16.39/f Fundamental frequency, Steel String, and tension?

Question

A 80cm-long steel string with a linear density of 1.2g/m is under 200N tension. It is plucked and vibrates at its fundamental frequency.

A) What is the wavelength of the sound wave that reaches your ear in a 20C room?

Lamda= ???m

Answer 1

♣ speed of waves in the string is v=√(T/ρ) =√(200N/(1.2e-3 kg/m));

fundamental freak is f0=v/λ0, where λ0 =2L =2*80e-2 m is fundamental wave length in the string;

thus f0=√(T/ρ) / (2L);

♦ now in the air:

Lambda = u/f0, where u=340m/s is speed of sound in the air at 20°C (check with your text book!)

Lambda =u *2L/√(T/ρ) = 340*2*80e-2 / √(200/1.2e-3) =1.33 m;

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