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1 month ago

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5. The speed of a transverse wave on a string is 170 m/s when the string tension is 120 ????. To what value must the tension be

changed to raise the wave speed to 180 m/s?

1 answer:

Sav [3.1K]1 month ago

3 0

Answer:

The tension in the string when the speed increased is 134.53 N

Explanation:

Given;

Tension in the string, T = 120 N

initial speed of the transverse wave, v₁ = 170 m/s

final speed of the transverse wave, v₂ = 180 m/s

The wave speed is expressed as;

$v = \sqrt{\frac{T}{\mu} }$

where;

μ represents mass per unit length

$v^2 = \frac{T}{\mu} \\\\\mu = \frac{T}{v^2} \\\\\frac{T_1}{v_1^2} = \frac{T_2}{v_2^2}$

The new tension T₂ will be computed as;

$T_2 = \frac{T_1 v_2^2}{v_1^2} \\\\T_2 = \frac{120*180^2}{170^2} \\\\T_2 = 134.53 \ N$

Consequently, the tension in the string when the speed was increased is 134.53 N

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