Video: Relating the Wavelength of a Sound Wave to Its Frequency

A guitar string oscillates at a frequency of 0.100 kHz and produces a sound wave. If the speed of the sound wave is 343 m/s, what is the wavelength of the sound wave?

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Video Transcript

A guitar string oscillates at a frequency of 0.100 kilohertz and produces a sound wave. If the speed of the sound wave is 343 meters per second, what is the wavelength of the sound wave?

Let’s start by highlighting some of the vital information were given in the statement. We’re told that the frequency of the string oscillation is 0.100 kilohertz; we’ll call that 𝑓. We’re also told to treat the speed of sound as 343 meters per second; we’ll call that 𝑉 sub 𝑠. We want to know the wavelength of the sound wave, which we’ll call 𝜆.

To start on our solution, let’s recall a relationship that tell us the speed of a wave, in terms of its wavelength and frequency. The speed of a wave, 𝑉, is equal to frequency times wavelength. When we apply this relationship to our scenario, we see that we can rearrange to solve for the wavelength 𝜆.

And that is equal to the speed of sound, 𝑉 sub 𝑠, divided by 𝑓. Since we’re given the speed of sound and frequency in the problem statement, we’re now ready to plug in with these values. As we do so, we’re careful to express the frequency in units of hertz. When we calculate this fraction, we find that the wavelength, 𝜆, is 3.43 meters. That’s one wavelength of the oscillating guitar string.

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