Question 520: Waves

Question

A student is performing the experiment of resonance Column. The diameter of the column tube is
4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38
o
C in which the speed
of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance
Column tube. When the first resonance occurs, the reading of the water level in the column is

Accepted Answer

A student is conducting a resonance column experiment. The tube has a diameter of 4 cm, and the tuning fork vibrates at 512 Hz. The air temperature is 38
o
C, where the speed of sound is 336 m/s. The zero mark on the meter stick aligns with the top of the tube. For the first resonance, the water level reads :
During the first resonance :
$$ \frac{\lambda}{4} = l_1 + e $$
where $ l_1 $ is the length of the air column at resonance
Given that :
$$ 	ext{end correction} = e = 0.6r = 0.6 	imes 2 = 1.2 \, 	ext{cm} $$
where $ r $ is the radius of the tube
The wavelength $ \lambda $ can be expressed as :
$$ \lambda = 4(l_1 + e) $$
The frequency $ f $ is related to the wavelength $ \lambda $ by :
$$ f = \frac{v}{\lambda} = \frac{v}{4(l_1 + e)} $$
Rearranging for $ l_1 $ :
$$ 4(l_1 + e) = \frac{v}{f} $$
Solving for $ l_1 $ :
$$ l_1 = \frac{v}{4f} - e $$
Substitute the given values :
$$ l_1 = \frac{336 \, 	ext{m/s}}{4 	imes 512 \, 	ext{Hz}} - 0.012 \, 	ext{m} $$
$$ l_1 = \frac{336}{2048} - 0.012 $$
$$ l_1 = 0.164 \, 	ext{m} - 0.012 \, 	ext{m} $$
$$ l_1 = 0.152 \, 	ext{m} $$
Converting to cm :
$$ l_1 = 15.2 \, 	ext{cm} $$

Answer

14.0 cm

Answer

15.2 cm

Answer

16.4 cm

Answer

17.6 cm

Waves

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