Given sound frequency of1500 Hz, determine the wavelength at 31 degrees and 41 degrees?

Asked on by edmonded

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to use the information that the speed of sound at `20^oC ` is of `343 m/s`  . Using the equation that relates the speed of sound and temperature yields:

`v_(sound) = 331 + 0.6*20`

`v_(sound) = 343/ m/s`

You need to use the equation that relates the wavelength and frequency is:

`lambda = (v_(sound))/f`

You need to find the speed of sound at `31^oC`  such that:

`v_(sound)= 343 + 0.6(31-20) =gt v_(sound) = 349.6 m/s`

You need to find the speed of sound at `41^oC`  such that:

`v_(sound) = 343 + 0.6(41-20) =gt v_(sound) = 355.6 m/s`

Now, you may evaluate the wavelengths such that:

`lambda_1 = 349.6/1500 =gt lambda_1 = 0.233 m`

`lambda_2 = 355.6 / 1500 =gt lambda_2 = 0.237 m`

Hence, evaluating the wavelengths at `31^o C`  and `41^o C`  yields `lambda_1 = 0.233 m`  and `lambda_2 = 0.237 m` .

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