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Chapter 14: Problem 27

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.

Short Answer

Expert verified
After solving, we get the spring tension 'T' to be approximately \(7.59 \mathrm{N}\).

Step by step solution

01

Calculating the wave speed v

Firstly, it's important to convert all units to standard ones. Therefore, we convert the wave speed to meters per second. In this case, we already have the wave speed, given to be \(6.7 \mathrm{m/s}\), so no calculations are necessary.
02

Calculating the mass per unit length \(\mu\)

Next, we need to convert the mass per unit length to the standard units. Since it's given as \(170 \mathrm{g/m}\), we need to convert grams into kilograms, therefore, \(\mu = 170 \mathrm{g/m} = 0.17 \mathrm{kg/m}\).
03

Use the wave speed equation to find the tension

Substitute our known values of 'v' and '\mu' back into the wave speed equation, and solve for 'T'. We can rearrange the equation to make 'T' the subject and then substitute our values: \(T = v^{2} * \mu\), therefore \( T = (6.7 \mathrm{m/s})^{2} * 0.17 \mathrm{kg/m} \).

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