Wavelength of the sounds at zero degrees

[moenste]

Homework Statement

A source of sound frequency 550 Hz emits waves of wavelength 600 mm in air at 20 °C. What is the velocity of sound in air at this temperature? What would be the wavelength of the sound from this source in air at 0 °C?

Answers: 330 m s^-1, 579 mm

2. The attempt at a solution
v = f λ = 550 * 0.6 = 330 m s^-1

Regarding the wavelength of the sound at 0 degrees I am not sure what to do. I looked up here that 0 degrees have a speed of 331.01 m s^-1, so λ = v / f = 0.601 m or 602 mm. Which is wrong.

I also substituted 20 °C and got 343 m s^-1. Why does the number differ with the one I got (330 m s^-1)?

 

[drvrm]

Regarding the wavelength of the sound at 0 degrees I am not sure what to do. I looked up here that 0 degrees have a speed of 331.01 m s-1, so λ = v / f = 0.601 m or 602 mm. Which is wrong.

how the velocity of sound in air varies with temperature?
your data given in the problem may not be exactly equal to experimental data?

 

[moenste]

how the velocity of sound in air varies with temperature?
your data given in the problem may not be exactly equal to experimental data?

v (or c) ∝ √T

Perhaps it is not exactly equal. What did I overlook in the second part?

 

[drvrm]

Perhaps it is not exactly equal. What did I overlook in the second part?

well i can not say...as i do not have your calculation before me...you may take the first data at 20 degree as the supplied one and calculate at zero degree and see what value it gives...pl. convert the centigrade to kelvin scale of temperature..

 

[moenste]

well i can not say...as i do not have your calculation before me...you may take the first data at 20 degree as the supplied one and calculate at zero degree and see what value it gives...pl. convert the centigrade to kelvin scale of temperature..

This

A source of sound frequency 550 Hz emits waves of wavelength 600 mm in air at 20 °C. What is the velocity of sound in air at this temperature?

is for

v = f λ = 550 * 0.6 = 330 m s-1

Why do we need 20 degrees in the first place if we can get 330 m / s using v = f λ?

And this:

What would be the wavelength of the sound from this source in air at 0 °C?

=

Regarding the wavelength of the sound at 0 degrees I am not sure what to do. I looked up here that 0 degrees have a speed of 331.01 m s-1, so λ = v / f = 0.601 m or 602 mm. Which is wrong.

Where 331.01 m / s is found using this formula (ϑ = 0 °C).

 

[drvrm]

Where 331.01 m / s is found using this formula (ϑ = 0 °C).

you are given with a speed of sound at 20 degree (as said in the problem) ; now you have to calculate the speed/velocity at zero degree from that value you can get the wavelength using V(at 0 degree) = frequency x wavelength , this number will be wavelength at 0degree as frequency does not change.
for calculating V(0) you have the relation V(0) / V(20) = SQRT ( T(0) / T (20))
i think the new wavelength will be around your answer.
now if you compare with standard data the speeds quoted at 20 degree is around 346 m/s and it gets to 331 m/s at zero.
so your problem setter/writer is not using standard values ..perhaps..though its not a good practice...

 

[moenste]

you are given with a speed of sound at 20 degree (as said in the problem) ; now you have to calculate the speed/velocity at zero degree from that value you can get the wavelength using V(at 0 degree) = frequency x wavelength , this number will be wavelength at 0degree as frequency does not change.
for calculating V(0) you have the relation V(0) / V(20) = SQRT ( T(0) / T (20))
i think the new wavelength will be around your answer.
now if you compare with standard data the speeds quoted at 20 degree is around 346 m/s and it gets to 331 m/s at zero.
so your problem setter/writer is not using standard values ..perhaps..though its not a good practice...

Alright, so to sum up:

(a) We have got a source of sound frequency 550 Hz that emits waves of wavelength 600 mm in air at 20 °C. At this temperature the velocity of sound is equal: v = f λ = 550 * 0.6 = 330 m s^-1 at 20 °C.

(b) Now we need to find the wavelength of the sound from this source in air at 0 °C. We re-arrange the abovementioned formula for the wavelength to get: λ = v / f. We don't have the velocity at 0 °C. So we use: v_{0 °C} / v_{20 °C} = √T_{0 °C} / T_{20 °C} (where temperature T is in Kelvin) and we have v_{0 °C} / 330 = √273.15 / 293.15. So, v_{0 °C} = 318.5 m s^-1. Substituting it into the formula gives us: λ = 318.5 / 550 = 0.579 m or 579 mm.

 

[drvrm]

Alright, so to sum up:

as far as your problem is concerned
you got the right answer but 'must' remember the data given is not physical and may not be used in future. must use data from a source 'table of velocities' at different temp.
it appears -it was an exercise to check whether one knows the variation of velocity of sound in a medium with temperature.