An arrangement for producing stationary waves in air in a tube that is closed at one end is shown in Fig. 6.1.

Q#8 (Past Exam Paper – November 2015 Paper 23 Q6)

An arrangement for producing stationary waves in air in a tube that is closed at one end is shown in Fig. 6.1.

Fig. 6.1

A loudspeaker produces sound waves of wavelength 0.680 m in the tube.

For some values of the length L of the tube, stationary waves are formed.

(a) Explain how stationary waves are formed in the tube. [2]

(b) The length L is adjusted between 0.200 m and 1.00 m.

(i) Calculate two values of L for which stationary waves are formed. [2]

(ii) On Fig. 6.2, label the positions of the antinodes with an A and the nodes with an N for the least value of L for which a stationary wave is formed.

Fig. 6.2

[1]

Solution:

(a)

Waves from the loudspeaker travel down the tube and are reflected at the closed end. This produces wave travelling in opposite directions to the waves from the loudspeaker but with the same frequency. When these two waves overlap, stationary waves are formed.

(b)

(i)

0.51 m

0.85 m

{For a tube closed at one end, the stationary waves formed are as follows:

Fundamental mo

de: λ = 4L    giving L = λ/4 = 0.680 / 4 = 0.17 m     (not in range)

1^st overtone: λ = 4L/3              giving L = 3λ/4 = 3×0.680 / 4 = 0.51 m

2^nd overtone: λ = 4L/5             giving L = 5λ/4 = 5×0.680 / 4 = 0.85 m}

(ii)

A at open end, N at closed end, with an N and A in between, equally spaced

(by eye)

{The least value of L is 0.51 m. This corresponds to the 1^st overtone: a node at the closed end and an antinode at the open end with an antinode and a node between them}