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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 (位)

To solve for the wavelength (位), 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 (位)

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 (位)

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

What is the wavelength of the radio waves transmitted by an FM station at 90 MHz? (Radio waves travel at \(3.0 \times 10^{8} \mathrm{m} / \mathrm{s} .\)
What is the frequency of a wave whose speed and wavelength are $120 \mathrm{m} / \mathrm{s}\( and \)30.0 \mathrm{cm},$ respectively?
(a) Plot a graph for $$ y(x, t)=(4.0 \mathrm{cm}) \sin [(378 \mathrm{rad} / \mathrm{s}) t-(314 \mathrm{rad} / \mathrm{cm}) x] $$ versus \(x\) at \(t=0\) and at \(t=\frac{1}{480} \mathrm{s}\). From the plots determine the amplitude, wavelength, and speed of the wave. (b) For the same function, plot a graph of \(y(x, t)\) versus \(t\) at \(x=0\) and find the period of the vibration. Show that \(\lambda=v T.\)
While testing speakers for a concert. Tom谩s sets up two speakers to produce sound waves at the same frequency, which is between \(100 \mathrm{Hz}\) and $150 \mathrm{Hz}$. The two speakers vibrate in phase with one another. He notices that when he listens at certain locations, the sound is very soft (a minimum intensity compared to nearby points). One such point is \(25.8 \mathrm{m}\) from one speaker and \(37.1 \mathrm{m}\) from the other. What are the possible frequencies of the sound waves coming from the speakers? (The speed of sound in air is \(343 \mathrm{m} / \mathrm{s} .\) )
The longest "string" (a thick metal wire) on a particular piano is $2.0 \mathrm{m}\( long and has a tension of \)300.0 \mathrm{N} .$ It vibrates with a fundamental frequency of \(27.5 \mathrm{Hz}\). What is the total mass of the wire?
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