A signal generator is linked to two loudspeakers $L_1$ and $L_2$, as shown in Fig. 2.1. A microphone $M$, which is attached to the Y-plates of a cathode-ray oscilloscope (c.r.o.), measures the sound intensity along the line ABC. The distances $L_1A$ and $L_2A$ are the same. The time-base of the c.r.o. is switched off. The traces on the c.r.o. when $M$ is at A, then at B and then at C are shown in Fig. 2.2, Fig. 2.3 and Fig. 2.4 respectively. For these traces, $1.0\,\text{cm}$ represents $5.0\,\text{mV}$ on the vertical scale.
(a(i))[1]
Explain why coherent waves are produced by the loudspeakers.
(a(ii))[3]
Use the principle of superposition to explain the traces shown when $M$ is at A, B and C.
(b)[3]
The sound from $L_1$ and $L_2$ has frequency $500\,\text{Hz}$. The time-base on the c.r.o. is switched on. The microphone $M$ is placed at A. On Fig. 2.5, draw the trace seen on the c.r.o. On the vertical scale, $1.0\,\text{cm}$ represents $5.0\,\text{mV}$. On the horizontal scale, $1.0\,\text{cm}$ represents $0.10\,\text{ms}$.
(ii(1))[1]
Use the principle of superposition to explain the traces shown with M at A.
(ii(2))[1]
Use the principle of superposition to explain the traces shown with M at B.
(ii(3))[1]
Use the principle of superposition to explain the traces shown with M at C.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “both loudspeakers are fed from the same signal generator” …