Experiment 9: String Telephone — Sound Through Solids

Two paper cups and a length of string can carry a whisper further than a shout. The string telephone works because a taut string guides vibrations from one cup to the other with very little spreading — and this experiment quantifies the guidance with the wave-speed law v = √(T/μ): tighten the string and the pulses literally arrive sooner.

The physics behind the practical

Your voice vibrates the base of the speaking cup; the base tugs the string; a pulse of tension races along the string; the far cup's base vibrates and re-radiates the sound into the listener's ear. Every link in that chain is a vibration handed on — sound never leaves the system as airborne waves until the very last step, which is exactly why so little is lost on the way.

The speed of a pulse on a string is v = √(T/μ), where T is the tension in newtons and μ (mu) is the string's mass per unit length in kg/m. The simulator's string has μ = 0.02 kg/m, so at T = 40 N, v = √(40/0.02) = √2000 = 44.7 m/s. Two lessons hide in that formula. First, tension helps only as a square root: quadrupling T (40 → 160 N) merely doubles v. Second, even a fast string pulse (tens of m/s) is far slower than sound in air (343 m/s) — the telephone wins on clarity, not speed, because the string funnels the vibration to one ear instead of letting it spread through the whole yard. Slack string fails for a related reason: with little tension the pulse is slow and weak, and the sagging string absorbs it before it arrives. Touching the string anywhere along its run damps the pulse the same way a fingertip kills a guitar note.

Variables and controls

In the virtual lab

Set String tension to 40 N and String length to 10 m, then press Speak into cup: the pulses race along the string and the readouts show Wave speed = 44.7 m/s and Travel time = 0.22 s. Drop the tension to 5 N — speed falls to 15.8 m/s and the travel time stretches to 0.63 s — then push it to 100 N and watch speed climb to 70.7 m/s and the time shrink to 0.14 s. Lengthen the string to 20 m at 40 N: the speed does not change (speed is a property of the string and its tension, not its length) but the travel time doubles to about 0.45 s. Follow the orange dot along the speed-vs-tension curve in the Data Visualization panel — steep at first, flattening later: the square-root shape. Log tension, speed and travel time for at least three settings.

Hands-on: building the telephone

Poke a small hole in each cup's base, thread the string through, and secure it with a knot or a paperclip inside. Walk apart until the string is taut — 10 to 20 m outdoors — keeping it clear of fences, branches and fingers. One partner speaks normally into the cup, mouth close but not touching; the other holds their cup to their ear. Test the variations one at a time: taut vs slack; a fingertip resting on the string; string swapped for wire. Watch your footing — a chest-high string across a path is a trip line.

A worked investigation

Using the sim's string (μ = 0.02 kg/m) over a 10 m run:

Step 1 — Check the middle row. v = √(40 ÷ 0.02) = √2000 = 44.7 m/s; t = 10 ÷ 44.7 = 0.22 s — matching the sim's readouts.

Step 2 — The square-root signature. Tension ×9 (10 → 90 N) gave speed ×3 (22.4 → 67.1 m/s): √9 = 3 exactly. If your data ever show speed doubling when tension doubles, something other than string physics is being measured.

Step 3 — Length's separate role. At 40 N and 20 m: v still 44.7 m/s, t = 20 ÷ 44.7 = 0.45 s. Length changes the delay, not the speed.

Step 4 — Bench reality check. On the real telephone, the equivalent observation is clarity: at full stretch (high tension) a whisper is intelligible at 15 m; at half stretch the same whisper is mush. The sim explains the bench: higher tension means faster, stronger pulses that survive the trip.

Conclusion and evaluation

Speed followed √(T/μ) at every setting, travel time scaled with length at fixed tension, and the failure modes (slack, touched string) all match the damping picture. The sim idealises the string as uniform and the cups as perfect transducers; on the bench, knots slip (tension drifts down mid-test), wind adds noise, and "clarity" is a judgement, not a number — two listeners should rate each condition without knowing which it is, a small blind test. None of that changes the law; it just sets how precisely a garden experiment can display it.

