Answer :
Final answer:
The tension required to vibrate a violin string at a fundamental frequency of 440 Hz when the length is 30 cm and mass is 0.36 g is 83.78 N. This is calculated using the wave speed formula and considering the linear density and frequency.
Explanation:
The situation described regarding the violin string prompts a physics problem related to the fundamental frequency and string tension, which can be solved using the formula for wave speed on a string. This formula is: v = sqrt(T/μ), where v is the wave speed, T is the tension and μ is the linear density. As we know, the wave speed can also be calculated as the product of wavelength and frequency. With a known fundamental frequency of 440 Hz, the wavelength for the fundamental frequency (the first harmonic) on a string is always twice the length of the string.
Firstly, calculate the linear density (μ) of the string. Convert the mass into kg and the length into m: μ = 0.36 g / 30 cm = 0.0012 kg/m.
You can then plug these values into the formula. Here's where we substitute the wave speed with the product of wave length and frequency: v = f * λ = 440 Hz * 2 * 0.3m = 264 m/s. And since v = sqrt(T/μ), we can rearrange this to find the tension (T): T = μ * v² = 0.0012 kg/m * (264 m/s)² = 83.78 N.
So, the string must be placed under a tension of 83.78 N.
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