Question

A 100 cm long string vibrates in 4 loops at 50 Hz.Linear density of the string is 0.0004 gm/cm.Calculate the tension in the string.

Answer 1

Answer Question #67081, Physics / Mechanics | Relativity

A 100 cm long string vibrates in 4 loops at 50 Hz. Linear density of the string is 0.0004 gm/cm. Calculate the tension in the string.

Find: T – ?

Given:

$$L = 1 \text{ m}$$ $$f = 50 \text{ Hz}$$ $$\mu = 0.0004 \frac{\text{gm}}{\text{cm}^3} = 0.0004 \times \frac{10^{-3} \text{ kg}}{\text{cm}^3} = 0.4 \frac{\text{kg}}{\text{m}^3}$$ $$n = 4$$

Solution:

$$f = \frac{n}{2L} \sqrt{\frac{T}{\mu}} \quad (1)$$ $$\text{Of } (1) \Rightarrow T = \frac{f^2 4L^2 \mu}{n^2} \quad (2)$$ $$\text{Of } (2) \Rightarrow T = 250 \text{ N}$$

Answer:

250 N

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