First slide

Stationary waves

Question

Two identical strings X and Z made of same material have tension $T_{X}$ and $T_{Z}$ in them. If their fundamental frequencies are 450Hz and 300Hz respectively, then the ratio $T_{X} / T_{Z}$ is

Easy

A

2.25
B

1.5
C

0.44
D

1.25

Solution

$f = \frac{V}{2 l} = \frac{1}{2 l} \sqrt{\frac{T}{μ}}$
For identical strings $\frac{f_{x}}{f_{z}} = \sqrt{\frac{T_{X}}{T_{Z}}} \Rightarrow \frac{T_{X}}{T_{Z}} = {(\frac{450}{300})}^{2} = 2.25$

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