The two examples that follow show how you can use the above equation to solve for frequency or velocity.
Calculating the Frequency of a Wave
Problem: Earthquakes can produce three types of waves. One of these is a transverse wave called an s wave. A typical s wave travels at 5000m/s. Its wavelength is about 417 m.
What is its frequency?
Information Velocity, v = 5000m/s
Strategy Hint: Remember, Wavelength, »= 417m
Hz= 1/s, so m/s divided by
m = 1/s = 1 Hz
Unknown Information frequency (f)
Equation to use v = » x f
Solution3 v = » x f, so f = v/»
= (5000m/s)/(412m) = 12 Hz
Calculating Velocity of a Wave
Problem: A wave is generated in a wave pool at a water amusement park. The wavelength is 3.2 m.
The frequency of the wave is 0.60 Hz.
What is the velocity of the wave?
Information wavelength, »= 3.2 m
Strategy Hint: Another way frequency, f = 0.60 Hz
To express Hertz is 1/second,
Therefore, m x 1/s = m/s.
Unknown information velocity (v)
Equation to use v = » x f
Solution3 v = » x f = 3.2 m x 0.60Hz = 1.92 m/s
Activity 1. Transverse waves
Problem: Resonance: How can wave energy be stored?
1. You and a partner should pull on each end of the slinky until it stretches about I meter.
2. Hold one end of the Slinky motionless and shake the other end to make the slinky vibrate in one segment transverse to its length.
3. Count the number of vibrations the spring makes in 10 seconds.
4. Make a second wave by moving the end of the spring from side to side twice as fast as before. Look for the spring to vibrate in two equal segments. Each segment will move in opposite directions.
5. Try to make the spring vibrate in three equal segments.
1. Draw pictures of the spring for each of the three forms of wave you made. How many transverse waves does each picture represent?
2. The spring can store energy when the wave is the right size to exactly “fit” onto the spring. That is, you produce a resonance. How many wavelengths fit onto the spring for each of the three forms of waves produced.
Conclude and Apply
3. If wave energy is to be stored in the spring, how must the length of the spring and the length of the wave compare?
4. Why could you store short wave energy in a long spring but are not able to store long wave energy in a short spring?
Answers to questions
1. Drawing should show
One half of wave.
One full wave
One and a half waves
2. The first-the spring holds one half of a wave. The second-the spring holds two halves of a wave. The third-the spring holds three halves of a wave.
3. Wave energy can be stored in the spring if the spring is some whole number or half number of waves in length.
4. In order to store wave energy, the spring must be at least a half wavelength long.
Activity 2. Frequency of Sound Waves
Problem: What is the frequency of a musical note?
1. Measure the length of the pipe and record it on the data table.
2. Stretch one end of the rubber band across the open end of the pipe and hold it firmly in place. Caution: Be careful not to release your grip on the ends of the rubber band.
3. Hold the rubber band close to your ear and pluck it.
4. Listen for a double note.
5. Slowly relax the tightness of the rubber band. Listen for one part of the double note to change and the other part to remain the same.
6. Continue to adjust the tightness until you hear only one note.
7. Exchange pipes with another group and repeat the experiment.
Data and Observation – sample data table
Sound Frequencies produced by an open Pipe
Length of Pipe = 0.2m
Length of wave = 0.4m
Frequency of sound = 855Hz
1. The wavelength you obtained in step 6 is twice the length of the pipe. Calculate the wavelength.
2. Assume the velocity of sound to be 342 m/s. Use the equation frequency = velocity/wavelength to calculate the frequency of the note.
3. What was the wavelength and frequency of the sound waves in the second pipe?
Conclude and Apply
4. How does the length of a pipe compare with the frequency and wave?
length of the sound it can make?
5. A pipe organ uses pipes of different lengths to produce various notes. What other musical instrument uses lengths of pipe to produce musical notes?
6. If you listen closely, you can hear longer pipes produce certain higher frequency sounds. How is this possible?
Answers to questions.
1. Longest wavelength = 2 X pipe length
2. 32,200 cm/se = 805 Hz
3. Answers will vary. Wavelength will increase and frequency decrease as the pipe become longer.
4. The longer the pipe, the longer the wavelength and the lower the frequency.
5. All horns and woodwinds as well as the human voice use a vibrating air column.
A xylophone uses open pipes to amplify the sound of the vibrating bars.
6. A series of shorter waves will “fit” the pipe if their wavelengths are 1 X, 2/3 X, ½ X, 2/5 X……the length of the pipe.