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 signal is monitored using a cathode-ray oscilloscope (CRO). The trace on the screen shows a clear sinusoidal wave. The time-base of the CRO is set to $250\text{ }\mu\text{s cm}^{-1}$ and the vertical gain is set to $5.0\text{ mV cm}^{-1}$.
One full cycle of the wave on the screen occupies a horizontal distance of $3.2\text{ cm}$, and the peak-to-peak height of the trace is $4.8\text{ cm}$.
(a)
3 marks
Calculate the frequency of the sound wave produced by the signal generator.
(b)
2 marks
The speed of sound in the laboratory is $344\text{ m s}^{-1}$. Determine the wavelength of this sound wave.
(c)
4 marks
The student moves a microphone, connected to the CRO, a distance of $0.50\text{ m}$ further away from the signal generator. The amplitude of the wave detected by the microphone decreases. Assuming the sound spreads out as a spherical wave from a point source, calculate the ratio:
$$\frac{\text{Amplitude at new position}}{\text{Amplitude at original position}}$$
if the original distance from the source was $1.20\text{ m}$.
