Calculating Air Temperature from Frequency of Sound

In summary, the conversation discusses how to calculate the air temperature given a column of air that resonates at a certain frequency. The summary includes the steps taken to find the speed of sound and the resulting temperature of 24.7 C. The conversation also mentions the importance of considering reasonable temperature ranges and using the correct distance in the calculations.
  • #1
Physics8944
12
0
Hi!
Q: A column of air length 36cm is closed at both ends, resonates to as sound of third lowest frequceny of 1445Hz. Calculate the air temperature given that the reasonable temperature falls between 10 and 20 C??

Here is what I tried:
Given T= 20 ( 30-10= 20)
Required: vs & T
Analysis: vs= 332m/s+T(0.60m/s C) & T= vs-332/0.60
Solution: vs= 332m/s+(20C)(0.60 C)
= 332m/s+12m/s
= 344m/s
now we the speed, & we can find the temperature:
=344m/s-332m/s/0.60m/s C
= 12/0.60
= 20
So the air temperature is 20 C.
I would really appericate if sum1 could help.
Thanks alot.
 
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  • #2
Hi! You have to solve the speed of sound from a measurement first. You can't just just decide that the temperature is 20 C! The air column should give you the speed of sound, which you can then use to calculate the temperature.
 
  • #3
Given: f= 1445 Hz.
Lambda= 0.36m (36 cm is converted)
Required: v and vs
Analysis: v=f(lambda)
Solution: v= (1445Hz)(0.36)
V= 520.2m/s
Now we can find the temperature:
Analysis: T= vs-332m/s
0.60
= 520.2-332/0.6
= -31.13 is the temperature is it correct??
 
  • #4
Does the speed of sound increase or decrease when temperature increases?
 
  • #5
speed increases when the temperature increases
 
  • #6
Speed of sound increases as temperature increases.
 
  • #7
That's right. Then you can answer yourself if your answer is right or not :)
 
  • #8
Im still not sure.Confused??
 
  • #9
520 m/s is much larger than the speed of sound in room temperature, therefore you'd expect a much higher temperature as well. -31 Celcius is well below room temperature, so it is clearly wrong. It is not even in your 'reasonable' range of 10-20 C.

First you should calculate the speed of sound again. What is the distance that the sound wave travels in one oscillation? It's not 36 cm.
 
  • #10
Given: f= 1445 Hz.
Length= 0.36m (36 cm is converted)
Required: v and vs
Analysis: v=f(lambda)
Solution:
Lambda=2l/n
=2(.36m)3
=0.24m
v= (1445Hz)(0.24)
V= 346.8m/s
Now we can find the temperature:
Analysis: T= vs-332m/s
0.60
= 346.8-332/0.6
= 24.7
is it correct now?
 
  • #11
Help please!Is the above Answer correct?
 

1. How is air temperature related to frequency of sound?

The speed of sound in air is directly proportional to the air temperature. As the air temperature increases, the speed of sound also increases. This means that higher air temperatures will result in a higher frequency of sound.

2. What is the formula for calculating air temperature from frequency of sound?

The formula for calculating air temperature from frequency of sound is: T = 273.15 + (v/0.606), where T is the air temperature in Kelvin and v is the frequency of sound in Hertz.

3. What are the units for air temperature and frequency of sound?

The unit for air temperature is Kelvin (K) and the unit for frequency of sound is Hertz (Hz).

4. Can this calculation be used for any type of sound?

No, this calculation is specifically for the speed of sound in air. Other factors, such as altitude and humidity, can also affect the speed of sound and therefore the calculation may not be accurate for other types of sound.

5. Is this calculation affected by changes in air pressure?

Yes, air pressure can also affect the speed of sound and therefore the calculation. However, for small changes in air pressure, the impact on the calculation is minimal.

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