# Speed of sound on a moving train

In summary, the two trains A and B are moving on the same track with speeds of 20m/s and 30m/s respectively. The engine of train A blows a whistle with a frequency range of 800Hz to 1120Hz. The speed of sound in air is 340m/s. The question is to find the speed of the whistle for passengers in both A and B. The correct answer is 360m/s for passengers in A and 310m/s for passengers in B. This is because the separation speed between the two trains adds to the speed of sound from the perspective of passengers on train B, leading to a lower speed of sound for them.

## Homework Statement

Two trains A and B are moving with speed 20m/s and 30m/s respectively in the same direction on the same straight track with B ahead of A. The engines are at the front ends. The engine of trains A blows a long whistle.

Assume that the speed of sound of whistle is composed of components varying in frequency from f1=800Hz to f2=1120 Hz as shown in the figure. The spread in the frequency (ie, highest frequency - lowest frequency) is thus 320 Hz. The speed of sound in air is 340m/s.

Find the speed of the whistle for passengers in A and passengers in B

## The Attempt at a Solution

Relative velocity between A and B=10m/s. So speed of sound for passengers in B would be 10m/s less than 340m/s i.e, 330m/s and for people in A the speed of sound would be 340m/s.
But my answer is wrong. The answer is 360m/s for people in A and 310m/s for people in B. I could not think of a possible explanation. Can anyone help?

Since the trains are pulling apart, the separation speed ADDS to the speed of sound from the reference point of the passenger on the train (B) that did not blow its whistle. Why did you think it would subtract?

Your statement that "speed of sound for passengers in B would be ... " is incorrect. The speed of sound is the same for both sets of passengers. What is not the same is the speed of the THE sound FROM THAT WHISTLE. Maybe that's how you are confusing yourself.

## 1. How does the speed of sound change on a moving train?

The speed of sound on a moving train is affected by two main factors: the speed of the train and the direction of the sound. As the train moves faster, the speed of sound coming from the front of the train will appear slower to a stationary observer outside the train. This is because the sound waves have to travel a longer distance to reach the observer due to the train's movement. On the other hand, sound coming from the back of the train will appear faster to the observer due to the train's movement adding to the speed of the sound waves.

## 2. Does the speed of sound on a moving train always decrease?

No, the speed of sound on a moving train does not always decrease. It depends on the direction of the sound relative to the direction of the train's movement. If the sound is traveling in the same direction as the train, its speed will increase. However, if the sound is traveling in the opposite direction of the train, its speed will decrease.

## 3. How is the speed of sound on a moving train measured?

The speed of sound on a moving train can be measured by using a stationary observer outside the train and recording the time it takes for a sound to travel a known distance. This distance can be measured between the source of the sound and the observer, or by using two observers at different distances from the source. The speed of the train can also be measured and taken into account when calculating the speed of sound.

## 4. How does the speed of sound on a moving train compare to the speed of light?

The speed of sound on a moving train is much slower compared to the speed of light. The speed of sound is approximately 340 meters per second, while the speed of light is approximately 299,792,458 meters per second. This means that sound cannot travel as fast as light, and its speed is also affected by the movement of the train.

## 5. Can sound travel faster than the speed of sound on a moving train?

No, sound cannot travel faster than the speed of sound on a moving train. The speed of sound is a constant and cannot be exceeded. However, the perceived speed of sound can be different due to the movement of the train. For example, a person on the train may hear a sound traveling faster than the speed of sound if it is moving in the same direction as the train's movement.

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