You are watching a marching band practice outdoors. Near you are two trumpet players, one marching directly towards you and one away from you at the same speed. Each trumpet player is playing an A (440 Hz) and you hear a beat between the two sounds at a frequency of 2 Hz. How fast are the trumpet players marching in m/s?

Details and assumptions

The speed of sound is 340 m/s.
The trumpet players aren't moving very fast.

From a student with an objectionable screenname:

Physics - Sm..., Monday, May 6, 2013 at 6:42am
Just solve
440/(1 + (340/v)) - 440/(1-(v/340)) = 2

Specifically 0.7709 ~ 0.771 And please don't cheat on brilliant ;)

Whats Brilliant Can you tell Me

Can anyone please clarify?

what formula did you use???

To calculate the speed of the trumpet players, we can use the formula:

Speed = Frequency × Wavelength

First, let's determine the wavelength of the beat. The beat frequency is the difference between the frequencies of the two trumpet players, which in this case is 2 Hz. Since the beat frequency is the difference between the two frequencies, we can express it as:

Beat frequency = | Frequency1 - Frequency2 |

In this case, we have two trumpet players playing an A (440 Hz). Therefore, the beat frequency can be written as:

2 Hz = | 440 Hz - 440 Hz |

Since the beat frequency is zero, it means that the two trumpet players are playing at the same frequency but with a phase difference. This creates constructive and destructive interference, resulting in a beat frequency of 2 Hz.

Since the beat frequency is zero, the wavelength is infinite. However, if we consider a short duration, we can use the formula:

Speed = Distance / Time

In this case, the distance between the trumpet players is the wavelength. Let's assume that the duration for which the beat is observable is 1 second. Therefore, the distance between the trumpet players can be calculated as:

Distance = Speed × Time

To calculate the speed, we rearrange the formula:

Speed = Distance / Time

Since the distance is the wavelength and we know that the wavelength is infinite, we can conclude that the speed of the trumpet players is also infinite.

Therefore, in this scenario, the trumpet players are technically not marching at a finite speed. They are stationary or standing still since the beat frequency is zero, indicating that both players are playing the same note with a phase difference.