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A wire is stretched between two posts. Another wire is stretched between two posts that are three times as far apart. The tension in the wires is the same, and they have the same mass. A transverse wave travels on the shorter wire with a speed of 170 m/s. What would be the speed of the wave on the longer wire?

Answer :

Answer:

[tex]v_1 =294.45\ m/s[/tex]

Explanation:

given,

Length of shorter wire is L and mass m and tension T

[tex]v_1 = \sqrt{\dfrac{TL}{m}}[/tex]

if all other dimension is same but length is increased by 3 times

[tex]v_1 = \sqrt{\dfrac{T(3 L)}{m}}[/tex]

[tex]v_1 =\sqrt{3} \sqrt{\dfrac{T L}{m}}[/tex]

[tex]v_1 =\sqrt{3}\ v_1[/tex]

[tex]v_1 =\sqrt{3}\ \times 170[/tex]

[tex]v_1 =1.732\ \times 170[/tex]

[tex]v_1 =294.45\ m/s[/tex]

the speed of the wave on the longer wire [tex]v_1 =294.45\ m/s[/tex]

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