Question 253: Waves

Question

Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously with tensions ' $\mathrm{T}_1$ ' and ' $\mathrm{T}_2$ ' respectively. On changing the tension slightly in one of them, the beat frequency remains unchanged. This will happen when (Given $\rightarrow \mathrm{T}_1>\mathrm{T}_2$ )

Accepted Answer

$$ 	ext { Using, } \mathrm{n}=\frac{1}{2 l} \sqrt{\frac{\mathrm{~T}}{\mathrm{~m}}} \Rightarrow \mathrm{n} \propto \sqrt{\mathrm{~T}} $$
Beat frequency $=\left|\sqrt{T_1}-\sqrt{T_2}ight|=6$
To keep beat frequency same:
If $T_1$ is decreased or $T_2$ is increased, $\left|\sqrt{T_1}-\sqrt{T_2}ight|$ remains 6.

Answer

$\mathrm{T}_1$ is increased or $\mathrm{T}_2$ is decreased

Answer

$\mathrm{T}_1$ is increased by 144

Answer

$\mathrm{T}_2$ is decreased by 144

Answer

$T_1$ is decreased or $T_2$ is increased

Waves

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