Calculating the Speed of Waves in a Vibrating String and Resonant Pipe

  • Thread starter JSmithDawg
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In summary, a 0.13-m string vibrating in its n = 4 harmonic excites a 0.88 m long pipe into its second overtone resonance. To find the speed of transverse waves on the string, the equation F=nv/(2L) is used, where n is the harmonic number, v is the wave velocity, and L is the length of the pipe. Plugging in known values, the resulting velocity is not 67.6 m/s as expected. Further clarification or calculation is needed to determine the correct answer.
  • #1
JSmithDawg
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Homework Statement


A 0.13-m string, fixed at both ends and vibrating in its n = 4 harmonic, excites a pipe that is 0.88 m long and open at both ends, into its second overtone resonance. What is the speed of transverse waves on the string? The speed of sound in air is 345 m/s.

Homework Equations


F=nv/(2L)

The Attempt at a Solution


I wasn't present when my class went over this, so keep in mind that this is just my speculation. Anyway, as the string excites the pipe, the frequencies of both waves should be the same.
f1=f2
I don't know the velocity of the first wave, but the velocity of the second wave should be the speed of sound. Now, plugging in numbers I know, I get
4(v)/(2*.13m)=3(345 m/s)/(2*.88m)
v=67.6 m/s

The online quiz I'm doing is telling me this is wrong, so what's wrong with my logic?
 
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  • #2
JSmithDawg said:
4(v)/(2*.13m)=3(345 m/s)/(2*.88m)
v=67.6 m/s

I don't get 67.6 m/s when solving your equation for v.
 

1. How do sound waves travel through tubes?

Sound waves travel through tubes by creating vibrations in the air particles within the tube. These vibrations then travel through the tube, bouncing off the walls and creating a resonant sound. The length and shape of the tube can also affect the quality and pitch of the sound produced.

2. What is the difference between a standing wave and a traveling wave in a tube?

A standing wave is a stationary pattern of vibrations in a tube, caused by the interference of two waves traveling in opposite directions. A traveling wave, on the other hand, is a wave that moves from one end of the tube to the other, with no interference or reflection.

3. How does the shape of a tube affect the sound produced?

The shape of a tube can greatly affect the sound produced. Tubes with a wider diameter tend to produce lower-pitched sounds, while tubes with a narrower diameter produce higher-pitched sounds. The length of the tube also plays a role, with longer tubes producing lower-pitched sounds and shorter tubes producing higher-pitched sounds.

4. How is the speed of sound affected by tubes?

The speed of sound is affected by the material and shape of the tube. In general, sound travels faster in denser materials, such as metal or water, compared to air. The shape of the tube can also affect the speed of sound, with sound traveling faster in narrower tubes compared to wider tubes.

5. Why do some tubes produce higher-pitched sounds than others?

The pitch of a sound produced by a tube is determined by the frequency of the sound wave, which is affected by the length and shape of the tube. Longer tubes tend to produce lower-pitched sounds, while shorter tubes produce higher-pitched sounds. The shape of the tube can also affect the pitch, with narrower tubes producing higher-pitched sounds compared to wider tubes.

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