Sound waves and Harmonics help

In summary, the conversation involves a question about a musical instrument design and the effects of changing the tension on the sound produced. The design consists of a metal tube with a string stretched across the open end, and the goal is to have the third-harmonic standing wave on the string match the fundamental frequency for sound waves in the air column of the tube. The equation ƒn=nv/2L is mentioned, and there is a discussion about what would happen to the sound if the tension is doubled. It is noted that the frequency of the waves would increase, but it is unsure if the sound would become a higher or lower pitch. Finally, there is a question about what other harmonics of the string would be in resonance
  • #1
Sky07
1
0
Hello, I am having a hard time solving this question. Any help is really appreciated.

1. Homework Statement
You have designed a new musical instrument of very simple construction. Your design consists of a metal tube with length L and diameter L/10. You have stretched a string of mass per unit length μacross the open end of the tube. The other end of the tube is closed. To produce the musical effect you're looking for, you want the frequency of the third-harmonic standing wave on the string to be the same as the fundamental frequency for sound waves in the air column in the tube. The speed of sound waves in this air column is vs.

b)What happens to the sound produced by the instrument if the tension is changed to twice the value calculated . The tension is vsound^2μ/60?

c) For the tension calculated vsound^2μ/60, what other harmonics of the string, if any, are in resonance with standing waves in the air column?

Homework Equations


ƒn=nv/2L

The Attempt at a Solution


[/B]
B) for this part my idea is because tension is increasing the the frequency of the waves will increase as per the formula. However, I am unsure if the sound would become a higher pitch or lower pitch.
C) I am not really sure about this one.

Thank you for your help!
 
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  • #2
Sky07 said:
The tension is vsound^2μ/60?
That's the tension before it is doubled? I get something different - please post your working. However, it is only different by a constant factor, so shouldn't change the answer to b.
Sky07 said:
the frequency of the waves will increase as per the formula. However, I am unsure if the sound would become a higher pitch or lower pitch.
You don't know whether a higher frequency is a higher or lower pitch?
Sky07 said:
What happens to the sound produced by the instrument if the tension is changed to twice the value calculated
You're not told how the instrument is to be played, but presumably the idea is to pluck the string. You need to think on this very carefully: What will happen when you do that with the original design?
What will happen when you pluck the string with twice the tension?
 

1. What are sound waves?

Sound waves are a type of mechanical wave that travel through a medium, such as air or water, as a series of compressions and rarefactions. They are created by vibrations, and can be heard by our ears when they reach a certain frequency.

2. How are sound waves produced?

Sound waves are produced when an object vibrates, creating a disturbance in the surrounding medium. This can be caused by various sources, such as a vibrating guitar string, a person's vocal cords, or even a loudspeaker.

3. What are harmonics?

Harmonics are frequencies that are whole number multiples of the fundamental frequency. In other words, they are frequencies that are related to the fundamental frequency by a simple mathematical ratio. This relationship is what gives a sound its characteristic tone or timbre.

4. How do harmonics affect sound?

Harmonics play a crucial role in the quality and tone of sound. They can determine whether a sound is perceived as smooth or harsh, and can also create unique sound characteristics, such as the overtones in a musical instrument.

5. How can harmonics be manipulated?

Harmonics can be manipulated by changing the frequency or amplitude of a sound wave. This can be done through various methods, such as using filters, equalizers, or adjusting the properties of the source of the sound wave. These manipulations can alter the perceived quality and tone of the sound.

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