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?

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Can anyone please clarify?

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But, how did u get the answer?

To find the speed at which the trumpet players are marching, we need to consider the frequency of the beat and the frequency of the sound produced by the players.

The beat frequency is the difference between the frequencies of the two trumpet players. In this case, the beat frequency is 2 Hz. That means one trumpet player has a frequency slightly higher than the other.

We know that when two sounds with different frequencies are played together, we perceive a beat at the frequency equal to the difference in their frequencies.

Let's call the frequency of the trumpet player marching towards you as f1 and the frequency of the trumpet player marching away from you as f2.

The beat frequency (B) can be expressed as the absolute value of the difference between f1 and f2: B = |f1 - f2|.

In this case, the beat frequency is 2 Hz, so we have: 2 Hz = |f1 - f2|.

Since both trumpet players are playing the same A note, their frequencies will differ only due to the Doppler effect caused by their relative motion towards or away from you.

The Doppler effect describes the perceived change in frequency of a sound source due to the relative motion between the source and the observer.

When a source is moving towards the observer, the frequency appears higher, while when the source is moving away, the frequency appears lower.

For simplicity, let's assume the speed of sound is constant. The Doppler effect equation in this case can be simplified as follows:

f1 = (speed of sound + speed of the player marching towards you) / (speed of sound) * base frequency

f2 = (speed of sound - speed of the player marching away from you) / (speed of sound) * base frequency

Since both trumpet players are playing an A note (440 Hz), we can rewrite the beat frequency equation as follows:

2 Hz = |((speed of sound + speed of the player marching towards you) / (speed of sound) * 440 Hz) - ((speed of sound - speed of the player marching away from you) / (speed of sound) * 440 Hz)|

Now, let's solve for the speed of the players marching toward you (V1) and away from you (V2) in m/s:

V1 = speed of sound * ((2 Hz + 440 Hz) / 440 Hz)

V2 = speed of sound * ((2 Hz - 440 Hz) / 440 Hz)

The speed of sound is approximately 343 m/s at room temperature.

By substituting the appropriate values, we can calculate the velocities of the players.