A string of 7 m length has a mass of 0.035 kg. If tension in the string is 60.5 N, then speed of a wave on the string is :

Options

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

Answer

To find the speed of a wave on the string, we can follow these steps:

### Step 1: Identify the given values
- Length of the string, \( L = 7 \, \text{m} \)
- Mass of the string, \( m = 0.035 \, \text{kg} \)
- Tension in the string, \( T = 60.5 \, \text{N} \)

### Step 2: Calculate the mass per unit length (linear density) of the string
The linear density \( \mu \) is given by the formula:
\[ \mu = \frac{m}{L} \]
Substituting the values:
\[ \mu = \frac{0.035 \, \text{kg}}{7 \, \text{m}} = 0.005 \, \text{kg/m} \]

### Step 3: Use the wave speed formula
The speed \( v \) of a wave on a string under tension is given by:
\[ v = \sqrt{\frac{T}{\mu}} \]
Substituting the values of tension and linear density:
\[ v = \sqrt{\frac{60.5 \, \text{N}}{0.005 \, \text{kg/m}}} \]

### Step 4: Calculate the speed
Now, calculate the value inside the square root:
\[ \frac{60.5}{0.005} = 12100 \]
Taking the square root:
\[ v = \sqrt{12100} \approx 110 \, \text{m/s} \]

### Step 5: Conclusion
The speed of the wave on the string is approximately \( 110 \, \text{m/s} \).

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