# Speed and Refraction of Water Waves Speed and Refraction of Water Waves

OBJECTIVES:

1. To measure the speed of a water wave in a ripple tank.
2. To study the speed and direction of a wave before and after refraction.

INTRODUCTION:

The speed of a wave in a medium depends upon the characteristics of the medium. For instance, the speed of a wave on a string depends upon the mass per unit length of the string as well as the tension in it. For a water wave, the speed depends upon the depth of the water. Thus, when a water wave passes from a region of water of one depth to another, it changes speed, just as if it had entered a new medium. If this change in speed occurs at an oblique angle to the boundary between the media, the wave will change its direction of motion, a phenomenon known as refraction. Snell’s Law predicts that the ratio between the sines of the angles of incidence and refraction should equal the ratio between the velocities of the incident and refracted waves.

Since wave velocity equals frequency times wavelength, whenever a wave changes speed, either its frequency or wavelength changes. However, if the frequency of the wave-generating source remains constant and the wave speed changes, the wavelength must change. Thus, in the experiment, you will detect changes in wave speed as changes in the wavelength (distance between successive crest or troughs) of water waves.

METHOD:

A strobe light will be mounted over a ripple tank containing water, a plexi-glass plate to vary depth, and a straight-wave generator. A mirror will project images of the wave crests and troughs onto a projection screen. Since crests tend to concentrate light whereas troughs spread it out, the wave crests will appear as bright bands while the troughs will appear as dark bands.

You will measure the velocity of the water waves in both depths of water by determining their frequency and wavelength. This will be done by two different methods. In the first method, you will synchronize the flashing of the strobe light with the production of each new wave-front by the wave generator, causing the waves to appear to stand still. When this is done, the frequency of the waves is the same as that of the flashing strobe, and the wavelength can be easily measured from the still images on the projection screen. The wavelengths in the shallow and deep water will be different, yielding two different wave speeds for the incident and refracted waves. Snell’s Law of refraction will be checked by comparing the ratio of the calculated incident and refracted wave speeds to the ratio of the sines of the angles of incidence and refraction. These angles will be measured by first drawing a normal line perpendicular to the water depth boundary on the projection screen. Rays representing the incident and refracted waves will then be drawn perpendicular to the wave fronts to the point where the normal and boundary meet. The angles between the rays and the normal can then be measured. In the second part of this experiment, you will use video analysis in LoggerPro to determine the wave speed and direction. You will use a video file which has already been prepared. To do this, follow the instructions given below:

1. Using Internet Explorer, navigate to the honors physics shared files folder (from either the school web site physics page or the Honors Physics I moodle page). Open the “Class Materials”, “videos”, and “Prepared” folders. Click on the “Library” tab above the picture of Mr. Ilyes. Click on the “Open with Explorer” button. Drag the “refraction” movie to a convenient location on your computer (such as the desktop). Alternatively, you may right click on your movie, select “Copy”, and then paste it to a convenient location. Open up LoggerPro and choose “Movie” from the “Insert” menu. Navigate to the location where you saved your movie. Select your movie, and click on "open." Enlarge the movie window.
2. Locate the origin at the left edge of the first white band (left side of screen of screen) in the deep water.
3. Rotate the origin angle by dragging the yellow dot attached to the x-axis. Make sure that the y-axis is parallel to the wave-fronts.
4. Mark a point at the left edge of the most distant, clearly visible wave front. Note that the computer will automatically advance to the next frame. You will need to back up to the previous frame to see your marked point.
5. Count the number of waves between the origin and selected wave front.
6. Select the ruler icon to scale the image. Note that the distance between the inside support poles for the tank is 41.5 cm. Make sure that the scaling line is perpendicular to the poles and runs between the inside shading of the poles.
7. View the data table to get the distance between the origin and the marked point.
8. Convert this to wavelength distance.
9. Using the advance frame, count a number of waves (at least 10) passing the origin.
10. Check the time from beginning to end (displayed in upper, right-hand corner of movie window.)
11. Use the time for the selected number of waves to determine the period.
12. Use the period to determine the frequency
13. Move the origin to the shallow water and set it at a position to the left of a wave as far to the left as possible.
14. Change the orientation of the origin, as in step 4.
15. Mark a new point at a distant wave in the shallow water.
16. Repeat steps 8-12.
17. Tape a piece of transparency paper to the screen and carefully trace the left edge of the wave fronts and the outline of the deep-shallow boundary.
18. Use this to draw the incident and refracted rays perpendicular to the wave fronts and to draw the normal line.
19. Measure the angle of incidence and refraction.

DATA:

## Part I: Strobe Light

### Speed of Wave in Deep Water

Trial / Frequency of Wave (Hz) / Length of ____ Waves (cm) / Wavelength (cm) / Speed (cm/s)
1
2
3
Avg. / XXXXXXXX / XXXXXXXX / XXXXXXXX

Speed of Wave in Shallow Water

Trial / Frequency of Wave (Hz) / Length of ____ Waves (cm) / Wavelength (cm) / Speed (cm/s)
1
2
3
Avg. / XXXXXXXX / XXXXXXXX / XXXXXXXX

Angles of Incidence and Refraction

Trial / Angle of Incidence (º) / Angle of Refraction (º)
1
2
3
Avg.
Ratio of Speed in Deep Water to Speed in Shallow
Water
Ratio of Sine of Angle of Incidence to Sine of Angle of Refraction
% Difference between Speed Ratio and Sine Ratio

## Part II: LoggerPro

### Speed of Wave in Deep Water

Trial / Frequency of Wave (Hz) / Length of ____ Waves (cm) / Wavelength (cm) / Speed (cm/s)
1
2
3
Avg. / XXXXXXXX / XXXXXXXX / XXXXXXXX

Speed of Wave in Shallow Water

Trial / Frequency of Wave (Hz) / Length of ____ Waves (cm) / Wavelength (cm) / Speed (cm/s)
1
2
3
Avg. / XXXXXXXX / XXXXXXXX / XXXXXXXX

Angles of Incidence and Refraction

Trial / Angle of Incidence (º) / Angle of Refraction (º)
1
2
3
Avg.
Ratio of Speed in Deep Water to Speed in Shallow
Water
Ratio of Sine of Angle of Incidence to Sine of Angle of Refraction
% Difference between Speed Ratio and Sine Ratio

DATA TREATMENT:

• Speed of waves

INTERPRETATIONS:

1. How does the speed of a wave change when it goes from deep to shallow water (does it increase or decrease)? What effect does this change of speed have on frequency? On wavelength?

2. As a wave passes obliquely from deep to shallow water, in what direction does it bend, towards the normal or away from the normal? Explain why.

3. If the wave instead passed obliquely from shallow water to deep water, what would happen to its speed, frequency, wavelength, and direction?

4. What does Snell's Law say (in words)? Do the results of this experiment support Snell's Law for the two angles of incidence used? Why or why not?

5. It is known that light waves travel more slowly in glass than in air. Predict what will happen to the direction of a light ray passing obliquely from air to glass (in which direction will it bend?). Be sure to explain why.

ANALYSIS OF ERRORS:

1. Discuss two sources of experimental error in Part I of this experiment.

2. Is it possible for the waves to have appeared stationary using a strobe light frequency of exactly one half of the wave frequency? Explain why or why not. How could you make sure that this error wasn’t occurring?

X:\LABS\Speed and Refraction of Water Waves.doc