A string of 7m length has a mass of `0.035 kg.` If tension in the string is `60.N,` then speed of a wave on the string is

Options

A. `77m//s`
B. `102 m//s`
C. `110 m//s`
D. `165 m//s`

Answer

To find the speed of a wave on 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,
- \( \mu \) is the mass per unit length of the string.

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

Given:
- Mass of the string \( m = 0.035 \, \text{kg} \)
- Length of the string \( L = 7 \, \text{m} \)

The mass per unit length \( \mu \) is calculated as:

\[ \mu = \frac{m}{L} = \frac{0.035 \, \text{kg}}{7 \, \text{m}} = 0.005 \, \text{kg/m} \]

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

Given:
- Tension \( T = 60 \, \text{N} \)

Now substitute \( T \) and \( \mu \) into the wave speed formula:

\[ v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{60 \, \text{N}}{0.005 \, \text{kg/m}}} \]

### Step 3: Calculate the value inside the square root

Calculating the fraction:

\[ \frac{60}{0.005} = 12000 \]

### Step 4: Take the square root

Now, take the square root of 12000:

\[ v = \sqrt{12000} \approx 109.54 \, \text{m/s} \]

### Final Answer

Thus, the speed of the wave on the string is approximately:

\[ v \approx 110 \, \text{m/s} \]