Sound Problem

[the_sunshine]

Could anyone point out my mistake? Thanks.

 

The range of human hearing extends from approximately 20 Hz to 20,000 Hz. Find the wavelengths of these extremes at a temperature of 40°C.

20 Hz = 1.07 m

Your answer differs from the correct answer by orders of magnitude.

20,000 Hz = 0.00107 m

Your answer differs from the correct answer by orders of magnitude.

 

V=(331)*(sq.root of T)/273K

T=40 C= 313K

 

V=(331)* (sq.root of 313K)/273= 21.5m/s

 

V=frequency*lambda

 

Lambda=21.5/20= 1.075m

Lambda=21.5/20000= 0.001075m

[swansont]

Could anyone point out my mistake? Thanks.

 

The range of human hearing extends from approximately 20 Hz to 20,000 Hz. Find the wavelengths of these extremes at a temperature of 40°C.

20 Hz = 1.07 m

Your answer differs from the correct answer by orders of magnitude.

20,000 Hz = 0.00107 m

Your answer differs from the correct answer by orders of magnitude.

 

V=(331)*(sq.root of T)/273K

T=40 C= 313K

 

V=(331)* (sq.root of 313K)/273= 21.5m/s

 

V=frequency*lambda

 

Lambda=21.5/20= 1.075m

Lambda=21.5/20000= 0.001075m

 

 

V=(331)*(sq.root of T)/273K has the wrong units, since you have a square root of temperature divided by temperature.

 

21.5 m/s is waaaay off for the speed of sound; it should be slightly higher at that higher temperature anyway. With practice you should learn to recognize reasonable and unreasonable answers, and it will help in cases like this.

 

The correct equation is [math]c_{air} = 331.3 \sqrt{1 + \frac{\Theta}{273.15}}[/math] m/s, where [math]\Theta[/math] is the temperature in ºC

[the_sunshine]

Thank you very much!

 

Regards!