6.3 Required practical: measuring waves

Aim

To investigate the speed, frequency and wavelength of waves, in a ripple tank and on a vibrating string, and to show that v = f \lambda.

Part A: waves in a ripple tank

Apparatus: ripple tank with shallow water, a motor with a vibrating bar (or a dipper), a lamp above, a white screen below, a stroboscope (or a camera), and a metre ruler.

Method

1. Fill the ripple tank so the water is about 5 mm deep. Switch on the lamp: the waves cast bright and dark lines on the white screen. The lamp must be above the tank and the screen underneath.
2. Switch on the motor to make straight waves. Adjust the speed so that the waves are clear.
3. Use the stroboscope (adjusted to match the frequency of the waves) or take a photograph or video with a camera, to make the waves appear to stand still.
4. Place a ruler on the screen, and measure the distance across several waves, for example 10 wavelengths. Divide by the number of waves to get the wavelength. Measuring many waves gives a smaller percentage uncertainty.
5. The frequency is the frequency of the motor (or stroboscope). Alternatively, count the number of waves passing a mark in a fixed time.
6. Calculate the speed: v = f \lambda.

Worked example. The motor frequency is 12 Hz. 10 wavelengths measure 0.30 m. The wavelength is \frac{0.30}{10} = 0.030 \text{ m}.

v = f \lambda = 12 \times 0.030 = 0.36 \text{ m/s}

Part B: waves on a string

Apparatus: a vibration generator connected to a signal generator, a string over a pulley with slotted masses to keep the tension constant, a metre ruler.

Method

1. Set up the string so that one end is attached to the vibration generator and the other passes over a pulley with a hanging mass.
2. Switch on the signal generator and slowly increase the frequency, until the string forms a clear standing wave with large vibrations (nodes and antinodes).
3. Read the frequency from the signal generator.
4. Measure the distance between several nodes. The wavelength is twice the distance between two neighbouring nodes (or between two antinodes).
5. Calculate v = f \lambda.
6. Repeat at different frequencies (higher frequencies give more loops). The speed should be the same, since it depends on the string and its tension.

A graph of wavelength against \frac{1}{f} is a straight line through the origin, and its gradient is the wave speed, 16 m/s.

Part C: the speed of sound (Edexcel)

• Echo method: stand at a measured distance d (e.g. 100 m) from a large wall and make a sharp sound. Use a stopwatch to time the interval t between the sound and its echo. The sound travels 2d, so v = \frac{2d}{t}.
• Two microphones: place two microphones a known distance apart, connected to an oscilloscope or data logger. Measure the time delay between the sound reaching the first and second microphones. v = \frac{\text{distance}}{\text{time}}.

Errors and precautions

• The ripple pattern should be observed with the stroboscope frequency matched, or the wave appears blurred.
• Measure across many waves, to reduce the percentage uncertainty in the wavelength.
• Keep the depth of the water and the string tension constant, because they change the wave speed.
• Safety: mop up spills and keep electrical equipment away from the water. Dry your hands.