A sound wave has a frequency of 686 Hz in air and a wavelength of 0.50 m. What is the temperature of the air?
-Find wavelengths for 20 hz:
-Find wavelengths for 20,000hz:
To find the temperature of the air when given the frequency and wavelength of a sound wave, we can use the formula for the speed of sound in air:
Speed of sound = wavelength × frequency
The speed of sound in air at a specific temperature can be calculated using the following approximation:
Speed of sound (m/s) = 331.4 + 0.6 × temperature (in Celsius)
Now we can solve for the temperature:
Speed of sound = wavelength × frequency
331.4 + 0.6 × temperature = wavelength × frequency
For the first part of your question:
Given the frequency of 686 Hz and a wavelength of 0.50 m, we can substitute these values into the equation:
331.4 + 0.6 × temperature = 0.50 × 686
Solving for the temperature:
0.6 × temperature = (0.50 × 686) - 331.4
Temperature (in Celsius) = [(0.50 × 686) - 331.4] / 0.6
Now you can calculate the temperature using the given formula.
For the second part of your question:
To find the wavelengths for different frequencies, we can use the formula for wavelength:
Wavelength (m) = Speed of sound / Frequency
Given a frequency of 20 Hz, we can substitute this value into the equation:
Wavelength = Speed of sound / 20
Using the speed of sound formula mentioned earlier (331.4 + 0.6 × temperature), we can substitute this formula into the equation:
Wavelength (m) = (331.4 + 0.6 × temperature) / 20
Similarly, for the frequency of 20,000 Hz, substitute this value into the equation and solve:
Wavelength (m) = (331.4 + 0.6 × temperature) / 20,000
By solving these equations, you can find the wavelengths for both 20 Hz and 20,000 Hz at the given temperature.