A steel of wire of length 25 cm is fixed at its ends to rigid walls. Young’s modulus of steel = 200 GPa, coefficient of linear thermal expansion = 10⁻⁵ /°C. Initially, the wire is just taut at 20°C temperature. The density of steel = 8.0 g cm⁻³. A tuning fork of frequency 200 Hz is touched to the wire, to execute oscillations. Simultaneously, the temperature is slowly lowered. At temperature T, resonance occurs corresponding to the third overtone, where T = (1.5 + x)°C. Then find the value of x.
Physics · Wave Motion
A steel of wire of length 25 cm is fixed at its ends to rigid walls. Young’s modulus of steel = 200 GPa, coefficient of linear thermal expansion = 10⁻⁵ /°C. Initially, the wire is just taut at 20°C temperature. The density of steel = 8.0 g cm⁻³. A tuning fork of frequency 200 Hz is touched to the wire, to execute oscillations. Simultaneously, the temperature is slowly lowered. At temperature T, resonance occurs corresponding to the third overtone, where T = (1.5 + x)°C. Then find the value of x.