Question

A transverse periodic wave on a string with a mass density of $0.200kg/m$ is described by the following equation
$y=0.05\sin (420t-21.0x)$,
where x and y are in meters and t is in seconds.
The tension in the string is equal to:

• A. $32N$
• B. $42N$
• C. $66N$
• D. $80N$

Answer 1

The correct option is D $80N$

Comparing with the equation of a standing wave, we can clearly see that the velocity of the wave,

$k=21$

$\omega =420$

$\mu =0.200kg/m$

Now, since $\frac{\omega }{k}=\sqrt{\frac{T}{\mu }}$

where T is the tension in the string and $\mu$ is the mass density.

Substitute the values

$T=\mu {\left(\frac{\omega }{k}\right)}^2$

$T=0.2\times {\left(\frac{420}{21}\right)}^2$

$T=0.2\times 400$

$T=80N$