Question 373: Waves

Question

A uniform string is vibrating with a fundamental frequency '$$n$$'. If radius and length of string both are doubled keeping tension constant then the new frequency of vibration is

Accepted Answer

$$\begin{aligned}
& l_2=2 l_1, \mathrm{R}_2=2 \mathrm{R}_1, \mathrm{~T}_1=\mathrm{T}_2 \
& \mathrm{n}=\frac{1}{2 l} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}} \
& 	ext { Where, } \mathrm{m}=	ext { mass per unit length }=\frac{\left(\pi \mathrm{R}^2 light) ho}{l} \
& 	herefore \quad \mathrm{m} \propto \mathrm{R}^2 \
& 	herefore \quad \frac{\mathrm{n}_2}{\mathrm{n}_1}=\frac{l_1}{l_2} 	imes \frac{\mathrm{R}_1}{\mathrm{R}_2} \
& 	herefore \quad \frac{\mathrm{n}_2}{\mathrm{n}_1}=\frac{l_1}{2 l_1} 	imes \frac{\mathrm{R}_1}{2 \mathrm{R}_1} \
& 	herefore \quad \mathrm{n}_2=\frac{\mathrm{n}_1}{4}=\frac{\mathrm{n}}{4}
\end{aligned}$$

Answer

$$2 \mathrm{n}$$

Answer

$$3 \mathrm{n}$$

Answer

$$\frac{\mathrm{n}}{4}$$

Answer

$$\frac{\mathrm{n}}{3}$$

Waves

A uniform string is vibrating with a fundamental frequency '$n$'. If radius and length of string both are doubled keeping tension constant then the new frequency of vibration is

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