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The sonometer is a long wooden box with a wire stretched over two bridges. When the wire matches a tuning fork, a small paper rider on it jumps. The calculations are short, but the viva questions catch people out. This post covers the principle, works both Class 11 experiments with sample readings, and explains the Class 12 AC version.
Where is the sonometer in the syllabus?
The CBSE Physics curriculum for 2026-27 lists two sonometer experiments in Section B of the Class 11 practicals: the relation between frequency and length at constant tension, and between length and tension at constant frequency. Section A of the Class 12 practicals adds "To find the frequency of AC mains with a sonometer." The JEE (Main) 2026 syllabus does not list the sonometer under Experimental Skills, but its waves unit includes standing waves in strings, which is the same physics. Check the documents for your year.
What is the principle?
Experiment 15 of the NCERT Class 11 physics lab manual gives the fundamental frequency of the wire between the bridges as:
n = (1/2l) √(T/m)
where l is the length between the bridges, T the tension (including the hanger) and m the mass per unit length. It comes from the NCERT waves chapter: the wave speed on a string is v = √(T/μ), and a string fixed at both ends has its fundamental at v/2L. Two results follow:
At fixed T, n × l is constant.
At fixed n, T/l² is constant, so l² ∝ T.
To find resonance, the manual has you place a paper rider at the middle of the wire, put the stem of a vibrating fork on the box and slide a bridge until the rider is thrown off. The middle of the wire is an antinode in the fundamental mode, so that is where the rider moves most.
Worked example A: frequency and length at constant tension
Sample numbers. Total load 3.0 kg, so T = 3.0 × 9.8 = 29.4 N.
256 Hz: l = 47.6 cm, n × l = 12,186 Hz cm
288 Hz: l = 41.9 cm, n × l = 12,067 Hz cm
320 Hz: l = 38.0 cm, n × l = 12,160 Hz cm
384 Hz: l = 31.6 cm, n × l = 12,134 Hz cm
480 Hz: l = 25.2 cm, n × l = 12,096 Hz cm
512 Hz: l = 23.8 cm, n × l = 12,186 Hz cm
The product stays within about 1 percent of its mean, 12,138 Hz cm, so n ∝ 1/l. A graph of 1/l against n is a straight line through the origin.
Since n = v/2l, the wave speed is v = 2nl = 2 × 121.38 Hz m = 242.8 m/s. Then m = T/v² = 29.4 / 242.8² = 4.99 × 10⁻⁴ kg/m, about 0.5 g per metre of wire.
Worked example B: length and tension at constant frequency
Sample numbers, 256 Hz fork, loads including the hanger:
1.0 kg, T = 9.8 N: l = 27.3 cm, l² = 745 cm², T/l² = 0.0132 N/cm²
1.5 kg, T = 14.7 N: l = 33.5 cm, l² = 1,122 cm², T/l² = 0.0131 N/cm²
2.0 kg, T = 19.6 N: l = 38.7 cm, l² = 1,498 cm², T/l² = 0.0131 N/cm²
2.5 kg, T = 24.5 N: l = 43.2 cm, l² = 1,866 cm², T/l² = 0.0131 N/cm²
3.0 kg, T = 29.4 N: l = 47.4 cm, l² = 2,247 cm², T/l² = 0.0131 N/cm²
T/l² is constant within the reading error, so l ∝ √T. Tripling the load from 1.0 kg to 3.0 kg lengthens the resonant wire by √3 ≈ 1.73 times: 27.3 × 1.73 = 47.3 cm, close to the 47.4 cm measured.
How does the Class 12 AC version work?
Experiment 8 of the NCERT Class 12 physics lab manual uses a soft iron sonometer wire and an electromagnet run from a step-down transformer, held near the middle of the wire. The magnet attracts the wire twice in each AC cycle, so at resonance the wire vibrates at twice the AC frequency, and f = n/2. The manual has you plot l² against T and get n from the slope, 1/(4n²m).
In the manual's variation, AC flows through the wire itself between the poles of a permanent horseshoe magnet. The force then reverses with the current, so the wire vibrates at the AC frequency and need not be iron.
What errors should you name in the viva?
The lab manuals list these sources of error:
Pulley friction. The tension in the wire is less than the weight hung, so the manual asks for a greased pulley.
Non-uniform wire, or kinks. m changes along the wire.
Blunt bridges. The vibrating length is not sharply defined.
Judging resonance. There is always some uncertainty in the final bridge setting.
Common mistakes and how to avoid them
Load in kg instead of newtons. T = Mg.
Measuring the whole wire. l is only the part between the bridges.
Getting the AC factor upside down. With the electromagnet, the wire's frequency is twice the mains frequency, not half.
Resonance at a harmonic. At the second harmonic the middle of the wire is a node, so a rider there will not move. Start with the bridges far apart and close them slowly.
For more on modes of strings and pipes, see our post on standing waves in strings and pipes. For viva preparation across all practicals, see CBSE physics practicals and viva.
A practice routine
Rework examples A and B from the sample numbers, including v and m.
Plot 1/l against n and l² against T on graph paper and check both lines pass near the origin.
Write one-line answers to: why a paper rider, why at the middle, why the pulley must be smooth.
If standing waves on a string are hard to picture, the Fermi Simulation Lab has interactive simulations for ideas easier to see than read.
Today, take example A and predict the resonant length for a 426.7 Hz fork before you check it with n × l.
