A piccolo is playing A6 (1760 Hz). What is the wavelength of that tone in air at standard conditions?
The correct answer and explanation is :
To find the wavelength of the sound produced by a piccolo playing A6 (1760 Hz), we need to use the formula that relates the speed of sound, frequency, and wavelength: v=f×λv = f \times \lambda
Where:
- vv is the speed of sound in air (at standard conditions),
- ff is the frequency of the sound,
- λ\lambda is the wavelength.
Step 1: Known Values
- The frequency of A6 is f=1760 Hzf = 1760 \, \text{Hz}.
- The speed of sound in air at standard conditions (20°C or 68°F) is approximately v=343 m/sv = 343 \, \text{m/s}.
Step 2: Solve for Wavelength
We can rearrange the formula to solve for the wavelength λ\lambda: λ=vf\lambda = \frac{v}{f}
Substitute the known values: λ=343 m/s1760 Hz≈0.195 m\lambda = \frac{343 \, \text{m/s}}{1760 \, \text{Hz}} \approx 0.195 \, \text{m}
Step 3: Interpretation of the Result
Thus, the wavelength of the tone produced by the piccolo at A6 (1760 Hz) is approximately 0.195 meters or 19.5 cm.
Explanation:
The speed of sound in air depends on the temperature and other factors like air pressure and humidity. Under standard conditions, which is typically considered as 20°C (68°F), the speed of sound is 343 m/s. Frequency is a property of sound that indicates how many vibrations (or cycles) occur per second. Higher frequencies correspond to higher pitches. A6 is in the higher range of the musical scale and has a frequency of 1760 Hz.
The wavelength is the physical distance between consecutive peaks (or troughs) of the sound wave. At higher frequencies, the wavelength is shorter because the cycles are occurring more frequently in a given time. Conversely, lower frequencies have longer wavelengths.
Thus, for a frequency of 1760 Hz, the wavelength of the sound is quite short, around 19.5 cm, which matches the high pitch of the A6 note.