it took for a crest to move from one end to the other would be 1 second, 3/1 = 3. 3/2 = 1.5. The wavelength is 1.5 and the wave speed is 3 meters per second.
