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Waves are disturbances that transport energy without transporting mass. Learn the mechanism underlying sound, deep ocean swells, light, and even the levitation of objects in mid air.

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 \(340~\mbox{m/s}\).
- The trumpet players aren't moving very fast.

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A string, which is fixed at point \(P,\) is stretched by a block with mass \(m\) at point \(Q,\) as shown in the above figure. Point \(P\) is generating a sinusoidal wave but the amplitude of \(P\) is small enough to be considered as a node. The distance between \(P\) and \(Q\) is \(L=1.50\text{ m},\) and the linear density of the string is \(\mu=1.60\text{ g/m}.\) If the oscillating frequency of \(P\) is \(f=130\text{ Hz}\) and is setting up sixth harmonic on the string, what is the approximate mass \(m\) of the block?

**Assumptions and Details**

- The gravitational acceleration is \(g=9.80\text{ m/s}^2.\)

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