A string is stretched by a force of 40 newton. The mass of 10 m length of this string is 0.01 kg. the speed of transverse waves in this string will be

Options

A. 400m/s
B. 40 m/s
C. 200 m/s
D. 80 m/s

Explanation

To find the speed of transverse waves in a string, we can use the formula:

\[ V = \sqrt{\frac{T}{\mu}} \]

where:
- \( V \) is the speed of the wave,
- \( T \) is the tension in the string (in Newtons),
- \( \mu \) is the mass per unit length of the string (in kg/m).

**Step 1: Calculate the mass per unit length (\( \mu \))**

Given:
- The mass of the string = 0.01 kg
- The length of the string = 10 m

We can calculate \( \mu \) using the formula:

\[ \mu = \frac{\text{mass}}{\text{length}} \]

Substituting the values:

\[ \mu = \frac{0.01 \, \text{kg}}{10 \, \text{m}} = 0.001 \, \text{kg/m} \]

**Step 2: Substitute the values into the wave speed formula**

We know:
- Tension \( T = 40 \, \text{N} \)
- Mass per unit length \( \mu = 0.001 \, \text{kg/m} \)

Now substitute these values into the wave speed formula:

\[ V = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{40 \, \text{N}}{0.001 \, \text{kg/m}}} \]

**Step 3: Simplify the expression**

Calculating the fraction:

\[ \frac{40 \, \text{N}}{0.001 \, \text{kg/m}} = 40000 \, \text{m}^2/\text{s}^2 \]

Now take the square root:

\[ V = \sqrt{40000 \, \text{m}^2/\text{s}^2} = 200 \, \text{m/s} \]

**Final Answer:**

The speed of transverse waves in the string is \( 200 \, \text{m/s} \).

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