Question

The identical radius of a 1 m long resonance tube is measured as 3.0 cm .A tuning form of frequency 2000 Hz. is used. Teh first resonating length is measured as 14.0 cm. We shall calculate the following

1) Maximum percenetage error in measurement of end correction, as give by Rayleigh's formula is 3.33%

2) Speed of sound at the room temperature is 376 m/s

3) End correction obtained in the experiment is 0.1 cm

4) None of these above is correct.

Answer 1

(1) Maximum percenetage error in measurement of end correction, d will be given as -

we know that, d = (0.6) R

change in end correction, d = (0.6) R

where, R = error in measurement of radius = 0.1 cm

d = [(0.6) (0.1 cm)

d = 0.06 cm

Therefore, the percentage error is given by a formula as -

Percentage error = (d / d) x 100%

Percentage error = [(0.06 cm) / (0.6) (3 cm] x 100%

Percentage error = (0.0333) x 100%

Percentage error = 3.33%

(2) Speed of sound at the room temperature which will be given as -

we know that, = 2 (L₂ - L₁) 2 [(14 cm) - (4.6 cm)]

= 18.8 cm

using a formula & we get

v = f [(0.188m) (2000 Hz)]

v = 376 m/s

(3) End correction obtained in the experiment will be given by -

d = (L₂ - 3 L₁) / 2

d = [(14 cm) - 3 (4.6 cm)] / 2

d = (0.2 cm) / 2

d = 0.1 cm