the speed of sound in air at a given temperature is 350m/sec. An engine blows whistle at a frequency of 1200c/s. it is approching the observer with a velocity of 50m/s. what will be the apparent frequency in c/s heard by the observer?

To find the apparent frequency heard by the observer when the engine is approaching, we can use the Doppler effect formula. The Doppler effect describes how the frequency of a wave changes for an observer moving relative to the source of the wave. In this case, the source is the whistle from the engine, and the observer is stationary. Let's break down the problem step by step.

Understanding the Variables

We have the following information:

• Speed of sound in air (v) = 350 m/s
• Frequency of the whistle (f₀) = 1200 Hz (c/s)
• Velocity of the engine (vₛ) = 50 m/s (approaching the observer)
• Velocity of the observer (vₒ) = 0 m/s (since the observer is stationary)

Applying the Doppler Effect Formula

The formula for the apparent frequency (f') when the source is moving towards a stationary observer is given by:

f' = f₀ × (v + vₒ) / (v - vₛ)

In this formula:

• f' is the apparent frequency
• f₀ is the actual frequency of the source
• v is the speed of sound
• vₒ is the speed of the observer
• vₛ is the speed of the source

Substituting the Values

Now, we can substitute the known values into the formula:

f' = 1200 Hz × (350 m/s + 0 m/s) / (350 m/s - 50 m/s)

This simplifies to:

f' = 1200 Hz × (350 m/s) / (300 m/s)

Calculating the Apparent Frequency

Now, let's perform the calculation:

f' = 1200 Hz × (350 / 300)

f' = 1200 Hz × 1.1667

f' ≈ 1400 Hz

Final Result

The apparent frequency heard by the observer as the engine approaches is approximately 1400 Hz. This increase in frequency is due to the Doppler effect, which causes the sound waves to compress as the source moves closer to the observer.