Safety

Keep the string below neck height, mark it or keep the area clear so nobody walks into it, take care with the scissors or pin when piercing cup bases, and never run while holding a cup.

Common mistakes

• Letting the string touch anything — a fence, a branch, a spare finger — and then concluding the telephone "stopped working".
• Changing length and tension together by simply walking further apart; the two variables arrive as a package unless you control them separately.
• Shouting into the cup and crediting the string — volume at the source is a variable too; speak at a fixed level.
• Loose knots that slip under tension, quietly shortening the string and dropping the tension mid-trial.
• Claiming the string beats air on speed — at ~45 m/s it is far slower than air's 343 m/s; it wins on guidance and clarity.

Exam Experience

Question 1 — calculation [4 marks]. For the simulator's string (μ = 0.02 kg/m), the tension is set to 62.5 N. Calculate the wave speed, and the travel time along a 20 m string.

Scoring guide:

• v = √(T/μ) = √(62.5 ÷ 0.02) = √3125 [1]
• v = 55.9 m/s [1]
• t = distance ÷ speed = 20 ÷ 55.9 [1]
• t = 0.36 s [1]

Question 2 — evaluation and design [4 marks]. Two students claim a wire "telephone" carries voices better than a string one. Design a fair comparison, and explain how you would make the judgement of "better" trustworthy.

Scoring guide:

• Independent variable: string vs wire; dependent: clarity/intelligibility of standard test phrases [1]
• Controls: same cups, same length, comparable tension (spring scale), same speaker and voice level, same listener positions [1]
• Trustworthiness: listener does not know which line is connected (blind test) and scores fixed phrases right/wrong [1]
• Repeat with several phrases and both partners swapping roles; compare scores, not impressions [1]

Multiple choice 1. The string telephone fails when the string goes slack mainly because:

• A. Sound cannot travel through solids
• B. Low tension makes the wave speed small and the slack string absorbs the weak pulse before it arrives
• C. The cups stop working without tension
• D. Air gets into the string

Answer: B. v = √(T/μ) collapses as T falls, and a sagging string damps what little pulse remains.

Multiple choice 2. Doubling the tension on a string multiplies the wave speed by:

• A. 2
• B. 4
• C. √2 (about 1.41)
• D. It stays the same

Answer: C. Speed goes as the square root of tension: √(2T) = √2 × √T.

Going deeper: why a square root? Checking the law by its units

v = √(T/μ) can be *checked* without any experiment, by units alone. Tension is a force: kg·m/s². μ is kg/m. Divide: (kg·m/s²) ÷ (kg/m) = m²/s² — and the square root gives m/s, a speed. No other simple combination of T and μ lands on speed units, so the law's *shape* is forced before a single measurement; the experiment's job is to confirm the constant in front is 1. Physicists call this dimensional analysis, and it is the cheapest error-detector in science: if your derived formula's units are not the units of the thing you wanted, the formula is wrong, full stop.

Test the law once more at the heavy end: a climbing rope with μ = 0.05 kg/m pulled to T = 200 N gives v = √(200/0.05) = √4000 = 63.2 m/s — a pulse crosses a 20 m rope in 0.32 s, which is why climbers feel a partner's tug almost at once, and why the "almost" is honest. The cups, meanwhile, are doing quieter work than the string: each acts as a small resonator and pressure coupler, funnelling the string's vibration into a patch of air against the eardrum. A string telephone is thus two transducers and a waveguide — the same architecture as fibre-optic calls, with tension standing in for total internal reflection as the thing that keeps the signal in its channel.

One more angle: the ends matter

A pulse reaching the far cup does its work only if the string's vibration couples into the cup's base — a loose knot is a bad handshake, and the telephone goes quiet even with a perfect string. The same coupling logic explains why the string must not brush anything mid-run: every touch is an unintended "listener" stealing energy from the line. Engineers call the general problem *impedance matching* — joining systems so energy crosses the join instead of reflecting back — and it recurs in fibre optics, loudspeaker design and ultrasound scans. Your knot-tightening was an early apprenticeship in it.