Question

A resonance tube can be used to measured the speed of sound in air. A tuning fork is held above the opening of the tube and struck, while the far end of the tube is lengthened or shortened. Resonances (loudnesses) are heard at a series of tube lengths, L, which are carefully measured.

resonance tube

The speed of sound in air is determined by measuring the distance between two consecutive resonances. A data set for a tuning fork with a frequency of 320 Hz are L1 = 25.8 cm; L2 = 78.4 cm; and L3 = 131.1 cm. Based on these data, what is the speed of sound in air?

Hint: the opening at the top is an antinode while the water surface is a node. Therefore, what fraction of a full wave is L1? What fractions are L2 and L3?

Answer 1

330.24 Hz

Step-by-step explanation:

Given:

Frequency, f = 320 Hz

L1 = 25.8 cm

L2 = 78.4 cm

L3 = 131.1 cm

Let the wavelength be λ

Then, L1 which is the length of the column of air is λ/4.

λ/4 = 25.8 cm

λ = 25.8 × 4 = 103.2 cm = 1.032 m

Then, speed of sound in air is:

v = λ f

⇒ v = 1.032 × 320 Hz

⇒ v = 330.24 m/s