What is the wavelength of a tuba’s A2 (110-Hz) tone in air at standard conditions?
The correct answer and explanation is :
To find the wavelength of the tuba’s A2 tone (110 Hz) in air at standard conditions, we can use the formula:
[
\lambda = \frac{v}{f}
]
Where:
- (\lambda) is the wavelength,
- (v) is the speed of sound in air,
- (f) is the frequency of the sound.
Step 1: Determine the Speed of Sound in Air
The speed of sound in air at standard conditions (at 20°C or 293 K and at sea level) is approximately 343 meters per second (m/s).
Step 2: Use the Given Frequency
The frequency of the tone in question is 110 Hz, which corresponds to the A2 note on the musical scale.
Step 3: Calculate the Wavelength
Now we can plug these values into the formula:
[
\lambda = \frac{343 \, \text{m/s}}{110 \, \text{Hz}}
]
[
\lambda \approx 3.12 \, \text{meters}
]
Thus, the wavelength of the A2 (110 Hz) tone in air at standard conditions is approximately 3.12 meters.
Explanation:
Sound is a mechanical wave that propagates through a medium (like air) by vibrating particles. The speed of sound in air is influenced by temperature, humidity, and air pressure, but the standard value of 343 m/s is commonly used under typical conditions (20°C and 1 atm pressure). The frequency of sound is the number of vibrations (or oscillations) per second, while the wavelength is the distance between two consecutive peaks of the wave.
In this case, the frequency of 110 Hz means the sound wave oscillates 110 times per second. By dividing the speed of sound (343 m/s) by the frequency (110 Hz), we determine that the distance between consecutive waves (the wavelength) is 3.12 meters. This is the physical length of each wave in the air at this frequency, giving us a tangible representation of how sound travels through space.