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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

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Cricetus

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,

⇒  [tex]V=(\frac{T}{u})^{\frac{1}{2}}[/tex]

On substituting the given values, we get

⇒  [tex]6=(\frac{9}{u} )^{\frac{1}{2}}[/tex]

⇒  [tex]36=\frac{9}{u}[/tex]

⇒  [tex]u=\frac{9}{36}[/tex]

⇒     [tex]=\frac{1}{4}[/tex]

Now,

For 81 N the velocity will be:

⇒  [tex]v=(\frac{81}{(\frac{1}{4} )} )^{\frac{1}{2} }[/tex]

⇒     [tex]=18 \ m/s[/tex]

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