Topic 9.7.312 min read
Experiment to Demonstrate Stationary Waves
A vibrating tuning fork is held above the open end of a glass tube whose lower end is closed by water. Lowering the water changes the air-column length. At particular lengths the air column resonates, producing loud sound and showing that only specific stationary-wave patterns are allowed.
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What the experiment shows
A sounding tuning fork is held above a glass tube containing water. When the water level is changed, the air column becomes longer or shorter. At special lengths the sound suddenly becomes loud. This loudness shows that the air column is resonating and a stationary wave has formed.
End conditions
- Water surface: closed end and displacement node.
- Top of tube: open end and displacement antinode.
- Loud sound: resonance has occurred.
- Several loud positions: several allowed stationary-wave modes exist.
Recommended for Class 11
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.
| Position | Physical condition | Displacement pattern |
|---|---|---|
| Water surface | Air cannot move through the water boundary | Node |
| Open top | Air can move freely | Antinode |
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
Using two resonant lengths
For a 500 Hz tuning fork, two successive resonant lengths are 0.17 m and 0.51 m. Find the wavelength and the speed of sound.
- f=500Hz
- L1=0.17m
- L2=0.51m
λ=2(L2-L1)=2(0.51-0.17)=0.68m
v=fλ=(500)(0.68)=340m s-1
Final answer: The wavelength is 0.68 m and the speed of sound is 340 m s⁻¹.
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
Check your understanding
Q. Why is the reservoir lowered?
A. Lowering it lowers the water surface and increases the length of the resonating air column.
Q. What identifies a resonant position?
A. A distinct maximum in loudness identifies resonance.
Q. Why are several resonant lengths possible?
A. Different allowed odd-harmonic stationary-wave patterns can fit between the water-surface node and open-end antinode.
Q. What is the difference between successive resonant lengths?
A. Ideally, the difference is one half-wavelength.
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.
Exam Focus
Exam Focus
Important points
- Water surface is a displacement node.
- Open top is a displacement antinode.
- Maximum loudness marks resonance.
- Successive resonant lengths differ by λ/2.
- The experiment demonstrates discrete stationary-wave modes.
Important formulas
- Ln=(2n-1)λ4
- Ln+1-Ln=λ2
- λ=2(Ln+1-Ln)
- v=fλ
Common exam traps
- Measure the air column, not the total glass tube.
- Use maximum loudness to mark resonance.
Long question structure
Aim → apparatus → arrangement → procedure → observation → explanation → conclusion → precautions
Common Mistakes
Common Mistakes
- Mistake
Recording any loudness change instead of the maximum.
- Mistake
Measuring tube length instead of air-column length.
- Mistake
Treating the water surface as a displacement antinode.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute 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.
A resonance-tube experiment demonstrates stationary waves by varying the length of a closed-open air column until it resonates with a vibrating tuning fork and produces a loud sound.
- Definition
- A resonance-tube experiment demonstrates stationary waves by varying the length of a closed-open air column until it resonates with a vibrating tuning fork and produces a loud sound.
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Exam Practice
Important Question
Q1. Describe an experiment to demonstrate stationary waves in an air column.
Important Question
Q2. Why does loud sound occur at certain water levels?
Important Question
Q3. Explain the end conditions in the resonance tube.
Derivation
Q4. Show how two successive resonant lengths can be used to find the wavelength.
Numerical
Q5. For a 500 Hz fork, successive resonant lengths are 0.17 m and 0.51 m. Find the speed of sound.