A transverse wave is propagating on a stretched string of mass per unit length`32 gm^(-1)`. The tension on the string is 80 N. The speed of the wave over the string is

Options

A. `(5)/(2)ms^(-1)`
B. `sqrt((5)/(2))ms^(-1)`
C. `sqrt((2)/(5))ms^(-1)`
D. `50 ms^(-1)`

Answer

To solve the problem of finding the speed of a transverse wave on a stretched string, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Mass per unit length (μ) = 32 gm/m = 32 × 10^(-3) kg/m
- Tension (T) = 80 N

2. **Use the Formula for Wave Speed**:
The speed of a wave (v) on a stretched string is given by the formula:
\[ v = \sqrt{\frac{T}{\mu}} \]
where:
- \( v \) = speed of the wave
- \( T \) = tension in the string
- \( \mu \) = mass per unit length of the string

3. **Substitute the Values into the Formula**:
\[ v = \sqrt{\frac{80 \, \text{N}}{32 \times 10^{-3} \, \text{kg/m}}} \]

4. **Calculate the Denominator**:
\[ 32 \times 10^{-3} = 0.032 \, \text{kg/m} \]

5. **Perform the Division**:
\[ \frac{80}{0.032} = 2500 \]

6. **Take the Square Root**:
\[ v = \sqrt{2500} = 50 \, \text{m/s} \]

7. **Final Result**:
The speed of the wave on the string is \( 50 \, \text{m/s} \).