A uniform rod AB of length $$0$$ . $$4$$ m and mass $$1$$ $$.2$$ kg is suspended by two identical wires from a ceiling as shown in fig. (3). Where should a mass of $$4.8$$ kg be suspended from the rod so that a tuning fork of frequency $$256$$ Hz is in resonance with the first wire at Awhile its first overtone resonates with second wire at B?

Question

A uniform rod AB of length $$0$$ . $$4$$ m and mass $$1$$ $$.2$$ kg is suspended by two identical wires from a ceiling as shown in fig. (3). Where should a mass of $$4.8$$ kg be suspended from the rod so that a tuning fork of frequency $$256$$ Hz is in resonance with the first wire at Awhile its first overtone resonates with second wire at B?

Infinity Learn · Accepted Answer

Here $$n1=12lT1m=256$$ and $$n2=12lT2m=2$$×$$256$$ From these equations, we have $$T1=4T2$$ Let the mass be suspended at a distance x ftom A $$T1+T2=4$$⋅$$8+1$$⋅$$2=6$$ Taking moments aboutA for equilibrium $$1$$⋅$$2$$×$$0$$⋅$$2+4$$⋅$$8$$×$$x=T2$$×$$0$$⋅$$4$$  From eqs. (1) and (2), $$T2=1.2$$ $$1$$⋅$$2$$×$$0$$⋅$$2+4$$⋅$$8$$×$$x=1$$⋅$$2$$×$$0$$⋅$$4$$ $$x=5cm$$

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