A wave pulse is travelling on a string of linear mass density `1.0 g cm^(-1)` under a tension of 1 kg wt. Calculate the time taken by the pulse to travel a distance of 50 cm on the string.Given `g = 10 ms^(-2)`.

Answer

To solve the problem of calculating the time taken by a wave pulse to travel a distance of 50 cm on a string, we will follow these steps:

### Step 1: Convert the linear mass density to standard units
The given linear mass density is \(1.0 \, \text{g/cm}^(-1)\). We need to convert this to kg/m.

\[ 1.0 \, \text{g/cm}^(-1) = 1.0 \times 10^{-3} \, \text{kg/m} = 0.01 \, \text{kg/m} \]

### Step 2: Calculate the tension in standard units
The tension is given as \(1 \, \text{kg wt}\). We need to convert this to Newtons (N). Since \(1 \, \text{kg wt} = g \, \text{N}\) and \(g = 10 \, \text{m/s}^2\):

\[ T = 1 \, \text{kg} \times 10 \, \text{m/s}^2 = 10 \, \text{N} \]

### Step 3: Calculate the speed of the wave on the string
The speed of a wave on a string is given by the formula:

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

Where:
- \(T\) is the tension (in N)
- \(\mu\) is the linear mass density (in kg/m)

Substituting the values we have:

\[ v = \sqrt{\frac{10 \, \text{N}}{0.01 \, \text{kg/m}}} = \sqrt{1000} = 31.62 \, \text{m/s} \]

### Step 4: Calculate the time taken to travel 50 cm
We need to find the time \(t\) taken to travel a distance \(d = 50 \, \text{cm} = 0.5 \, \text{m}\). The formula for time is:

\[ t = \frac{d}{v} \]

Substituting the values:

\[ t = \frac{0.5 \, \text{m}}{31.62 \, \text{m/s}} \approx 0.0158 \, \text{s} \]

### Step 5: Final answer
The time taken by the pulse to travel a distance of 50 cm on the string is approximately:

\[ t \approx 0.0158 \, \text{s} \approx 0.016 \, \text{s} \]