An aeroplane pilot hears a slow beat from the two engines of his plane. He increases the speed of the right engine and now hears a slower beat. What should be the pilot now do, to eliminate the beat?

Options

A. Increase the speed of the left engine.
B. Decrease the speed of the right engine.
C. Increase the speed of both engines.
D. Increase the speed of the right engine.

Explanation

To solve the problem, we need to analyze the situation of the pilot hearing beats from the two engines of the airplane. Let's break it down step by step.

### Step 1: Understand the concept of beats
Beats occur when two sound waves of slightly different frequencies interfere with each other. The beat frequency is given by the absolute difference between the two frequencies:
\[ \text{Beat Frequency} (f_b) = |f_1 - f_2| \]
where \( f_1 \) and \( f_2 \) are the frequencies of the two engines.

### Step 2: Identify the initial conditions
Let:
- \( \nu_r \) = frequency of the right engine
- \( \nu_l \) = frequency of the left engine

Initially, the pilot hears a slow beat, which indicates that the frequencies of the two engines are close but not equal.

### Step 3: Analyze the effect of increasing the right engine's speed
When the pilot increases the speed of the right engine, the frequency \( \nu_r \) increases. The pilot then hears a slower beat, which means the difference between the two frequencies has decreased:
\[ f_b = |\nu_l - \nu_r| \]
Since the beat frequency has decreased, it implies that the frequencies are getting closer together.

### Step 4: Determine what to do next
To eliminate the beat completely, the pilot needs to make the frequencies equal. Since the right engine's frequency has already been increased and the beat frequency has decreased, the pilot should continue to increase the speed of the right engine until:
\[ \nu_r = \nu_l \]
This will result in a beat frequency of zero.

### Conclusion
The pilot should **further increase the speed of the right engine** to eliminate the beat.

### Final Answer
The correct action for the pilot is to **increase the speed of the right engine**.

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