How can a wavelength of sound be longer than a string that produces it?
First, the wavelength of a sound depends on the frequency of the sound and the speed of sound in the medium. The formula is speed/frequency = wavelength. So, the wavelengths of sound that a string produces in air will depend on the frequencies that the string can produce. The wavelengths don’t equal the wavelengths of the waves produced on the string, but they are related.
A string fixed at both ends can vibrate with certain “standing wave frequencies.” These standing waves are so called because they look like a travelling wave, but instead of the wave peaks moving down the string, the wave peaks rise and fall in place. The more wave peaks in a standing wave pattern, the higher the frequency and the shorter the wavelength. Now, the lowest frequency of standing wave has just one peak rising and falling. I call it the jump-rope mode because that is what it looks like. This single peak only covers half of a wavelength. So, the standing waves in this mode have a wavelength that is twice the length of the string. And, if the speed of sound in air is larger than the speed of waves on the string, then the wavelength of the sound in air will be even longer than that. The thing that stays the same between the string and the air is the frequency of the sound.
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Answer:
How can a wavelength of sound be longer than a string that produces it?
First, the wavelength of a sound depends on the frequency of the sound and the speed of sound in the medium. The formula is speed/frequency = wavelength. So, the wavelengths of sound that a string produces in air will depend on the frequencies that the string can produce. The wavelengths don’t equal the wavelengths of the waves produced on the string, but they are related.
A string fixed at both ends can vibrate with certain “standing wave frequencies.” These standing waves are so called because they look like a travelling wave, but instead of the wave peaks moving down the string, the wave peaks rise and fall in place. The more wave peaks in a standing wave pattern, the higher the frequency and the shorter the wavelength. Now, the lowest frequency of standing wave has just one peak rising and falling. I call it the jump-rope mode because that is what it looks like. This single peak only covers half of a wavelength. So, the standing waves in this mode have a wavelength that is twice the length of the string. And, if the speed of sound in air is larger than the speed of waves on the string, then the wavelength of the sound in air will be even longer than that. The thing that stays the same between the string and the air is the frequency of the sound.