Concept explainers
The energy required to make a pulse with twice the amplitude in a stretched spring.
Explanation of Solution
Introduction:
The energy of sound wave or pulse is related to its amplitude. The energy required to make a pulse with twice the amplitude is four times of the energy.
Energy of waves is directly proportional to the square of the amplitude of the wave. Wave is actually a displacement acted upon by a restoring force. In a spring the restoring force is given as,
Here
Energy is given by the integral of force,
Here,
From equation (2) it is clear that, the energy is equal to the square of the displacement.
In case of a pulse, this displacement is the amplitude. If amplitude is twice then the energy required is four times.
Conclusion:
Hence, the energy required to make a pulse with twice the amplitude is four times of the energy.
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