Question

Waves travel along a 100-m length of string which has a mass of 55 g and is held taut with a tension of 75 N. What is the speed of the waves?

Answer 1

Answer:

$v=369.27\frac{m}{s}$

Explanation:

The speed of the waves in a string is related with the tension and mass per unit length of the string, as follows:

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

First, we calculate the mass per unit length:

$\mu=\frac{m}{L}\\\mu=\frac{55*10^{-3}kg}{100m}\\\mu=5.5*10^{-4}\frac{kg}{m}$

Now, we calculate the speed of the waves:

$v=\sqrt\frac{75N}{5.5*10^{-4}\frac{kg}{m}}\\v=369.27\frac{m}{s}$

Answer 2

The speed of the waves will be "369.27 m/s".

Given values,

• Mass, $m = 55 \ g$

or,                   $= 55\times 10^{-3} \ kg$

• Length, $L = 100 \ m$

As we know,

→ $v = \sqrt{\frac{T}{\mu} }$

or,

→ $\mu = \frac{m}{L}$

By putting the values,

      $= \frac{55\times 10^{-3}}{100}$

      $= 5.5\times 10^{-4} \ kg/m$

hence,

The speed of wave:

→ $v = \sqrt{\frac{75}{5.5\times 10^{-4}} }$

     $= 369.27 \ m/s$

Thus the above response is correct.  

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