Music Mystery: 2(Vsound) for the 2nd Harmonic?

In summary, the question asks how fast the guitar player must move towards or away from the stationary observer for the observer to mistake the fundamental frequency for the second harmonic. The answer given (2x the speed of sound) is incorrect, as it would result in the observer not being able to hear the player approaching. The correct answer is 1/2 the speed of sound.
  • #1
vetgirl1990
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3

Homework Statement


A guitar player is plucking a strong of length 30cm. How fast must the player move towards or away from the stationary observer, in order for the observer to mistake the fundamental frequency for the second harmonic?

ANSWER: 2(Vsound) towards the observer

Homework Equations


Frequency for string fixed on both ends: f = 2n/vL
Doppler effect for source moving towards stationary observer (observer will hear higher frequency):
f" = vsound / vsound - Vsource

The Attempt at a Solution


f = 2n/vL = 2(1) / 343(0.3) = 205.8 Hz for the fundamental frequency --> set as f in the doppler equation
f = 2(2) / 343(0.3) = 411.5Hz for the second harmonic --> set as f" in the doppler equation

411.6 = 343 (205.8) / (343-vsound)
Vsound = 171.5 m/s = 1/2 vsound

I am getting 1/2 the speed of sound, rather than 2x the speed of sound which is the answer. What am I doing wrong?
 
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  • #2
vetgirl1990 said:
I am getting 1/2 the speed of sound, rather than 2x the speed of sound which is the answer. What am I doing wrong?
Twice the speed of sound is clearly nonsense. The observer would not hear the player approach. Must be a typo.
Your answer looks right.
 
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  • #3
haruspex said:
Twice the speed of sound is clearly nonsense. The observer would not hear the player approach. Must be a typo.
Your answer looks right.

LOL thank you! My initial reaction to the "answer" was that it was an extremely hypothetical situation. Thanks for verifying!
 

1. What is the significance of the 2nd harmonic in music?

The 2nd harmonic in music is an important component of sound waves. It is the second frequency that is produced when a musical instrument is played, and it is twice the frequency of the fundamental note. This harmonic is responsible for creating the unique timbre and tone of different musical instruments.

2. How is the 2nd harmonic related to the concept of resonance?

The 2nd harmonic is closely related to the concept of resonance. When an object is exposed to the 2nd harmonic frequency, it will vibrate at its resonant frequency, which amplifies the sound produced. This is why some musical instruments, like string instruments, have a specific shape and size to amplify the 2nd harmonic and produce a richer sound.

3. Can the 2nd harmonic be manipulated or controlled in music?

Yes, the 2nd harmonic can be manipulated and controlled in music. Musicians can use techniques such as overtones, harmonics, and resonance to enhance or suppress the 2nd harmonic in their music. This allows for a wide range of musical expression and creativity.

4. How does the 2nd harmonic affect the perception of music?

The 2nd harmonic plays a crucial role in how we perceive music. It adds depth and complexity to the sound, making it more interesting and pleasing to the ear. The 2nd harmonic also helps to distinguish between different musical instruments and create a sense of harmony in music.

5. Is the 2nd harmonic present in all types of music?

Yes, the 2nd harmonic is present in all types of music. It is a fundamental aspect of sound waves and is naturally produced when any musical instrument is played. The amount of emphasis on the 2nd harmonic may vary depending on the style of music, but it is always present in some form.

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