Question

calculate the length of pipe 4cm diameter
and open at both ends when it set into
Vibrations by a turming fork of frequency 288hz​

Answer 1

we have to calculate the length of pipe 4cm diameter and open at both ends when it set into

vibrations by a tuning fork of frequency 288 Hz.

solution : we know, end correction, e = 0.6r

where r is the radius of pipe.

for fundamental frequency, λ/2 = l + 2e

⇒λ = 2(l + 2e) = 2l + 4 × 0.6r

⇒λ = 2l + 2 × 0.6 × 2r

⇒λ = 2l + 1.2d

here d = 4cm

so, λ = 2l + 1.2 × 4 = 2l + 4.8 cm

now frequency, f = v/λ

⇒288 = (33200 cm/s)/(2l + 4.8 cm)

⇒2l + 4.8 = 33200/288 = 115.27

⇒2l = 115.27 - 4.8 = 110.47

⇒l = 55.235 cm ≈ 55.23 cm

Therefore the length of the pipe is 55.23 cm