Question

Another example of square-root relationships is the relation between the speed of a wave along a string under tension and the tension itself. Suppose you hold one end of a string and attach the other end to a wall. If you hold the string taut, and wiggle the free end up and down, a wave travels along the string. If the tension in the string is 9 N, the wave travels along the string at 6 m/s; if the tension in the string is 36 N, the wave speed along the string is 12 m/s. If the tension in the string is increased to 81 N , how fast will you expect a wave to travel along the string if you wiggle its free end

Answer 1

Answer:

The right answer is "18 m/s".

Explanation:

The given values are:

Velocity,

V = 6 m/s

Tension,

T = 9 N

As we know,

⇒  $V=(\frac{T}{u})^{\frac{1}{2}}$

On substituting the given values, we get

⇒  $6=(\frac{9}{u} )^{\frac{1}{2}}$

⇒  $36=\frac{9}{u}$

⇒  $u=\frac{9}{36}$

⇒     $=\frac{1}{4}$

Now,

For 81 N the velocity will be:

⇒  $v=(\frac{81}{(\frac{1}{4} )} )^{\frac{1}{2} }$

⇒     $=18 \ m/s$