All waves obey a fundamental relationship between frequency, wavelength, and the speed of the wave as it passes through the medium. This relationship is known as the universal wave equation, which states that the product of the wave frequency and wavelength are always equal to the speed of the wave.
Quantity |
Symbol |
SI Unit |
speed |
v |
m/s |
frequency |
f |
Hz |
wavelength |
λ |
m |
Expressed as an equation, it is
The simulation will be used to verify the universal wave equation. On the simulation, select the “Transverse” () wave type.
SC 9. Complete the following table by entering the wavelength and frequency of each wave and recording the necessary data. You can randomly start and pause each of the specified waves to collect the necessary data.
(m) |
Frequency (Hz) |
Total Distance Wave Travels |
Time Elapsed (s) |
Speed of Wave (m/s) |
40 |
0.25 |
|
|
|
90 |
1.0 |
|
|
|
50 |
1.3 |
|
|
|
80 |
1.6 |
|
|
|
75 |
0.8 |
|
|
|
SC 10. Pick two different waves from the preceding table, and use the universal wave equation to solve for the wave speed. Do the wave speeds determined by the universal wave equation match the observed speeds that were calculated in the table?
SC 9. The answers below for distance and time are sample answers and yours will probably be different. The values for speed, however, should be close to the ones below.
(m) |
Frequency (Hz) |
Total Distance Wave Travels |
Time Elapsed (s) |
Speed of Wave (m/s) |
40 |
0.25 |
1000 |
100.0 |
10.0 |
90 |
1.0 |
3600 |
40.0 |
90.0 |
50 |
1.3 |
1300 |
20.0 |
65.0 |
80 |
1.6 |
2450 |
19.0 |
129 |
75 |
0.8 |
2225 |
37.0 |
60.1 |
SC 10.
The speeds do match to 2 significant digits. This means you have verified the universal wave equation.
Read “Universal Wave Equation” on pages 408 and 409 of your textbook.
SC 11. Complete question 1 of “Practice Problems” on page 409 of your textbook.
SC 11.
f = 440 Hz
v = 350 m/s
the length of the sound wave (λ)
Use the universal wave equation to calculate the length.
The length of the sound wave is 0.795 m.
Remember to submit the answer to TR 3 to your teacher as part of your Module 8: Lesson 1 Assignment.
TR 3. Complete question 5 of “8.2 Check and Reflect” on page 410 of your textbook.