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Chapter 11: Problem 13

What is the wavelength of a wave whose speed and period are $75.0 \mathrm{m} / \mathrm{s}\( and \)5.00 \mathrm{ms}$, respectively?

Short Answer

Expert verified
Answer: The wavelength of the wave is 375 m.

Step by step solution

01

Rearrange the formula to solve for wavelength (λ)

To solve for the wavelength (λ), we can rearrange the formula as follows: $$\lambda = v \cdot T$$ This gives us the formula we need to solve for the wavelength using the given values for wave speed (v) and period (T).
02

Plug in the given values and solve for the wavelength (λ)

We are given that the wave's speed (v) is \(75.0 m/s\) and its period (T) is \(5.00 ms\). We need to convert the period from milliseconds to seconds before we can plug the values into the formula. $$T = 5.00 ms \cdot \frac{1 s}{1000 ms} = 0.00500 s$$ Now, we can plug in the values for wave speed (v) and period (T) into the formula: $$\lambda = (75.0 m/s) \cdot (0.00500 s)$$
03

Calculate the wavelength (λ)

Now, we can perform the multiplication to find the wavelength: $$\lambda = 375 m$$ So, the wavelength of the wave is \(375 m\).

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Most popular questions from this chapter

When the tension in a cord is \(75 \mathrm{N}\), the wave speed is $140 \mathrm{m} / \mathrm{s} .$ What is the linear mass density of the cord?
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