Question 430: Waves

Question

A pipe closed at one end has length $$0.8 \mathrm{~m}$$. At its open end $$0.5 \mathrm{~m}$$ long uniform string is vibrating in its $$2^{	ext {nd }}$$ harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $$50 \mathrm{~N}$$ and the speed of sound is $$320 \mathrm{~m} / \mathrm{s}$$, the mass of the string is

Accepted Answer

$$\begin{aligned} & 2 	imes\left[\frac{1}{2 \ell_1} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}ight]=\frac{v}{4 \ell_2} \ & \quad \frac{1}{0.5} \sqrt{\frac{50}{\mathrm{~m}}}=\frac{320}{4 	imes 0.8} \ & 	herefore \quad \mathrm{m}=0.02 \mathrm{~kg} / \mathrm{m} \ & 	herefore \quad 	ext { Total mass of the string } \ & \quad=0.02 	imes 0.5 \mathrm{~kg}=10 \mathrm{gm}\end{aligned}$$

Answer

20 gram

Answer

10 gram

Answer

5 gram

Answer

15 gram

Waves

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