Calculating Doppler Effect with Wind: 900 Hz Siren, 15.0 ms-1 Wind Speed

[joshs0194]

Homework Statement

A siren emits a frequency of 900 Hz. Wind is blowing at a steady speed of 15.0 ms-1. The speed of sound in calm air is 343 ms-1. What is the frequency heard by someone approaching at 15.0 ms¹,
(i) when the wind blows from the person to the siren, and
(ii) when the wind blows from the siren to the person?

Homework Equations

f^'=f/((1-v_s/v) ) source approaching

The Attempt at a Solution

for i) i figured that since the sound is no longer in calm air that the velocity v_s would be 343-15=328m/s, and v would be 15m/s.. so that comes out to -.1916Hz? frequency can't be negative can it? i imagine ii) is the same method? please help

 

[anathema]

You are on the right track with your attempt at a solution. The formula you have used is correct for calculating the frequency heard by someone approaching a sound source. However, there are a few things to consider in this scenario.

Firstly, the speed of sound in calm air (343 m/s) is the speed at which sound travels in still air. When wind is present, it can either add to or subtract from the speed of sound, depending on its direction. In this case, since the wind is blowing towards the person, it would add to the speed of sound. Therefore, the velocity of the sound (v_s) would be 343 + 15 = 358 m/s.

Next, we need to consider the direction of the wind in relation to the person and the siren. When the wind is blowing from the person to the siren, the sound waves will be traveling in the same direction as the wind, resulting in a higher speed of sound. This means that the frequency heard by the person would be higher than the emitted frequency of 900 Hz.

Using the formula you have provided, the frequency heard by the person (f^') can be calculated as follows:

f^'=900/((1-358/343))= 900/0.044= 20454.55 Hz

Note that this is a positive value, indicating that the frequency heard is higher than the emitted frequency. This makes sense as the person is approaching the sound source, resulting in a higher frequency due to the Doppler effect.

For the second scenario, where the wind is blowing from the siren to the person, the sound waves will be traveling against the direction of the wind, resulting in a lower speed of sound. In this case, the calculated frequency would be lower than the emitted frequency of 900 Hz.

f^'=900/((1-358/373))= 900/-0.040= -22500 Hz

Note that this is a negative value, indicating that the frequency heard is lower than the emitted frequency. This also makes sense as the person is moving away from the sound source, resulting in a lower frequency.

In conclusion, the frequency heard by someone approaching a sound source can be affected by the speed of the wind and its direction. It is important to consider these factors when calculating the frequency heard in a given scenario. I hope this helps to clarify your understanding. Keep up the good work in your scientific studies