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Chapter 14: Problem 4

If you doubled the tension in a string, what would happen to the speed of waves on the string?

Short Answer

Expert verified
If the tension in the string is doubled, the speed of waves on the string will increase by approximately 41.4%.

Step by step solution

01

Understanding the Problem

Recognize that you are being asked about the relationship between the speed of waves on a string and the tension of that string. Remember that this problem should be analyzed based on the wave speed formula \(v = \sqrt{\frac{T}{\mu}} \). Here \(T\) is the tension in the string and \(\mu\) is the linear density.
02

Deducing the Impact of Doubling the Tension

You understand from the wave speed formula that wave speed and tension have a direct relationship. Hence, if tension is increased, the wave speed will also increase. Particularly, the speed of the wave is proportional to the square root of the tension. If the tension is multiplied by four, the wave speed doubles. So, here when the tension is doubled, the wave speed will be multiplied by \(\sqrt{2}\), or in other words, it will increase by approximately 41.4%.

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Most popular questions from this chapter

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