https://file.aiquickdraw.com/mathbot/file/1727796739781l4zq045r.jpg

From the image you provided, the problem contains the following values and symbols:

- \(\mu = 0.045 \, \text{kg/m}\) (linear mass density of the string)
- \(m = 0.015 \, \text{kg} = 15 \, \text{g}\) (mass)
- \(n = 4\) (harmonic number)
- \(f = 130 \, \text{Hz}\) (frequency of the wave)
- \(T = ?\) (tension in the string)
- \(L = ?\) (length of the string)

This appears to be a problem involving the frequency of a standing wave on a string. The relationship between the tension \(T\), linear density \(\mu\), frequency \(f\), and length \(L\) is given by the formula for the frequency of the \(n\)-th harmonic:

\[
f = \frac{n}{2L} \sqrt{\frac{T}{\mu}}
\]

We'll need to solve this for \(T\) (tension) and \(L\) (length). Let's work step by step to solve for these unknowns.

Would you like me to proceed with the calculations?

Find the tension (T) and the length (L) of the string given: linear mass density (μ = 0.045 kg/m), mass (m = 0.015 kg = 15 g), harmonic number (n = 4), and frequency (f = 130 Hz).

Learn how to calculate the tension and length of a string producing a standing wave in the 4th harmonic with a frequency of 130 Hz. Given the string's linear mass density (0.045 kg/m) and mass (0.015 kg), follow step-by-step calculations using the harmonic wave equation. Suitable for high school students studying physics.

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