Waves of amplitude 1.1 cm and wavelength 40 cm move along a 12-m long string that has a mass of 70 g and is under a tension of 15 N.Calculate the velocity of the wave.
A)51 m/s
B)2570 m/s
C)16 m/s
D)15 m/s
E)331 m/s

Question

Quizplus · Accepted Answer

The velocity of a wave on a string is given by the formula $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension in the string and $\mu$ is the mass per unit length of the string. Here, $T = 15\,N$ and the mass per unit length $\mu = \frac{70\,g}{12\,m} = \frac{70}{12 \times 1000}\,kg/m = \frac{7}{1200}\,kg/m$. Plugging these values into the formula gives $v = \sqrt{\frac{15}{7/1200}} = \sqrt{\frac{15 \times 1200}{7}} = \sqrt{2571.43}$ which is approximately $51\,m/s$.

Waves of Amplitude 1