
A string with linear mass density is under a tension of How much power must be applied to the string to generate sinusoidal waves at a frequency of and amplitude of
A.
B.
C.
D.
Answer
486.3k+ views
Hint: The relation to find the power supplied to the string is given by using this relation try to analyze the terms that are present in the above relation and find out the power supplied by finding out the unknowns in the above relation with the given data.
Complete answer:
We know that the relation to find the power supplied to the string is
Where is the power, is the mass density, is the angular frequency, is the amplitude of the wave and is the velocity
We know that wave speed on the string is
Given the frequency is
Therefore angular frequency is
Given amplitude of the wave is
Also given that the mass density
Put all these values in the above relation of the power
Therefore the power required to supply for the string is
Hence the correct answer is option A.
Note:
While calculation make sure that all the terms involved in the formula are in the same system of units if not convert them in such a way that the whole terms are in the same system of units. And when there are some unknown terms in the formula we are using then try to find those terms using the given data and then put those values in the formula to find the required answer.
Complete answer:
We know that the relation to find the power supplied to the string is
Where
We know that wave speed on the string is
Given the frequency is
Therefore angular frequency is
Given amplitude of the wave is
Also given that the mass density
Put all these values in the above relation of the power
Therefore the power required to supply for the string is
Hence the correct answer is option A.
Note:
While calculation make sure that all the terms involved in the formula are in the same system of units if not convert them in such a way that the whole terms are in the same system of units. And when there are some unknown terms in the formula we are using then try to find those terms using the given data and then put those values in the formula to find the required answer.
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