A tuning fork is struck lightly and then modified in several steps as described below. Take the speed of sound in air as 340m/s unless stated otherwise.
Original condition: frequency 256Hz, amplitude 2.0mm.
(a) Calculate the wavelength of the sound produced by the fork in its original condition.
(b) The fork is struck harder so that its amplitude doubles while the frequency remains unchanged. Explain quantitatively how this affects the loudness and pitch of the sound.
(c) The prongs are then filed so that the frequency increases by 20%. Keeping the speed of sound unchanged, calculate the new wavelength and state the expected change in perceived pitch.
(d) Finally, the fork from part (c) is struck with the higher amplitude described in part (b). Summarise the combined effect on loudness and pitch compared with the sound in the original condition.