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Answer :
The required tension to double the wave speed from 18.3 m/s to 36.6 m/s in the same string is 29.36 N.
The student's question involves finding the tension required for a wave speed of 36.6 m/s in a string when it is known that a transverse wave travels at 18.3 m/s under a tension of 7.34 N. To solve this, we use the formula that relates wave speed v to the tension Ft in the string and the linear mass density μ:
v = √(Ft/μ)
For a constant mass density of the string, the speed of the wave on the string is proportional to the square root of the tension. We can set up a proportionality relationship between the wave speeds and their corresponding tensions:
(v₁/v₂)² = Ft₁/Ft₂
Plugging in the known values:
(18.3 m/s / 36.6 m/s)² = 7.34 N / Ft₂
Solving for Ft₂ gives us:
Ft₂ = (36.6 m/s / 18.3 m/s)² * 7.34 N
Ft₂ = (2)² * 7.34 N
Ft₂ = 4 * 7.34 N
Ft₂ = 29.36 N
Therefore, the required tension to achieve a wave speed of 36.6 m/s in the same string is 29.36 N.
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