State the requirements for a stationary wave to be formed.
A sound wave in air has speed $330\,\text{m s}^{-1}$ and wavelength $0.18\,\text{m}$. Calculate its frequency.
Find the time-base setting, in $\text{s cm}^{-1}$, of the c.r.o.
A microphone connected to a cathode-ray oscilloscope (c.r.o.) detects the sound from a loudspeaker. Fig. 4.1 displays the trace on the c.r.o. screen. In air, the sound wave travels at $330\,\text{m s}^{-1}$ and has wavelength $0.18\,\text{m}$.
The sound intensity from the loudspeaker is now reduced to half. The wavelength of the sound stays the same. Assume that the amplitude of the trace is proportional to the amplitude of the sound wave. On Fig. 4.1, sketch the new trace shown on the c.r.o. screen.
In (b), the loudspeaker is positioned above a vertical tube of liquid, as shown in Fig. 4.2. A tap at the base of the tube is opened so that liquid drains away at a constant rate. The wavelength of the sound from the loudspeaker is $0.18\,\text{m}$. The sound initially heard becomes much louder when the liquid surface reaches level A. It next becomes much louder when the liquid surface reaches level B, as shown in Fig. 4.3.
Calculate the vertical separation between level A and level B.
On Fig. 4.3, place the letter N at the positions of the nodes of the stationary wave formed in the air column when the liquid surface is at level B.
The mass of liquid flowing out of the tube each second is $6.7\,\text{g s}^{-1}$. The tube’s internal cross-sectional area is $13\,\text{cm}^2$. The liquid has density $0.79\,\text{g cm}^{-3}$. Calculate the time taken for the liquid surface to move from level A to level B.