The String Telephone, Priced Honestly: A Level Budget and the Distance at Which Speech Gives Out

The two-cup string telephone is usually demonstrated across a classroom and described without a distance limit. This paper prices it honestly, as a level budget. Raised speech coupled into the sending cup is assigned a reference level of 95 dB on the string; the sending and receiving cup couplings are charged 20 dB and 15 dB as stated assumptions; intelligibility at the ear requires 40 dB on the same scale, leaving a total budget of 55.0 dB, of which the fixed couplings consume 35.0 dB (63.6 percent) before the string spends anything. The 20.0 dB remaining for the string, at a tension of 10 N, gives a maximum intelligible distance of 25.0 m on cotton twine (0.80 dB per metre), 40.0 m on nylon line (0.50 dB per metre), and 80.0 m on taut steel wire (0.25 dB per metre). For the familiar cotton version, the honest bound is a few tens of metres, and the term that sets it is the coupling loss at the two cups, not the string. SIMULATED, NOT MEASURED.