A cylindrical metal tube has a length of 50 cm and is open at both ends. Find the frequencies between 1 kHz to 2 kHz at which the air column in the tube resonates. The temperature on that day is $20^{\circ} c$

1020, 11360, 1700 Hz

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1026, 1368, 1710 Hz

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1328, 1660, 1922 Hz

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none of these

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Solution

The correct option is B 1026, 1368, 1710 Hz
$v (T) = 330 \sqrt{1 + \frac{20}{273}}$
$= 330 \sqrt{\frac{293}{273}} = 342 m s^{- 1}$
$f = \frac{v}{λ} = \frac{342}{1} = 342 H z .$

Checking from options for frequencies with a difference of 342 , gives option B

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A cylindrical metal tube has a length of 50 cm and is open at both ends. Find the frequencies between 1 kHz to 2 kHz at which the air column in the tube resonates. The temperature on that day is 20∘c

The correct option is B 1026, 1368, 1710 Hzv(T)=330√1+20273=330√293273=342ms−1f=vλ=3421=342Hz.Checking from options for frequencies with a difference of 342 , gives option B

A cylindrical metal tube has a length of 50 cm and is open at both ends. Find the frequencies between 1 kHz to 2 kHz at which the air column in the tube resonates. The temperature on that day is $20^{\circ} c$

The correct option is B 1026, 1368, 1710 Hz
$v (T) = 330 \sqrt{1 + \frac{20}{273}}$
$= 330 \sqrt{\frac{293}{273}} = 342 m s^{- 1}$
$f = \frac{v}{λ} = \frac{342}{1} = 342 H z .$

Checking from options for frequencies with a difference of 342 , gives option B