Mechanical Waves

The objective of the experiment is to determine what relation, if any, exists between wavelength and frequency of a mechanical wave.

Procedure:
1. Measure length of spring
2. Set so that it is possible to oscillate harmonically
3. Measure the time for 20 cycles
4. Shorten the distance3 times and repeat for a total of four trials

Data and Observations

	Spring Length (m)	20 Cycles (s)
Trial 1	1.75	15.81
Trial 2	1.50	14.32
Trial 3	1.25	12.61
Trial 4	1.00	8.8

The measured values are half the total wavelength ± 0.05 m and the time measured is 20 periods ± 0.2 seconds. Also, frequency (f) is equal to the reciprocal of period (T). The actual values for the waves are:

	Wavelength-λ (m)	Frequency-f (Hz)
Trial 1	2.00±0.1	2.27±0.05
Trial 2	2.50±0.1	1.586±0.05
Trial 3	3.00±0.1	1.397±0.05
Trial 4	3.50±0.1	1.265±0.05

The graph seems to suggest an inverse relation, meaning λ~k/f or λf~k. The units (m*Hz) are equivalent to the units for velocity (m/s), so the relation between wavelength and frequency is the velocity of the wave. The calculated values for wave velocity are

Trial 1	4.54±0.33 m/s
Trial 2	3.97±0.284 m/s
Trial 3	4.20±0.290 m/s
Trial 4	4.43±0.302 m/s

All values are reasonable since they all overlap.

Summary
Even though the wave velocity is small, compared to the speed of sound (343 m/s), this speed of wave propagation created by a human is reasonable. It also shows that since wave speed is constant, wavelength and frequency must be inversely related.