Calculating the Wavelength of Sound in Air at 10°C and 256 Hz
In the world of physics, understanding the relationship between the speed of sound in a medium, its frequency, and the resulting wavelength is a fundamental concept. In this article, we will derive the wavelength of sound in air when the temperature is 10°C and the tuning fork emits sound at a frequency of 256 Hz. We will explore the formula, step-by-step calculations, and provide some insights into the properties of sound.
Understanding the Formula
The wavelength of sound in a given medium can be calculated using the following formula:
[ text{Wavelength} lambda frac{v}{f} ]
Where:
( lambda ) is the wavelength of the sound wave, measured in meters (m). ( v ) is the speed of sound in the medium, measured in meters per second (m/s). ( f ) is the frequency of the sound wave, measured in Hertz (Hz).Determining the Speed of Sound in Air
Calculating the speed of sound in air can be done using the following empirical formula:
[ v approx 331.3 0.6 times T ]
Where:
( v ) is the speed of sound in air. ( T ) is the temperature in degrees Celsius (°C).Given that the temperature ( T 10°C ), we can calculate the speed of sound ( v ) as follows:
[ v approx 331.3 0.6 times 10 ]
[ v approx 331.3 6 ]
[ v approx 337.3 , text{m/s} ]
Calculating the Wavelength
With the speed of sound ( v 337.3 , text{m/s} ) and the frequency ( f 256 , text{Hz} ), we can now calculate the wavelength ( lambda ) using the formula:
[ lambda frac{v}{f} ]
Substituting the given values:
[ lambda frac{337.3 , text{m/s}}{256 , text{Hz}} ]
[ lambda approx 1.316 , text{m} ]
Therefore, the wavelength of the sound in air emitted by a tuning fork of frequency 256 Hz at a temperature of 10°C is approximately 1.316 meters.
Conclusion
Understanding the relationship between the speed of sound, its frequency, and the resulting wavelength is crucial for various applications, including acoustics, engineering, and physics. The speed of sound in air can vary with temperature, and the formula ( lambda frac{v}{f} ) is a fundamental tool for calculating these relationships.