Question

The transverse displacement of a string fixed at both ends is given by $y=0.06 \sin \left(\frac{2 \pi x}{3}\right) \cos (100 \,\pi t)$ where $x$ and $y$ are in metre and $t$ is in second. The length of the string is $1.5 \,m$ and its mass is $3.0 \times 10^{-2} \,kg$. What is die tension in the string?

• A. 225 N
• B. 300 N
• C. 450 N
• D. 675 N

Answer 1

Answer: (D)

675 N

Answer 2

$y=0.06 \sin \left(\frac{2 \pi}{3}\right) \cos (100 \pi t)$ Comparing on standard equation $y=2 a \sin \frac{2 \pi x}{\lambda} \cos \frac{2 \pi v t}{\lambda}$ We will get frequency, $n=\frac{v}{\lambda}=50$ Frequency of vibration $n=\frac{1}{2 l} \sqrt{\frac{T}{m}}$ $50=\frac{1}{2 \times 1.5} \sqrt{\frac{T}{3 \times 10^{-2}}}$ $50 \times 50=\frac{1}{3 \times 3} \cdot \frac{T}{3 \times 10^{-2}}$ or $T=50 \times 50 \times 3 \times 3 \times 3 \times 10^{-2}$ $T=675\, N$