We know that the following equation gives the average power carried by a sinusoidal wave on a string:
And the following equation describes the relationship between a wave's frequency and angular speed:
The mass of the wire is
, its length is
l=80.0 cm=0.800 m
and the tension in it is ;
The wave traveling along the wire has frequency of and its amplitude is
(A) We are aware that the mass per unit length corresponds to the linear mass density; Consequently, the wire's linear mass density is given as follows:
We substitute for f into relation (R.1), so we get:
Now, we plug our values for , F, and A into equation (1), so we get:
(b) We can observe from equation (1) that the average power is related to the amplitude's square;
As a result, when the amplitude is cut in half, the average power is cut in half as well:
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