Question

An observer at rest near the source of sound energy of frequency 684Hz.Another the sound of 676Hz moving towards the observer at 2n/s. If the speed of sound waves in air is 340m/s then what is the best frequency heard by the observe?

Answer 1

To determine the frequency heard by the observer, we need to apply the concept of the Doppler effect. The Doppler effect describes how the frequency of a wave appears to change when there is relative motion between the source of the wave and the observer.

Let's denote the frequency of the source as f₀ = 684 Hz and the speed of sound in air as v = 340 m/s. The observer is at rest near the source. Another source emitting sound with a frequency of f' = 676 Hz is moving towards the observer at a speed of v' = 2 m/s.

The formula for the observed frequency (f) due to the Doppler effect when the observer is at rest is given by:

f = f₀ * (v + v') / (v + vs)

Where: f₀ = frequency of the source v = speed of sound in the medium v' = velocity of the source relative to the medium vs = velocity of the observer relative to the medium

In this case, the observer is at rest near the source, so vs = 0. Plugging in the given values, we can calculate the observed frequency:

f = 684 Hz * (340 m/s + 2 m/s) / (340 m/s + 0 m/s) = 684 Hz * 342 m/s / 340 m/s ≈ 686.4 Hz

Therefore, the observed frequency heard by the observer is approximately 686.4 Hz.