8.1 Stationary Waves

A stationary wave on a string is shown in Fig. 1.1.

Explain how the wave is formed, referring to the principle of superposition in your answer.

On Fig. 1.1, draw the stationary wave that would be formed on the string in part (a) with two more nodes and two more antinodes.

Fig. 1.2 shows the appearance of a stationary wave on a stretched string at one instant in time.

For the wave in Fig. 1.2 the frequency of vibration is 180 Hz and the speed of the waves along the string is 60 m s^–1.

For this wave

Fig. 1.1 shows a stationary wave formed on a guitar string fixed at P and Q when it is plucked at its centre.

X is a point on the string at maximum displacement.

Explain why a stationary wave is formed on the string

The stationary wave in Fig. 1.1 is the D string of the guitar which has a frequency of 146.83 Hz.

Calculate the time taken for the string at point X to move from maximum displacement to its next maximum displacement.

The progressive waves on the string travel at a speed of 190 m s^–1.

Calculate length of the D string.

A guitarist presses on the string at point R to shorten it and create the higher note ‘E’. The distance between R and Q in Fig. 1.2 is 0.29 m.

The speed of the progressive wave remains at 190 m s^–1 and the tension remains constant.

Calculate the frequency of note E.