Physics 2000 JAMB Past Questions - Question 24: A transverse wave is applied to a string whose mass per unit length is 3 x 10²kg¹. If the string is under a tension of 12N. the speed of propagation of the wave is

Correct Answer

C

Explanation

The speed of propagation of a transverse wave on a string is given by the formula:

\[v = \sqrt{\frac{T}{μ}}\]The speed of propagation of a transverse wave on a string can be calculated using the formula:

v = √(T/μ)

Where:
- v is the speed of propagation of the wave.
- T is the tension in the string.
- μ is the mass per unit length of the string.

Given the values provided:
- Tension (T) = 12 N
- Mass per unit length (μ) = 3 x 10² kg/m

Substituting these values into the formula, we get:

v = √(12 N / (3 x 10² kg/m))

Simplifying the expression:

v = √(12 N / 300 kg/m)

v = √(0.04 N/kg)

v = 0.2 m/s

Therefore, the speed of propagation of the wave on the string is 0.2 m/s.

Where:
- \(v\) is the speed of the wave.
- \(T\) is the tension in the string.
- \(μ\) is the mass per unit length of the string.

In this case, you have the following values:
- Tension (\(T\)) = 12 N
- Mass per unit length (\(μ\)) = 3 x 10² kg/m

Now, you can plug these values into the formula to find the speed (\(v\)):

\[v = \sqrt{\frac{12 \, \text{N}}{3 \times 10^2 \, \text{kg/m}}}\]

First, calculate the tension-to-mass per unit length ratio:

\[v = \sqrt{\frac{12 \, \text{N}}{3 \times 10^2 \, \text{kg/m}}} = \sqrt{\frac{4}{100}} \, \text{m/s}\]

Now, simplify the square root:

\[v = \sqrt{\frac{4}{100}} \, \text{m/s} = \frac{2}{10} \, \text{m/s} = \frac{1}{5} \, \text{m/s}\]

So, the speed of propagation of the transverse wave on the string is \(\frac{1}{5}\) m/s or 0.2 m/s.