Waves - Problem Solving


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.

A wire with mass \(100\text{ g}\) and length \(10.00\text{ m}\) is held on the two points \(P\) and \(Q\) under a tension of \(240\text{ N}.\) Pulse \(1\) is sent along the wire from \(P\) at time \(t=0,\) and pulse \(2\) is sent along the wire from \(Q\) at time \(t=35.0\text{ ms}.\) Approximately, at what distance \(x\) from \(P\) do the pulses begin to meet?

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 \(g=9.80\text{ m/s}^2.\)

If the linear densities of the heaviest and lightest steel wires of a certain piano are \(3.1 \text{ g/m}\) and \(0.26\text{ g/m},\) respectively, what is the approximate ratio of the diameter of the two wires?

What is the approximate speed of a transverse wave in a rope of length \(1.75\text{ m}\) and mass \(60.0\text{ g}\) under a tension of \(700\text{ N}?\)


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