A $5.5$ metre length of string has a mass of $0.035 \,kg$. If the tension in the string in $77\, N$, the speed of a wave on the string is

Question

A steel wire with mass per unit length $ 7.0 \times 10^{-3} \, \text{kg/m} $ is under a tension of $ 70 \, \text{N} $. The speed of transverse waves in the wire will be:

Answer 1

To find the speed of a wave on the string, we use the formula for wave speed on a stretched string:

v = \sqrt{\frac{T}{\mu}},

where:

v is the wave speed,
T is the tension in the string (in newtons),
\mu is the mass per unit length of the string (in kilograms per metre).

First, we need to calculate the mass per unit length of the string (\mu) using the given mass and length:

\mu = \frac{\text{mass of the string}}{\text{length of the string}}

\mu = \frac{0.035 \, \text{kg}}{5.5 \, \text{m}}

\mu = 0.00636 \, \text{kg/m} (approx).

Now, substitute the values of tension and mass per unit length into the wave speed formula:

v = \sqrt{\frac{77 \, \text{N}}{0.00636 \, \text{kg/m}}}

v = \sqrt{12102.52}

v = 110 \, \text{ms}^{-1} (approx).

The correct answer is 110 \, \text{ms}^{-1}.

Answer 2