A student connects a microphone to a cathode-ray oscilloscope (CRO) to study a pure musical note. Initially the screen shows a wave of amplitude 2 divisions and time period 4ms. The student now turns only the volume control of the sound source. The new trace has an amplitude of 4 divisions while the time period remains 4ms. Answer the following:
(i) Calculate the frequency of the sound before and after the volume change.
(ii) State whether the pitch of the note has changed. Give a reason.
(iii) Explain why the loudness of the note is different after the adjustment and identify the physical quantity that has been altered.
(iv) Derive the mathematical relationship between frequency (f) and time period (T) of a wave.