Standing Waves or Stationary Waves

Q2. The diagram shows a structure that supports a horizontal copper aerial wire W used for transmitting radio signals.

The copper aerial wire is 12 m long and its area of cross-section is 1.6 × 10^–5 m².

The tension in the copper aerial wire is 5.0 × 10² N.

Young modulus of copper = 1.2 × 10¹¹ Pa

(a) Show that the extension produced in a 12 m length of the aerial wire when the tension is 5.0 × 10² N is less than 4 mm.

[2 marks]

(b) The cables that support each mast are at an angle of 65° to the horizontal.

Calculate the tension in each supporting cable so that there is no resultant horizontal force on either mast.

[1 mark]

Explain how stationary waves are produced and why only waves of specific frequencies can form on the aerial wire.

[4 marks]

(d) Calculate the mass of a 1.0 m length of the aerial wire.

Density of copper = 8,900 kg m^–3

[1 mark]

(e) Calculate the frequency of the wave when the third harmonic is formed on the aerial wire.

[2 marks]

(f) Sketch, on the diagram below, the standing wave on the wire when the third harmonic is formed.

[1 mark]

(g) High winds produce large amplitudes of vibration of the aerial wire.

Explain why the wire may sag when the high wind stops.

[2 marks]

(Total 13 marks)