Question

A string of linear density 0.2kg per metre is stretched with a force of 500N. A transverse wave of length 4.0 metre and amplitude \[\dfrac{1}{\pi }metre\] is travelling along it. Then the speed of the wave is

A. 50m/s

B. 12.5m/s

C. 62.5m/s

D. 2500m/s

Answer 1

Hint: \[v = \sqrt {\dfrac{T}{\mu }} \], use this formula to speed to find the value. Place the values from the question to find the correct answer.

Complete step by step solution:

Write all the values which are provided,

Mass per unit length \[\mu  = 0.2kg/metre\]

Tension= 500N

L= 4m

A=\[\dfrac{1}{\pi }\,metre\]

Now we know the formula that,

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

We know the values of T and \[\mu \] from the question

Now putting them in the above equation we get,

\[v = \sqrt {\dfrac{{500}}{{0.2}}} \]

Now adjusting we get,

\[v = \sqrt {\dfrac{{5000}}{2}} \]

We get,

\[v = \sqrt {2500} \] by dividing

Now removing the root, we get,

\[v = 50m/s\]

Therefore, the correct option is (A).

Additional information:
The speed of a wave depends on the characteristics of the medium. For example, in the case of a guitar, the strings vibrate to produce the sound. The speed of the waves on the strings, and the wavelength, determine the frequency of the sound produced. The strings on a guitar have different thickness but may be made of similar material. They have different linear densities, where the linear density is defined as the mass per length.

Note: Students will get confused as some extra information is given which is just to confuse but we don’t need those values to solve the problem because we know the formula and all the values are given to find it. So, students need to solve the sum patiently using only the values needed.