The note produced by a stretched string has a fundamental frequency of 400Hz. If the length of the string is doubled while the tension in the string is incr...

Question 1 Report

The note produced by a stretched string has a fundamental frequency of 400Hz. If the length of the string is doubled while the tension in the string is increased by a factor of 4, the frequency is

200Hz

400Hz

800Hz

1600Hz

Answer Details

F = $\frac{1}{2 L}$ $\sqrt{\frac{T}{m}}$

T2 = 4T1 ; L2 = 2L1

$\frac{2 F_{1} L_{1}}{2 F_{2} L_{2}}$ = $\sqrt{\frac{T_{1}}{T_{2}}}$

$\frac{400 \times L_{1}}{F \times L_{1}}$ = $\sqrt{\frac{T_{1}}{4 T_{1}}}$

F = 400Hz

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