A way pulse is travelling on a string of linear mass density `6.4 xx 10^(-3)kg m^(-1)` under a load of `80 kgf`. Calculate the time taken by the pulse to traverse the string, if its length is `0.7 m`.

Options

A. `2xx10^(-3)s`
B. `3xx10^(-3)s`
C. `4xx10^(-2)s`
D. `5xx10^(-2)s`

Answer

To solve the problem, we need to calculate the time taken by a wave pulse to traverse a string of a given length, given its linear mass density and the load applied to it.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Linear mass density (μ) = \(6.4 \times 10^{-3} \, \text{kg/m}\)
- Load (Tension, T) = \(80 \, \text{kgf}\)
- Length of the string (L) = \(0.7 \, \text{m}\)
- Acceleration due to gravity (g) = \(9.8 \, \text{m/s}^2\)

2. **Convert Load to Tension:**
- The tension in the string can be calculated using the formula:
\[ T = \text{Load} \times g \]
- Substituting the values:
\[ T = 80 \, \text{kgf} \times 9.8 \, \text{m/s}^2 = 80 \times 9.8 = 784 \, \text{N} \]

3. **Calculate the Velocity of the Wave Pulse:**
- The velocity (v) of a wave on a string is given by the formula:
\[ v = \sqrt{\frac{T}{\mu}} \]
- Substituting the values for T and μ:
\[ v = \sqrt{\frac{784 \, \text{N}}{6.4 \times 10^{-3} \, \text{kg/m}}} \]

4. **Perform the Calculation:**
- First, calculate the denominator:
\[ \mu = 6.4 \times 10^{-3} = 0.0064 \, \text{kg/m} \]
- Now, calculate:
\[ v = \sqrt{\frac{784}{0.0064}} = \sqrt{122500} = 350 \, \text{m/s} \]

5. **Calculate the Time Taken to Traverse the String:**
- The time (t) taken to traverse the length of the string is given by:
\[ t = \frac{L}{v} \]
- Substituting the values:
\[ t = \frac{0.7 \, \text{m}}{350 \, \text{m/s}} = 0.002 \, \text{s} = 2 \times 10^{-3} \, \text{s} \]

### Final Answer:
The time taken by the pulse to traverse the string is \(2 \times 10^{-3} \, \text{s}\).

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