Question

THE TENSION IN A WIRE 80CM LONG IS 5KGWT. WHAT CHANGE MUST BE DONE IN ORDER TO RAISE THE PITCH BY ONE OCTAVE ,IF THE TENSION IS INCREASED TO 7.2KGWT. ?

Answer 1

Answer on Question #37370

Physics - Mechanics | Kinematics | Dynamics

Question:

THE TENSION IN A WIRE 80CM LONG IS 5KGWT. WHAT CHANGE MUST BE DONE IN ORDER TO RAISE THE PITCH BY ONE OCTAVE, IF THE TENSION IS INCREASED TO 7.2KGWT. ?

Solution:

Frequency:

$$f = \frac {1}{2 L _ {1}} \sqrt {\frac {F}{\rho S}}$$

where $L_{1} = 0.8 \, m$ , $F$ is a tension force, $\rho$ is a wire density and $S$ is a wire cross-section area. While we raise pitch by one octave, frequency is doubled, we can change length of a wire:

$$\frac {f _ {2}}{f _ {1}} = 2 = \frac {L _ {2}}{L _ {1}} \sqrt {\frac {F _ {2}}{F _ {1}}} \Rightarrow L _ {2} = 2 L _ {1} \sqrt {\frac {F _ {1}}{F _ {2}}} = 2 \cdot 0. 8 \cdot \sqrt {\frac {5}{7 . 2}} = 1. 3 \, m$$

Answer:

New length should be equal $1.3 \, m$ .

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