the length radius tension and density of string A are twice the same parameters of string B gind the ratio of fundamental frequency of B to the fundamental frequencey of A if both ends of each wire is fixed
Question
the length radius tension and density of string A are twice the same parameters of string B gind the ratio of fundamental frequency of B to the fundamental frequencey of A if both ends of each wire is fixed
Solution
The fundamental frequency of a vibrating string is given by the formula:
f = (1/2L) * sqrt(T/μ)
where:
- f is the frequency,
- L is the length of the string,
- T is the tension in the string, and
- μ is the linear density of the string.
Given that the length, radius, tension, and density of string A are twice that of string B, we can substitute these values into the formula for the fundamental frequency.
For string A, the frequency f_A = (1/2*2L) * sqrt((2T)/(2μ)) = (1/4L) * sqrt(T/μ) For string B, the frequency f_B = (1/2L) * sqrt(T/μ)
The ratio of the fundamental frequency of B to A is then f_B/f_A = [(1/2L) * sqrt(T/μ)] / [(1/4L) * sqrt(T/μ)] = 2.
So, the fundamental frequency of string B is twice that of string A.
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