The equation of a transverse wave propagating | vedclass

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

Question

(C) The standard equation of a transverse wave is $y = A \sin(kx + \omega t)$.Comparing this with the given equation $y = 3 \sin(4x + 200t)$, we get:W

Vedclass · Accepted Answer

$0.2$

Vedclass · Answer

(C) The standard equation of a transverse wave is $y = A \sin(kx + \omega t)$.Comparing this with the given equation $y = 3 \sin(4x + 200t)$, we get:Wave number $k = 4 \ m^{-1}$Angular frequency $\omega = 200 \ rad \ s^{-1}$The wave speed $v$ is given by $v = \frac{\omega}{k} = \frac{200}{4} = 50 \ m/s$.The speed of a transverse wave on a stretched string is also given by $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension and $\mu$ is the linear mass density.Squaring both sides, we get $v^2 = \frac{T}{\mu}$, which implies $\mu = \frac{T}{v^2}$.Substituting the given values $T = 500 \ N$ and $v = 50 \ m/s$:$\mu = \frac{500}{(50)^2} = \frac{500}{2500} = \frac{1}{5} = 0.2 \ kg \ m^{-1}$.Thus, the linear density of the string is $0.2 \ kg \ m^{-1}$.

The equation of a transverse wave propagating on a stretched string is given by $y = 3 \sin (4x + 200t)$, where $x$ and $y$ are in metres and the time $t$ is in seconds. If the tension applied to the string is $500 \ N$, the linear density of the string is: (in $kg \ m^{-1}$)

Similar Questions

$A$ steel wire of length $81 \text{ cm}$ has a mass of $5 \times 10^{-3} \text{ kg}$. If the wire is under a tension of $50 \text{ N}$, then the speed of transverse waves on the wire is (in $\text{ m s}^{-1}$)

$A$ string of mass $M$ is under a tension $T$. The length of the string is $L$. $A$ transverse wave starts at one end of the string. The time required for the disturbance to reach the other end is

If the initial tension on a stretched string is doubled,then the ratio of the initial and final speeds of a transverse wave along the string is:

$A$ steel wire with mass per unit length $7.0 \times 10^{-3} \, kg \, m^{-1}$ is under tension of $70 \, N$. The speed of transverse waves in the wire will be $......... \, m/s$.

$A$ transverse wave propagating on a string can be described by the equation $y = 2 \sin (10x + 300t)$,where $x$ and $y$ are in meters and $t$ is in seconds. If the vibrating string has a linear mass density of $0.6 \times 10^{-3} \, g/cm$,then the tension in the string is .............. $N$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module