Experiment to Demonstrate Stationary Waves

Aim

To demonstrate the formation of stationary sound waves and resonance in a variable-length air column.

Apparatus

• A glass resonance tube open at the top
• Water in the tube
• A movable water reservoir connected to the tube
• A tuning fork of known frequency
• A metre scale for measuring air-column length

Experimental arrangement

The water surface closes the lower end of the air column, while the upper end remains open. The effective air column therefore behaves as a pipe closed at one end and open at the other.

Procedure

• Fill the glass tube with water and keep the reservoir initially raised so the air column is short.
• Strike the tuning fork gently on a rubber pad and hold it just above the open end of the tube.
• Lower the reservoir slowly. The water level in the tube falls and the air-column length increases.
• Listen carefully for a sudden maximum in loudness.
• Measure the air-column length at the loudest position; this is a resonant length.
• Continue lowering the water level to find further positions of maximum loudness.

Observation

The sound is not equally loud for every air-column length. It becomes much louder at certain distinct water levels. Several such resonant positions may be obtained.

Why resonance produces loud sound

The tuning fork sends sound into the tube, and the wave reflects from the water surface. When the fork frequency equals a natural frequency of the air column, the incident and reflected waves reinforce one another repeatedly. The vibration amplitude becomes large, so a loud sound is heard.

Allowed resonant lengths

Because the water surface is a displacement node and the open end is an antinode, the ideal resonant lengths contain odd numbers of quarter-wavelengths.

Spacing between successive resonances

Subtracting two successive ideal resonant lengths gives half a wavelength.

If the tuning-fork frequency f is known, the speed of sound can then be found from v=fλ.

Worked example

Precautions

• Strike the tuning fork on a rubber pad, not on a hard surface.
• Hold the vibrating fork close to the tube without touching it.
• Keep the tuning-fork prongs oriented consistently above the opening.
• Move the reservoir slowly near resonance and identify the maximum loudness carefully.
• Measure the air-column length from the water surface to the open end at eye level.
• Repeat the observation and use successive resonant lengths to reduce end-effect error.

Resonance and earthquakes

The same resonance principle can affect tall buildings during earthquakes. A building may vibrate strongly when the frequency of ground motion approaches one of its natural frequencies. Buildings closer to the epicentre are not automatically the most damaged; damage also depends on how closely the earthquake frequency matches a building's natural frequency.

Common mistakes

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Quick revision

• The apparatus uses a vibrating tuning fork, a glass tube, water and a movable water reservoir.
• The water surface acts as the closed end of the air column, while the top of the tube is open.
• Lowering the reservoir lowers the water level and increases the length of the air column.
• At certain air-column lengths, the sound becomes distinctly loud because resonance occurs.
• At resonance, the tuning-fork frequency equals a natural frequency of the air column.
• A displacement node forms at the water surface and a displacement antinode forms at the open end.
• Several resonant lengths can be found because more than one allowed odd-harmonic pattern can fit in the tube.
• The experiment confirms that stationary waves occur only at discrete resonant lengths and frequencies.