1.1. 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

1.2. 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.

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

Calculate length of the D string.

1.4. 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.