A tuning fork of frequency 440 Hz resonates with a tube closed at one end of length 1.8 cm and diameter 5 cm in fundamental mode. The velocity of sound in air is

Question

A tuning fork of frequency 440 Hz resonates with a tube closed at one end of length 1.8 cm and diameter 5 cm in fundamental mode. The velocity of sound in air is (A) 336 m s-1 (B) 343 m s-1 (C) 300 m s-1 (D) 350 m s-1

Tardigrade Admin · Accepted Answer

In the fundamental mode of vibration, (l+0.3 D)=(λ/4)=(v/4 upsilon) ∴ v=4 upsilon(l+0.3 D)=4 ×440 (0.18+0.3×0.05) v=343 m s-1

Q. A tuning fork of frequency $440 Hz$ resonates with a tube closed at one end of length $1.8 c m$ and diameter $5 c m$ in fundamental mode. The velocity of sound in air is

$336 m s^{- 1}$

$343 m s^{- 1}$

$300 m s^{- 1}$

$350 m s^{- 1}$

In the fundamental mode of vibration,
$(l + 0.3 D) = \frac{λ}{4} = \frac{v}{4 υ}$
$∴ v = 4 υ (l + 0.3 D) = 4 \times 440 (0.18 + 0.3 \times 0.05)$
$v = 343 m s^{- 1}$

Q. A tuning fork of frequency 440Hz resonates with a tube closed at one end of length 1.8cm and diameter 5cm in fundamental mode. The velocity of sound in air is

336ms−1

343ms−1

300ms−1

350ms−1