Question

The equation of a transverse wave propagating along a stretched string of length 80 cm is $y = 1.5 \sin ( (5 \times 10^3)x + 20t )$, here 'x' and 'y' are in cm and the time 't' is in seconds. If the mass of the string is 3 g, then the tension in the string is

• A. 12 N
• B. 4 N
• C. 6 N
• D. 8 N

Hint:

Focus on understanding the wave speed formula and how it relates to tension and wavelength.

Answer 1

The Correct Option is A

The wave equation is $y = 1.5 \sin ( (5 \times 10^3)x + 20t )$. The speed of the wave is given by the formula $v = \frac{1}{T} . \lambda$, where $\lambda$ is the wavelength and $T$ is the tension in the string. By substituting the given values and solving for $T$, we get the tension to be 12 N.