Problem structure
(a) 3 marks, numerical, Oscilloscope interpretation and frequency/amplitude definitions.
(b) 4 marks, numerical, Wave equation and phase difference calculation.
(c) 3 marks, numerical, Intensity definition and proportionality to amplitude squared.
Plan your route before writing. Use equations, diagrams, units, and a clear final justification where needed.
A student uses a signal generator to produce a sound wave in a laboratory. The wave is detected by a microphone connected to an oscilloscope. The oscilloscope screen shows a trace of the wave with the time-base set to $50\text{ \mu s cm}^{-1}$ and the vertical sensitivity set to $20\text{ mV cm}^{-1}$. The trace has a peak-to-peak height of $4.8\text{ cm}$ and the horizontal distance between three consecutive peaks is $13.6\text{ cm}$.
(a)
3 marks
Determine the frequency of the sound wave and the amplitude of the signal in mV.
(b)
4 marks
The sound wave travels through air at a speed of $343\text{ m s}^{-1}$. Calculate the wavelength of the wave and the phase difference, in radians, between two points in the air separated by a distance of $12.5\text{ cm}$ along the direction of wave travel.
(c)
3 marks
The sound wave is incident normally on a rectangular aperture of area $0.025\text{ m}^2$. The total power of the wave passing through this area is $1.8 \times 10^{-5}\text{ W}$. If the amplitude of the wave is doubled while the frequency remains constant, calculate the new intensity of the wave.
