Question 438: Waves

Question

An air column in a pipe, which is closed at one end will be in resonance with a vibrating tuning fork of frequency 264 Hz for various lengths. Which one of the following lengths is not possible? (V = 330 m/s)

Accepted Answer

$$\mathrm{n}=264 \mathrm{~Hz}, \mathrm{~V}=300 \mathrm{~m} / \mathrm{s}$$
For fundamental frequency, $$\mathrm{n}=\frac{\mathrm{V}}{4 l}$$
$$l=\frac{\mathrm{V}}{4 \mathrm{n}} \quad=\frac{330}{4 	imes 264}=0.3125 \mathrm{n} \quad=31.25 \mathrm{~cm}$$
For fundamental mode, $$l=\frac{\lambda}{4}$$
other possible lengths are $$\frac{3 \lambda}{4}, \frac{5 \lambda}{4}, \ldots \ldots$$
$$	ext { i.e. } 93.75 \mathrm{~cm}, 156.25 \mathrm{~cm}, \ldots \ldots$$
Hence, $$62.50 \mathrm{~m}$$ is not possible.

Answer

62.50 cm

Answer

93.75 cm

Answer

156.25 cm

Answer

31.25 cm

Waves

An air column in a pipe, which is closed at one end will be in resonance with a vibrating tuning fork of frequency 264 Hz for various lengths. Which one of the following lengths is not possible? (V = 330 m/s)

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