# Sound Resonance: How to Calculate Speed of Sound

A tuning fork is an object that resonates, or vibrates, at a specific frequency and pitch. The sound of a tuning fork depends on the length of the prongs and can be used to tune musical instruments.

### Problem:

Calculate the speed of sound in air.

### Materials:

• Tuning fork with known frequency
• Large, tall cylindrical glass container
• Water
• Rubber mallet
• Ruler

### Procedure

1. Fill the glass container halfway up with water.
2. Strike the tuning fork with the rubber mallet. Why should you use a mallet to strike the tuning for rather than a hard surface like a table?
3. Hold the tuning fork over the opening of the glass container as pictured. Record your observations. How does holding the fork over the container change the sound you hear? Why does this happen?

1. While keeping the tuning fork over the opening of the container, slowly pour more water into the cylinder. If you cannot do it yourself, ask a friend or family member to help you. Listen for the point when there is a change in pitch (frequency).
2. Remove some water and experiment with adding it again until you can identify the height of the water at which the frequency jumps. Why does the frequency jump?
3. Calculate the velocity of sound at this height using the following equation:
v = 4f (H + 0.4D)
 v is the velocity of sound f is the frequency of the tuning fork in Hz H is the height distance between the top of the water and the lip of the cylinder D is the diameter of the water container in meters

### Results

The speed of sound in air is 343 m/s (nearly a mile in 5 seconds!) at 20°C. Compare your experimental value to the true value. If it is warmer, the speed will be faster.

### Why?

The change in sound in the water column will occur when the graduated cylinder produces the same resonance as the tuning fork. Simply put, this means that one period of the wave goes to the bottom of the cylinder and back in the same amount of time it takes for the tuning fork to vibrate one time.

The fundamental frequency is the frequency of one period of a wavelength. The second harmonic, also called the 1st overtone, is an integer (whole number) multiple of the fundamental frequency. Many people will not hear the difference between harmonics, but they are commonly used in music, and examples of harmonics can even be found in the human voice.

Here are a few examples of frequencies applied to musical notes:

 Approximate Note Frequency (Hz) Wavelength (m) Fundamental height (m) 2nd Harmonic height (m) C 256 1.34 0.33 0.17 C# 278 1.23 0.31 0.16 D 294 1.17 0.29 0.15 Eb 311 1.10 028 0.14 E 330 1.04 0.26 0.13 F 349 0.98 0.24 0.12 F# 370 0.93 0.23 0.12 G 392 0.88 0.22 0.11 Ab 415 0.83 0.20 0.11 A 440 0.78 0.19 0.10 B 494 0.69 0.18 0.09

Wavelength is the length in meters of one period of the wave, from peak to peak. It is often denoted by the Greek symbol lambda λ and can be calculated by the equation

v = λ f
 v is the velocity in m/s λ is wavelength in meters f is frequency in Hz, or s-1​

Sound in water is 1484 m/s, more than 4 times the speed of air. This is why whales and dolphins can communicate quickly over large distances.
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