If the tension in a length of string is doubled, the wavelength of standing waves in the string changes by what factor?Select one:a.1/√2b.1/2c.1d.2e.√2
Question
If the tension in a length of string is doubled, the wavelength of standing waves in the string changes by what factor?
Select one:
- a. 1/√2
- b. 1/2
- c. 1
- d. 2
- e. √2
Solution
The speed of a wave on a string under tension is given by v = sqrt(T/μ), where T is the tension and μ is the linear mass density (mass/length).
If the tension is doubled, the speed of the wave becomes v' = sqrt(2T/μ) = sqrt(2) * sqrt(T/μ) = sqrt(2) * v.
The speed of a wave is also given by v = λf, where λ is the wavelength and f is the frequency.
Assuming the frequency remains constant (as it often does in problems like this), the new speed v' = λ'f, where λ' is the new wavelength.
Setting these equal gives sqrt(2) * v = λ'f, or λ' = sqrt(2) * λ.
So, the wavelength of the standing waves in the string changes by a factor of sqrt(2) when the tension is doubled.
Therefore, the correct answer is e. √2.
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