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Chapter 11: Problem 12

Periodic Waves What is the speed of a wave whose frequency and wavelength are $500.0 \mathrm{Hz}\( and \)0.500 \mathrm{m},$ respectively?

Short Answer

Expert verified
Answer: The speed of the wave is 250.0 m/s.

Step by step solution

01

Identify the given values and formula#####

We are given the frequency (\(f = 500.0 \mathrm{Hz}\)) and the wavelength (\(\lambda = 0.500 \mathrm{m}\)), and we want to find the wave speed (\(v\)). The formula we need to use is the wave speed formula: $$v = f \cdot \lambda$$
02

Plug in the given values#####

Now, let's plug in the given values for frequency and wavelength into the formula: $$v = (500.0 \mathrm{Hz}) \cdot (0.500 \mathrm{m})$$
03

Calculate the wave speed#####

By multiplying the frequency by the wavelength, we will get the wave speed: $$v = 250.0 \mathrm{m/s}$$
04

Write the final answer#####

The speed of the wave with a frequency of \(500.0 \mathrm{Hz}\) and a wavelength of \(0.500 \mathrm{m}\) is \(250.0 \mathrm{m/s}\).

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Most popular questions from this chapter

Two speakers spaced a distance \(1.5 \mathrm{m}\) apart emit coherent sound waves at a frequency of \(680 \mathrm{Hz}\) in all directions. The waves start out in phase with each other. A listener walks in a circle of radius greater than one meter centered on the midpoint of the two speakers. At how many points does the listener observe destructive interference? The listener and the speakers are all in the same horizontal plane and the speed of sound is \(340 \mathrm{m} / \mathrm{s} .\) [Hint: Start with a diagram; then determine the maximum path difference between the two waves at points on the circle. I Experiments like this must be done in a special room so that reflections are negligible.
The equation of a wave is $$ y(x, t)=(3.5 \mathrm{cm}) \sin \left\\{\frac{\pi}{3.0 \mathrm{cm}}[x-(66 \mathrm{cm} / \mathrm{s}) t]\right\\} $$ Find (a) the amplitude and (b) the wavelength of this wave.
What is the speed of the wave represented by \(y(x, t)=\) $A \sin (k x-\omega t),\( where \)k=6.0 \mathrm{rad} / \mathrm{cm}\( and \)\omega=5.0 \mathrm{rad} / \mathrm{s} ?$
A traveling sine wave is the result of the superposition of two other sine waves with equal amplitudes, wavelengths, and frequencies. The two component waves each have amplitude \(5.00 \mathrm{cm} .\) If the superposition wave has amplitude \(6.69 \mathrm{cm},\) what is the phase difference \(\phi\) between the component waves? [Hint: Let \(y_{1}=A \sin (\omega t+k x)\) and $y_{2}=A \sin (\omega t+k x-\phi) .$ Make use of the trigonometric identity (Appendix A.7) for \(\sin \alpha+\sin \beta\) when finding \(y=y_{1}+y_{2}\) and identify the new amplitude in terms of the original amplitude. \(]\)
A uniform string of length \(10.0 \mathrm{m}\) and weight \(0.25 \mathrm{N}\) is attached to the ceiling. A weight of \(1.00 \mathrm{kN}\) hangs from its lower end. The lower end of the string is suddenly displaced horizontally. How long does it take the resulting wave pulse to travel to the upper end? [Hint: Is the weight of the string negligible in comparison with that of the hanging mass?]
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