A sound wave has a frequency of 707 Hz in air and a wavelength of 0.50 m. What is the temperature of the air?
figure the velocity first (frequency*wavelength)
then, knowing the velocity, solve for temp
velocity= 343(1+.6temp)
check that formula
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To find the temperature of the air, we can use the formula for the speed of sound in air, which is given by:
v = λ * f
where:
v = speed of sound (m/s)
λ = wavelength (m)
f = frequency (Hz)
Substituting the given values:
v = 0.50 m * 707 Hz
Now, we can use another formula to calculate the speed of sound in air at a given temperature:
v = 331.5 + 0.6 * T
where:
T = temperature (°C)
Substituting the known speed of sound formula into the temperature formula, we have:
331.5 + 0.6 * T = 0.50 m * 707 Hz
Now, we can solve for T.
0.6 * T = 0.50 m * 707 Hz - 331.5
0.6 * T = 353.5 m·Hz - 331.5
T = (353.5 m·Hz - 331.5) / 0.6
T ≈ 372.5 °C
Therefore, the temperature of the air is approximately 372.5 °C.
To determine the temperature of the air, we can use the formula for the speed of sound in air as a function of temperature:
v = λ * f
where:
v is the speed of sound in air,
λ is the wavelength of the sound wave, and
f is the frequency of the sound wave.
The speed of sound in air varies with temperature, given by the equation:
v = 331.4 + (0.6 * T)
where T is the temperature in Celsius.
To solve for the temperature, we can rearrange the equation to:
T = (v - 331.4) / 0.6
Now, we can substitute the values given in the problem:
- The frequency (f) of the sound wave is 707 Hz.
- The wavelength (λ) of the sound wave is 0.50 m.
First, calculate the speed of sound using the equation v = λ * f:
v = 0.50 m * 707 Hz
v = 353.5 m/s
Now, substitute the speed of sound into the equation to solve for the temperature:
T = (353.5 m/s - 331.4 m/s) / 0.6
T ≈ 36.8°C
Therefore, the temperature of the air is approximately 36.8°C.