A World of Light and ColorActivity 22

Standing Waves (Part 2)

Procedure & Results Sheet (No Prediction Sheet)

Key Questions:

  • How does frequency and wavelength of waves on a string relate to their speed?
  • Do the amplitude, frequency, and wavelength of sound affect its speed?
  • How are standing waves formed on a string?
  • What is the famous Wave Equation?

Materials:

  • Frequency Generator and Speaker (1)
  • Flexible string and metal stand (1)
  • Ruler

Part 1: Introduction to waves on a string

We will use waves on a string to better understand the properties of waves and, hence, better understand light. Waves in strings display interesting properties. When a speaker vibrates the string, there are onlycertain frequencies at which the string will vibrate with a clear standing wave pattern. These frequencies are called resonant frequencies.

Just as in the case of the wave machine, in a vibrating string, we can have the following standing wave patterns.

Node Antinode Node

Notice there are places where the string molecules oscillate a lot; these points are known as antinodes. At the same time, there are places on the string which do not vibrate at all; these points are called nodes. For example, in the first wave picture above, the wave has an antinode in the middle of the string, and two nodes at the two ends of the string.

As we will discuss later in class, there is a relationship between the wavelength of each wave shown above and the fixed length L of the tube. For example, the first standing wave is equal to half a wavelength, so that L = / 2. This also means that we can find the wavelength  using = 2L.

In this activity, you’ll investigate the relationship between the wavelength of the sound wave and the frequencies at which resonance occurs. We will also introduce the famous wave equation which expresses the speed of a wave in terms of its frequency and its wavelength.

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Part 2 : Procedure

Set up the frequency generator, speaker and flexible string as shown below.

Adjust the frequency of the generator to around 5 Hertz and slowly increase the frequency until you generate the first of the standing wave patterns shown above. Ask for your instructor’s help if necessary.

  1. Record the value of this resonant frequency. Measure the length of the vibrating string using a ruler. From the length of the ruler and the fact that for this smallest wave L = / 2, find the wavelength of the standing wave on the string.

Resonant frequency = (Hertz)

Length of tube L= (meters)

Wavelength of standing wave = (meters)

  1. Raise the frequency slowly until you find a new resonant frequency. Again, record the frequency and calculate the new wavelength. Repeat the procedure for at least four more frequencies. Continue finding still higher resonant frequencies. You should have at least five data sets. Record your data in the table on the next page.

On the last column of your table calculate the product of the wavelength and the frequency for each standing wave. This product represents the speed v = f of the wave on the string! Find also the average speed of the wave on the string.

Frequency (Hertz) / Relationship of L and L / Calculated wavelength  (meters) / Calculated product f (meters/sec)

Average speed of wave on the string = ______(meters/sec)

  1. By looking at your data, what would you say is the relationship between the frequency and the wavelength of the sound wave?

(a)As the frequency of the wave increases, the wavelength of the wave ______

(b)As the wavelength of the wave increases, the frequency of the wave ______

(c)In all cases, the product of the wavelength and the frequency seems to be about ______

  1. What we have found above is known as the wave equation v =f, which is applicable for any type of wave in nature, including light waves!

(a)What is the speed of red light of wavelength 650 nm in air? ______

(b)What is the frequency of the red light in air? ______

(c)What is the speed of the red light inside a glass material with n = 1.512? ______

(d)What is the wavelength of the red light inside the glass? ______

(e)What is the frequency of the red light inside the glass? ______

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