take wire of the same material but of three different diameters and find the value of l for a given frequency n and tension T
Answers
Explanation:
Perimter=sum of all lengths of sides of triangle
⇒ Perimeter =3a {a= side of triangle }
⇒45=3a
⇒a=15cm.
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Answer: To find the value of "l" (length) for a given frequency "n" and tension "T", we need to use the formula for the fundamental frequency of a stretched wire, which is given by:
f = (n * v) / 2l
where "n" is the mode number (1 for the fundamental frequency), "v" is the velocity of sound in the material of the wire, and "l" is the length of the wire.
Rearranging the formula to solve for "l", we get:
l = (n * v) / (2 * f)
The tension "T" of the wire also affects the frequency, and it can be related to the linear density "μ" of the wire using the formula:
T = μ * v^2 / l
where "μ" is the linear density of the wire, defined as the mass per unit length of the wire.
Now, we have two equations with two unknowns, "l" and "μ". We can use these equations to solve for "l" by eliminating "μ". Substituting the expression for "T" from the second equation into the first equation, we get:
l = (n * v) / (2 * f * √(T / μ))
Since the wire is made of the same material, the velocity of sound "v" and the linear density "μ" are constant for all three wires, regardless of the diameter. Thus, we can simplify the expression for "l" to:
l = C / √(d)
where "C" is a constant that depends on the material properties and the mode number, and "d" is the diameter of the wire.
So, to find the value of "l" for a given frequency "n" and tension "T", we need to know the velocity of sound "v" and the linear density "μ" of the material, as well as the frequency "f" and the diameter "d" of the wire.
Learn more about frequency here
https://brainly.in/question/26452373
Learn more about tension here
https://brainly.in/question/1958326
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