Topic 3 of 5
Determining wave speed
In one period, a repeating wave pattern advances by one wavelength. Its speed is wavelength divided by period.
Speed is distance divided by time. For a periodic wave, the distance is one wavelength λ and the time is one period T. Frequency f is 1/T.
Worked example
Use the rope graph values
The period is 0.40 s and the wavelength is 0.80 m.
- Frequency: f = 1/0.40 = 2.5 Hz.
- Wave speed: v = 2.5 x 0.80 = 2.0 m/s.
- Check the meaning: in 0.40 s the pattern advances 0.80 m, giving the same speed 0.80/0.40 = 2.0 m/s.
Rearrange for the unknown
A wave with speed 3.6 m/s and frequency 12 Hz has wavelength 3.6/12 = 0.30 m. Dividing frequency by speed would not give a length.
Controlled comparison
Higher frequency at unchanged sound speed
Use a supplied sound speed of 340 m/s under unchanged propagation conditions.
- At 500 Hz, λ = 340/500 = 0.68 m.
- At 1000 Hz, λ = 340/1000 = 0.34 m.
Doubling frequency halves wavelength because the speed is held fixed. Do not apply that conclusion without checking the stated speed or conditions; not every possible water-wave comparison has frequency-independent speed.
Measure several wavelengths and several cycles
For a steady ripple-tank pattern at fixed water depth, measure the separation of equivalent crests in a correctly calibrated top view. Time complete source oscillations separately. The following are supplied model readings.
Six crests enclose five wavelengths
A supplied calibrated span is 40.0 cm from crest 1 to crest 6. Use that reading, not the displayed size of the picture.
One wavelength is 40.0/5 = 8.00 cm = 0.0800 m. Count the five gaps between the six crests rather than dividing by the number of crests.
| Trial | Time / s |
|---|---|
| 1 | 4.90 |
| 2 | 5.00 |
| 3 | 5.10 |
The mean time is (4.90 + 5.00 + 5.10)/3 = 5.00 s. Start and finish the count at the same stage of the source's motion.
T = 5.00/20 = 0.250 s
v = 4.00 x 0.0800 = 0.320 m/sThe 5.00 s interval is for 20 oscillations. It is not the time for one crest to travel from the first to the sixth position.
Choose improvements that address a cause
- Uncertain crest positions: measure a longer span containing several wavelengths and divide by the number of intervals. A similar endpoint-reading uncertainty then forms a smaller fraction of the full span.
- Start/stop reaction time: time several complete cycles. This reduces the fractional effect of reaction time compared with timing only one cycle.
- Incorrect length scale: calibrate the image or ruler in the observed plane and read without parallax. A projected image need not have the same physical scale as the water surface.
- Unclear pattern: keep the source steady and the water depth unchanged, and avoid an area where reflected waves overlap the incident pattern.
Repetition shows the variation in readings. It does not correct counting six intervals instead of five, using an incorrect scale, or changing the propagation conditions between the length and time measurements.
A different direct method follows the same pulse between two marked positions and uses distance divided by travel time. That travel time is not automatically the oscillation period. Identify which event starts and stops the timing.
Keep a spacing measurement separate from a cycle count. First find one wavelength and the number of cycles per second; then use v = fλ.