1. a) Two trumpeters are standing at opposite ends of a large hall, both are playing...

a) Two trumpeters are standing at opposite ends of a large hall, both are playing a 440 Hz note. What beat frequency would a person hear if they were waking directly from one trumpeter towards the other one?

b) A 10 m long organ pipe has both ends open. Assume that the velocity of sound is 340ms^-1.

i) Calculate the fundamental frequency of the organ pipe.

ii) What is the fundamental frequency of the pipe of one end is closed?

iii) Can a standing wave be observed without resonance occurring?

Solutions

Expert Solution

Standing waves do not form under just any circumstances. They require that energy be fed into a system at an appropriate frequency. That is, when the driving frequency applied to a system equals its natural frequency. This condition is known as resonance. Standing waves are always associated with resonance.

In our case, for open pipe - the ends must have antinodes for standing waves; for one end closed - the closed end should have a node and the open node an antinode for standing waves. We have calculated the case where the wavelength is maximum possible that satisfies the above constraints.

genius_generous answered 1 year ago

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