A stretched wire of length 1.00 m is fixed on a movable laboratory trolley. The wire is vibrated in its second harmonic and gives 5 beats per second with a tuning fork of frequency 256 Hz when the trolley is at rest. The tension in the wire is kept unchanged throughout the experiment.
The trolley is now made to move directly towards a student who is holding the tuning fork stationary. The beat frequency observed by the student increases to 15 s⁻¹.
Take the speed of sound in air to be 340 m s⁻¹.
(i) Calculate the two possible values of the frequency of the wire when it vibrates in its second harmonic while the trolley is at rest.
(ii) Assuming the trolley moves towards the student, determine its speed.
(iii) Which of the two frequencies obtained in part (i) is consistent with the observed increase in beat frequency? Give reason.