Module 8—Mechanical Waves

The Universal Wave Equation

 

universal wave equation the speed of the wave is equal to the product of the wave frequency and the wavelength

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.

 

Self-Check

 

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.

 


Wavelength

(m)

Frequency

(Hz)

Total Distance Wave Travels
(1 grid square = 250 m)

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?

 

Check your work.
Self-Check Answers

 

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.

 


Wavelength

(m)

Frequency

(Hz)

Total Distance Wave Travels
(1 grid square = 250 m)

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

 

Read “Universal Wave Equation” on pages 408 and 409 of your textbook.

 

Self-Check

 

SC 11. Complete question 1 of “Practice Problems” on page 409 of your textbook.

 

Check your work.
Self-Check Answers

 

SC 11.

 

Given

 

f = 440 Hz

v = 350 m/s

 

Required

 

the length of the sound wave (λ)

 

Analysis and Solution

 

Use the universal wave equation to calculate the length.

 

     

 

Paraphrase

 

The length of the sound wave is 0.795 m.

 

Module 8: Lesson 1 Assignment

 

Remember to submit the answer to TR 3 to your teacher as part of your Module 8: Lesson 1 Assignment.

 

Try This

 

TR 3. Complete question 5 of “8.2 Check and Reflect” on page 410 of your textbook.