Speed of Sound in Air Problem- Is this correct?

[leehana10]

The speed of sound at 0°C in open air is 331.3 m/sec. At what temperature would the wavelength of a 440 Hz sound wave be 0.82 meters?

Equation to find the speed of sound: Vт = Vo √(T/273)

T = 273 + t(°C)

My calculations:

Vт = 440 Hz (0.82 m) = 360.8 m/s

Vт = Vo √(T/273)
360.8 m/s = 331.3 m/s (t^2)
-331.3 m/s = -331.3 m/s (t^2)
29.5 = t^2
√(29.5) = t
5.431 = t

 

[supratim1]

360.8 m/s = 331.3 m/s (t^2)
-331.3 m/s = -331.3 m/s (t^2)

How did you get that?

 

[leehana10]

Nvm. I got help from a friend. Thank you for your help though!

 

[supratim1]

welcome!

 

[rwisz]

Based on my calculations, the temperature at which the wavelength of a 440 Hz sound wave would be 0.82 meters is approximately 5.4°C.

However, it is important to note that this calculation assumes ideal conditions and does not take into account factors such as air pressure and humidity, which can also affect the speed of sound. It is also important to consider the precision and accuracy of the given values for the speed of sound at 0°C and the frequency of the sound wave.

I would recommend conducting further research and experiments to verify the accuracy of this calculation and to account for any other variables that may affect the speed of sound in air. Additionally, it may be helpful to compare these results with known values and data from other sources to ensure consistency and validity.