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Chapter 14: Problem 7

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

Short Answer

Expert verified
Doubling the tension in the string would increase the speed of waves on the string by a factor of \(\sqrt{2}\)

Step by step solution

01

Understand Concept

Recognize that the speed (v) of a wave traveling through a string is given by the formula \(v = \sqrt{T/\mu}\), where T is the tension in the string and \(\mu\) is the mass per unit length of the string.
02

Apply Change

Apply the change given in the exercise, that is doubling the tension. The new tension is represented as \(2T\). The formula for speed becomes \(v' = \sqrt{2T/\mu}\)
03

Compare Speeds

Compare the new speed with the old speed. Since the tension was doubled, the new speed \(v'\) is \(v' = \sqrt{2} * v\). Hence, the speed of waves on the string has increased by a factor of \(\sqrt{2}\)

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Most popular questions from this chapter

When a \(340-\mathrm{g}\) spring is stretched to a total length of \(40 \mathrm{cm},\) it supports transverse waves propagating at \(4.5 \mathrm{m} / \mathrm{s} .\) When it's stretched to \(60 \mathrm{cm},\) the waves propagate at \(12 \mathrm{m} / \mathrm{s} .\) Find (a) the spring's unstretched length and (b) its spring constant.

A transverse wave with 3.0 -cm amplitude and 75 -cm wavelength propagates at \(6.7 \mathrm{m} / \mathrm{s}\) on a stretched spring with mass per unit length \(170 \mathrm{g} / \mathrm{m} .\) Find the spring tension.

What distinguishes a wave from an oscillation?

At a point \(15 \mathrm{m}\) from a source of spherical sound waves, you measure the intensity \(750 \mathrm{mW} / \mathrm{m}^{2}\). How far do you need to walk, directly away from the source, until the intensity is \(270 \mathrm{mW} / \mathrm{m}^{2} ?\)

Medical ultrasound waves travel at about \(1500 \mathrm{m} / \mathrm{s}\) in soft tissue. Higher frequencies provide clearer images but don't penetrate to deeper organs. Find the wavelengths of (a) 8.0 -MHz ultrasound used in fetal imaging and (b) 3.5 -MHz ultrasound used to image an adult's kidneys.
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