Measuring wave speed, frequency and wavelength

Practical method

Aim

Measure the frequency, wavelength and speed of waves in a ripple tank and on a stretched string, and check that v = fλ.

Variables

Independent variable: frequency of the signal generator (vibrator)
Dependent variable: wavelength (and so wave speed)
Control variables: depth of water in the ripple tank; tension and length of the string; the same vibrator.

Apparatus

• Ripple tank with a lamp above and white card below
• Signal generator and vibrating bar
• Metre rule
• String over a pulley with hanging masses
• Vibration generator
• Stroboscope or camera (optional)

Method

1. Ripple tank: set the vibrator to a known frequency, for example 12 Hz.
2. Place a ruler on the card under the tank. Measure across as many wave shadows as possible (for example 10 wavelengths) and divide by the number of waves to find one wavelength.
3. Calculate wave speed v = fλ. Alternatively, time one wavefront crossing a measured distance.
4. String: attach the string to the vibration generator, run it over a pulley and hang masses to provide tension.
5. Adjust the frequency until a clear stationary wave forms. Measure the length of a whole number of half-wavelengths (loops) and calculate λ.
6. Calculate v = fλ. Repeat at several frequencies; v should stay about the same for the same tension.

Sample results

Ripple tank at constant depth (top) and string at constant tension, vibrating length 1.20 m (bottom).

Analysis

In each medium the wave speed stays constant when the frequency changes: increasing the frequency reduces the wavelength in proportion. Ripple tank: v = 12 × 0.018 = 0.216 m/s. String: 3 loops = 1.5 wavelengths = 1.20 m, so λ = 0.80 m and v = 60 × 0.80 = 48 m/s.

Errors and improvements

Risk assessment

Common mistakes

• Counting one loop on a string as a full wavelength (it is half).
• Forgetting to convert cm to m.
• Thinking a higher frequency makes the wave faster in the same medium.

Worked analysis

A stationary wave on a 1.20 m string has 3 loops at 60 Hz. Each loop is half a wavelength, so 1.5λ = 1.20 m and λ = 0.80 m. v = fλ = 60 × 0.80 = 48 m/s.

Common misconception

Changing the frequency of the vibrator does not change the wave speed in the same medium; it changes the wavelength.

Variations required by some exam boards

Sound in a metal rod (Pearson Edexcel): support a metal rod at its centre and strike one end with a hammer. Record the sound with a microphone and frequency app (or oscilloscope) to find its frequency. For the fundamental, the wavelength is twice the rod length (λ = 2L), so v = f × 2L. For example, a 1.00 m steel rod ringing at 2500 Hz gives v = 2500 × 2.00 = 5000 m/s.