How Does the Doppler Effect Alter the Frequency Heard by the Engineer?

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In summary: In the general expression the relative velocity of sound is to be taken with respect to air. Here I have taken it with respect to source and observer. Therefore the confusion.In summary, this conversation discusses the calculation of the frequency of sound heard by an engineer on a train moving at a certain speed, based on the speed of sound and the velocity of the train. The formula used is f' = f(v+vo)/(v+vs), where v is the speed of sound and vo and vs represent the velocities of the observer and source respectively. It is important to consider the relative velocities of the observer and source with respect to air in order to determine the correct formula to use.
  • #1
phEight
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Frequency Problem, need urgent help please

Homework Statement



A train moving west at a speed of 30 m/s emits a whistle at a frequency of 348 Hz. On another train behind the first train and moving west at a speed of 20 m/s, the engineer hears the whistle from the first train. If the speed of sound in air is 343 m/s what is the frequency of the sound heard by the second train engineer?

Homework Equations



(I believe this is it)

f' = (1/1+- u/v)f

The Attempt at a Solution



To be honest I've tried my best to figure this out but I'm simply lost on it. Thanks.
 
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  • #2
f’ = f(v+vo)/(v+vs), where v is the speed of sound.

The observer is moving toward the source in the air frame, and the source is moving away from the observer. Hence, this particular choice of signs.
 
  • #3
Ah that makes sense, so if they were moving away from each other it would f' = f(v-vo)/(v+vo) ?
 
  • #4
You are right, excepting your typo. The bottom one should be vs.
 
  • #5
Ah that makes sense, so if they were moving away from each other it would f' = f(v-vo)/(v+vs) ? This formula is wrong.
The direction of the velocity of sound must be always towards the observer because is the person who listens the apperent change in the frequency. In this question source and observer are moving towards west and velocity of sound is towards east. Therefore
f' = f(v+vo)/(v+vs)
 
  • #6
These small techinal errors I make! In this example, they are actually moving away from each other, and I have given the correct formula.

For the 2nd case, by "moving away from each other", I meant that when they are moving in opp directions wrt the air.
 
  • #7
In all such cases we have to consider the relative velocities of sound with respect to source and the observer. If they are moving in the same direction take -ve sign in the general expression which I have written. Other wise put +ve sign. And the direction of the velocity of sound must be always towards the observer.
 
  • #8
I have not said anything to the contrary. If the observer moves wrt air toward the source, the sign in the numerator is +ve, else –ve. If the source moves wrt air toward the observer, then the sign in the denominator is –ve, else +ve.
 
  • #9
I am sorry. It is my fault. You have written it correctly.
 

1. What is the frequency problem?

The frequency problem refers to the issue of determining the most common or repeated element in a set of data. It is often encountered in statistical analysis and is important in understanding patterns and trends within the data.

2. Why is the frequency problem important?

The frequency problem is important because it allows us to identify and analyze patterns and trends within data, which can provide valuable insights for decision making and problem solving. It also helps in understanding the distribution of data and detecting outliers.

3. How is the frequency problem solved?

The frequency problem is typically solved by organizing the data into a frequency distribution table or graph, where the frequency of each element is represented. This helps in visualizing the most common elements and identifying any outliers. Statistical measures such as mean, median, and mode can also be used to determine the most frequent element.

4. What are some common challenges in solving the frequency problem?

One of the common challenges in solving the frequency problem is dealing with large and complex data sets. It can also be challenging to determine the appropriate bin size or class intervals for organizing the data in a frequency distribution table. Additionally, outliers or extreme values can skew the frequency results and need to be carefully addressed.

5. How can the frequency problem be applied in real-world situations?

The frequency problem has various real-world applications, such as in market research to understand consumer preferences, in healthcare to study the frequency of diseases, and in quality control to identify defects. It can also be used in social sciences to study the frequency of certain behaviors or attitudes among a population.

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