How Does Temperature Affect the Speed of Sound?

AI Thread Summary
The speed of sound in air is directly related to the square root of the absolute temperature, with a known speed of 343 m/s at 20 °C. To find the speed of sound at -10 °C, the correct method involves using the proportionality without calculating an intermediate constant. The calculated speed of sound at -10 °C is approximately 324.92 m/s. The discussion emphasizes the importance of understanding proportional relationships rather than unnecessary calculations. This approach is crucial for exam success in physics.
chawki
Messages
504
Reaction score
0

Homework Statement


The speed of sound in the air is proportional to the square root of the absolute temperature. At 20 °C the speed of sound is 343 m/s.

Homework Equations


What is the speed of sound at –10 °C? (0 °C = 273 K).


The Attempt at a Solution


speed of sound= x*\sqrt{}T
x*\sqrt{}293.15=343m/s
x=20.03

so the speed of sound at -10 C (263.15K) is: 20.03*\sqrt{}263.15 = 324.92m/s.
 
Physics news on Phys.org
hi chawki! :smile:

your answer is correct, and your method works, but it will lose you marks in the exam

you do not need to find the value of x …

the whole point of questions like this is to see whether you understand this point

you have done this in two steps: you found x, and then you eliminated x …

that is a waste of time (and introduces an opportunity for error)

the correct method (to be used in all "proportionality" cases) is:

speed at -10° C (263.17° K) = 343 x √(263.15)/√(293.15) = 324.92​
 
Ah the yellow fish again :P
Thank you for your help tiny-tim :)
I try to understand your method
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Struggle to understand the concept of the question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

Kinematics/speed of sound question
Replies
3
Views
3K
Are the 2nd and 3rd problems in this video correctly solved? (charged dipole and organ pipe problems)
Replies
3
Views
1K
Depth of a well (using speed of sound)
Replies
6
Views
3K
Wavelength of the sounds at zero degrees
Replies
7
Views
6K
Speed of Sound using a Resonant tube
Replies
12
Views
4K
Measuring the Speed of Sound: Examining the Frequency of Clicks
Replies
3
Views
4K
Sound Waves in Different Mediums
Replies
3
Views
2K
Calculating Wavelength in a Medium with Different Speed of Sound
Replies
4
Views
1K
Sound Interference Problem -- Observer moving between two speakers
Replies
3
Views
4K
Frequency of Reflected Underwater Sound Wave
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top