A resonance air column of length 20 cm resonates with a tuning fork of frequency 450 Hz. Ignoring the correction, the velocity of sound in air will be

Question

A resonance air column of length 20 cm resonates with a tuning fork of frequency 450 Hz. Ignoring the correction, the velocity of sound in air will be (A) 920 m/s (B) 720 m/s (C) 820 m/s (D) 360 m/s

Tardigrade Admin · Accepted Answer

We know that the minimum length of the air column in a resonance tube corresponds to the fundamental mode of vibrations. Hence by ignoring end correction.

l = \frac{λ}{4}

\Rightarrow λ = 4 l = 4 \times 20 = 80 c m = 0.8 m

Resonant frequency

u = 450 Hz

∴

Speed of sound

v = v λ

= 450 \times 0.8 = 360 m / s

Q. A resonance air column of length 20cm resonates with a tuning fork of frequency 450Hz. Ignoring the correction, the velocity of sound in air will be

920 m/s

720 m/s

820 m/s

360 m/s

We know that the minimum length of the air column in a resonance tube corresponds to the fundamental mode of vibrations. Hence by ignoring end correction. l=4λ​ ⇒λ=4l=4×20=80cm=0.8m Resonant frequency u=450Hz ∴ Speed of sound v=vλ =450×0.8=360m/s

Q. A resonance air column of length $20 c m$ resonates with a tuning fork of frequency $450 Hz$ . Ignoring the correction, the velocity of sound in air will be