Physics

9. Figure shows an aluminium wire of length 60 cm joined to a steel wire of length 80 cm and stretched between

two fixed supports. The tension produced is 40 N. The cross-sectional area of the steei wire is 1.0 mm2 and

that of the aluminium wire is 3.0 mm2. The minimum frequency of a tuning fork which can produce standing

waves in the system with the joint as a node is 10P (in Hz) then find P. Given density of aluminium is

2.6 g/cm3 and that of steel is 7.8 g/cm3.

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  1. Hint:
    Stress in steel = 40N/1mm^2
    Stress in aluminum = 40N/3mm^2
    Speed of sound = (stress/density)^1/2
    Wavelength × Frequency = Speed
    Minimum frequency corresponds to a half wavelength in one of the two wires. Find out which wire and use the corresponding frequency.

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