The fundamental frequency of a plucked wire under a tension of 400N is 250Hz. When the frequency is changed to 500 Hz at constant length, the tension is

The fundamental frequency of a plucked wire under a tension of 400N is 250Hz. When the frequency is changed to 500 Hz at constant length, the tension is

Answer Details

The tension in a wire affects its fundamental frequency. As tension increases, so does the frequency. The relationship between tension and frequency is given by the following formula: f = (1/2L)√(T/μ) where f is the frequency, L is the length of the wire, T is the tension, and μ is the linear mass density of the wire. We are given that the wire has a tension of 400N and a frequency of 250Hz. If we keep the length of the wire constant and increase the frequency to 500Hz, we can use the formula to find the new tension: f = (1/2L)√(T/μ) Rearranging the formula, we get: T = (4L^2μ)(f^2) Since we are keeping the length of the wire constant, we can simplify the formula to: T ∝ f^2 This means that the tension is proportional to the square of the frequency. If we increase the frequency by a factor of 2 (from 250Hz to 500Hz), the tension will increase by a factor of 2^2 = 4. Therefore, the new tension is: T = 4(400N) = 1600N So the answer is 1600N.