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 m/s340~\mbox{m/s}.
  • The trumpet players aren't moving very fast.

A wire with mass 100 g100\text{ g} and length 10.00 m10.00\text{ m} is held on the two points PP and QQ under a tension of 240 N.240\text{ N}. Pulse 11 is sent along the wire from PP at time t=0,t=0, and pulse 22 is sent along the wire from QQ at time t=35.0 ms.t=35.0\text{ ms}. Approximately, at what distance xx from PP do the pulses begin to meet?

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

Assumptions and Details

  • The gravitational acceleration is g=9.80 m/s2.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 g/m3.1 \text{ g/m} and 0.26 g/m,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 m1.75\text{ m} and mass 60.0 g60.0\text{ g} under a tension of 700 N?700\text{ N}?


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