# Longitudinal Waves in Air (Experimentally determining the speed of sound)

• Von Neumann
In summary, the equation v=2l'f/(n-1) correlates to the situation involving a pipe with 2 open or 2 closed ends, but it has no relevance in this experiment having to do with a pipe with 1 open end.
Von Neumann
Problem:

In my physics class, we conducted an experiment involving a column of air set vibrating by a tuning fork of a known frequency f held at the upper end. The wave travels from the source to a fixed end (namely the water in the lower end of the tube) & reflected back to the source.

Assuming it takes a half-integral number of periods,

(n-1/2)T=(n-1/2)/f

for the wave to return to the source, then the compressional wave sent from the tuning fork in its downward motion and reflected by the water will arrive back at the fork just in time to aid its upward motion. Since there is no phase change in the compressional wave reflected off of the water, the condition for resonance is

(n-1/2)/f=2l/v

where n is a positive integer, and l is the length of the column of air, and v is the speed of the wave (the speed of sound). Solving for v,

v=2lf/(n-1/2)

We then compare the results of the experimentally determine v to the theoretically calculated v using the formula

v=$\sqrt{\frac{(\gamma)RT}{M}}$

Where $\gamma$ is the thermodynamic constant for air, R is the universal gas constant, T is the absolute temperature, and M is the average molecular weight of air.

However, an alternate formula for v in terms of the distance l' from the first node to the bottom of the air column is

v=2l'f/(n-1)

This formula is given with no explanation, and I am wondering if it is mathematically equivalent to the other experimental formula for v. It is obvious that this particular formula will not yield a result when n=1.

Last edited:
The last formula corresponds to two open (or two closed) ends.

mfb said:
The last formula corresponds to two open (or two closed) ends.

If you wouldn't mind, can you elaborate on why this is the case?

With a closed end, you get pressure differences a both sides, so you should match a wave of high pressure from one end, traveling 2l through the pipe, with the next (or next to next, or ...) time of high pressure. This gives an integer multiple of wavelengths in 2l.
You can drop the -1 if you like.

If, as you claim, the equation v=2l'f/(n-1) correlates to the situation involving a pipe with 2 open or 2 closed ends, then it certainly has no relevance in this experiment having to do with a pipe with 1 open end. Correct?

Von Neumann said:
If, as you claim, the equation v=2l'f/(n-1) correlates to the situation involving a pipe with 2 open or 2 closed ends, then it certainly has no relevance in this experiment having to do with a pipe with 1 open end. Correct?
Correct

Von Neumann said:
I am not sure how to interpret that post...

## 1. What is a longitudinal wave?

A longitudinal wave is a type of mechanical wave that travels through a medium by causing the particles of the medium to vibrate parallel to the direction of the wave's motion. This means that the particles of the medium are moving back and forth in the same direction that the wave is traveling.

## 2. How are longitudinal waves created in air?

Longitudinal waves in air are created by a disturbance, such as a vibrating object, that causes the air particles to compress and expand. This creates a series of high pressure and low pressure regions that travel through the air as a wave.

## 3. How can the speed of sound be determined experimentally?

The speed of sound can be determined experimentally by using a device called an echo chamber. This device produces a sound and then measures the time it takes for the sound to travel to a reflective surface and back. By knowing the distance between the two points and the time it takes for the sound to travel, the speed of sound can be calculated using the equation speed = distance/time.

## 4. What factors can affect the speed of sound in air?

The speed of sound in air can be affected by several factors, including temperature, humidity, and altitude. In general, sound travels faster in warmer, less humid air and slower in colder, more humid air. It also travels faster at higher altitudes due to the decrease in air density.

## 5. Why is it important to know the speed of sound in air?

Knowing the speed of sound in air is important for various reasons. It allows us to accurately measure distances using sound waves, such as in sonar technology. It also helps us understand the behavior of sound in different environments and can be used in industries such as aviation and meteorology. Additionally, the speed of sound can provide valuable information about the properties of the medium through which it is traveling.

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