A transverse wave is travelling on a string w | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The speed of a transverse wave on a stretched string is given by $V = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the mass per uni

Vedclass · Accepted Answer

$(1.22) V$

Vedclass · Answer

(B) The speed of a transverse wave on a stretched string is given by $V = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the mass per unit length.According to Hooke's Law,$T = kx$,where $k$ is the spring constant and $x$ is the extension.Since the mass of the string remains constant,$\mu = \frac{m}{L}$. When the string is extended,its length $L$ increases. However,for small extensions,the change in $\mu$ is negligible compared to the change in tension $T$.Thus,$V \propto \sqrt{T} \propto \sqrt{x}$.Given the initial extension is $x_1 = x$ and the final extension is $x_2 = x + 0.5x = 1.5x$.The ratio of the speeds is $\frac{V_2}{V_1} = \sqrt{\frac{x_2}{x_1}} = \sqrt{\frac{1.5x}{x}} = \sqrt{1.5}$.Calculating the value,$\sqrt{1.5} \approx 1.2247$.Therefore,the new speed $V_2 \approx 1.22 V$.

$A$ transverse wave is travelling on a string with velocity $V$. The extension in the string is $x$. If the string is extended by $50 \%$,the speed of the wave along the string will be nearly (Hooke's law is obeyed).

Similar Questions

$A$ uniform metal wire has length $L$,mass $M$,and density $\rho$. It is under tension $T$,and $v$ is the speed of a transverse wave along the wire. The area of cross-section of the wire is:

Which of the following graphs is correct?

$A$ string of length $L$ and mass $M$ hangs freely from a fixed point. The velocity of transverse waves along the string at a distance $x$ from the free end is

Which of the following graphs is $CORRECT$?

The equation of a wave on a string of linear mass density $0.02 \text{ kg m}^{-1}$ is $Y = 0.01 \sin [2\pi (t/0.02 - x/0.50)] \text{ m}$. The tension in the string is (in $\text{ N}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module