Wave Calculations by Greg W. Lowe

We have observed in the wave table that the waves created by the frequency generator created waves that moved with nearly constant speed. This could also be observed in the videos on Essay 2.1 as well as walking along any beach. We measure the wavelength as the distance between two similar points: crest to crest or trough to trough. Below is a picture of a wave making device at the University of Miami:

Problem 1
If the wall of the wave maker is 3 meters tall and the speed of these water waves is 0.5 m/s, calculate

a) the time it would take for a wave to pass a point on the wall

b) the frequency of the wave generator

Solutions:

The hight of the door is about the same distance as the waves are from crest to crest. Thus, the wavelength is about 3 meters.

speed = wavelength / period

a) period = wavelength / speed = (3 m) / (0.5 m/s) = 6 seconds

b) frequency = 1 / period = 1 / (6 s) = 0.167 Hz

Problem 2
What if the wave generator's frequency was changed to 2.4 Hz?

a) What would be the new wavelength? How may would fit in the "old wave"

b) How many seconds would it take for one complete wave to pass by? (recall, since the speed is fixed and the wavelength gets shorter, one should wait for less time)

Solutions:

a) speed = wavelength times frequency

Solve for wavelength:

wavelength = speed / frequency = 0.5 m/s / 2.4 1/s (recall 1 Hz = 1/s)

wavelength = 0.208 m

dividing old wavelength by new wavelength we get "how many would fit": 14.4 waves

b) Period = 1 / frequency = 1 / (2.4) seconds = 0.417 seconds (or about a half of a second)

Problem 3

Mr. Lowe has the wave table set up and you observe waves traveling with a wavelength of 8 cm.
a) Name three things you can do to make the wavelength shorter.
b) Name the easiest way to make the new wavelength 2 cm.

Solution:

a) We can do one of three things:
1) increase the frequency of the generator
2) change the speed by making the water more shallow (placing flat plastic object in the pool)
3) change the density of the water by adding salt, sugar, maple syrup, ect.

b) since hte new wavelength is 1/4 the old wavelength, simple increase the reading on the wavemachine to 4 times the previous frequency reading.