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

The right answer is "18 m/s".

Step-by-step explanation:

The given values are:

Velocity,

V = 6 m/s

Tension,

T = 9 N

As we know,

⇒
`V=((T)/(u))^{(1)/(2)}`

On substituting the given values, we get

⇒
`6=((9)/(u) )^{(1)/(2)}`

⇒
`36=(9)/(u)`

⇒
`u=(9)/(36)`

⇒
`=(1)/(4)`

Now,

For 81 N the velocity will be:

⇒
`v=((81)/(((1)/(4) )) )^{(1)/(2) }`

⇒
`=18 \ m/s`