Question

If the speed of transverse waves on a stretched wire of linear density \(7\times 10^{-3}\,\text{kg m}^{-1}\) is \(100\,\text{m s}^{-1}\), then the tension in the wire is

• A. \(60\,\text{N}\)
• B. \(600\,\text{N}\)
• C. \(700\,\text{N}\)
• D. \(70\,\text{N}\)
• E. \(80\,\text{N}\)

Hint:

For waves on a string, always remember \(v=\sqrt{T/\mu}\). Rearranging gives \(T=\mu v^2\), which is very useful in numerical problems.

Answer 1

The Correct Option is D

Step 1: Recall the formula for wave speed.
The speed of a transverse wave on a stretched string is: \[ v=\sqrt{\frac{T}{\mu}} \] where \(T\) is tension and \(\mu\) is linear density.

Step 2: Rearrange the formula.
\[ T=\mu v^2 \]

Step 3: Substitute the given values.
\[ \mu=7\times 10^{-3}\,\text{kg m}^{-1}, \quad v=100\,\text{m s}^{-1} \]

Step 4: Calculate \(v^2\).
\[ v^2=100^2=10000 \]

Step 5: Find the tension.
\[ T=7\times 10^{-3}\times 10000 \] \[ T=70\,\text{N} \]

Step 6: Compare with options.
The calculated value \(70\,\text{N}\) matches option \((4)\)
Thus, mathematically the answer is: \[ \boxed{70\,\text{N}} \]