Measuring sound velocity from a P-T graph?

In summary, the conversation discusses the concept of measuring the velocity of sound by plotting a graph of position vs. flight time and calculating the slope of the graph. The slope represents the velocity of sound and it is recommended to use multiple measurements for more accurate results.
  • #1
apeldoorn
1
0
I don't have any specific numerical values for this, as it's a general question, but hopefully I explain it well enough using only words:

If you plot a graph of position vs. flight time (of a sound pulse, for example), what is the slope of that graph going to be? (That is, what does the slope represent?)

Also, if you were to calculate the slope of a position-time graph, how would you determine the velocity of sound from that calculated information? (I believe that you can theoretically do that, right?) I've heard that can't you calculate the velocity of sound by taking a single measurement and dividing the time of flight into the total distance the sound pulse travel, but I'm not exactly clear as to why.

If anyone has any response to either of those questions, I'd very much appreciate your insight.
 
Physics news on Phys.org
  • #2
You can measure speed of sound in a medium by measuring propagation time of a pulse over a known distance. This will be the group velocity. For a non-dispersive medium it will be equal to the phase velocity as well.
As for any measurement, it is better to use several measurements rather than just one.
You can vary the distance and measure the corresponding times, for example from the slope of the d-t graph representing your results.
 

1. How do you measure sound velocity from a P-T graph?

In order to measure sound velocity from a P-T graph, you need to first plot the pressure (P) and temperature (T) data points on a graph. Then, calculate the slope of the line connecting these data points. This slope represents the change in pressure over the change in temperature, which is known as the adiabatic constant (K). Finally, use the formula v = √(K/ρ), where v is the sound velocity and ρ is the density, to calculate the sound velocity at that specific point on the P-T graph.

2. What is the significance of measuring sound velocity from a P-T graph?

Measuring sound velocity from a P-T graph can provide valuable information about the physical properties of a substance, such as its density and adiabatic constant. This can be helpful in various fields of science, including geology, meteorology, and material science. It can also be used to understand the behavior of different substances under different temperature and pressure conditions.

3. Can sound velocity be measured at any point on a P-T graph?

No, sound velocity can only be accurately measured at points where the data points on the P-T graph form a straight line. This is because the formula used to calculate sound velocity relies on the slope of this line. If the data points do not form a straight line, the calculated sound velocity will not be accurate.

4. How does the sound velocity change with temperature and pressure?

The sound velocity generally increases with increasing temperature and pressure. This is because as temperature and pressure increase, the molecules in a substance are more closely packed together, resulting in a higher density and faster sound velocity. However, this relationship is not linear and can vary depending on the substance and its physical properties.

5. Are there any limitations to measuring sound velocity from a P-T graph?

Yes, there are some limitations to measuring sound velocity from a P-T graph. As mentioned earlier, the data points must form a straight line for accurate measurements. Additionally, this method is only applicable for substances that follow the ideal gas law, meaning that they behave like an ideal gas at different temperatures and pressures. Real substances may deviate from this behavior, resulting in less accurate measurements.

Similar threads

B Kinematic equations ##\textbf{purely}## from graphs
    • Mechanics
2
Replies
49
Views
1K
B What sound frequencies can pass through a hole in a wall?
    • Mechanics
Replies
31
Views
712
Position vs. time graph and the derivative
    • Mechanics
Replies
5
Views
2K
Expressing Elliptic Orbitals As Speed Functions.
    • Mechanics
Replies
2
Views
836
Why Are My Newton's Rings Experiment Results Inconsistent?
    • Mechanics
Replies
5
Views
11K
Amplitudes of longitudinal sound waves
    • Mechanics
Replies
8
Views
2K
Quick Question about Pendulum Graphs
    • Mechanics
Replies
8
Views
5K
I How is the damping of sound (over distance) affected by air properties?
    • Classical Physics
Replies
8
Views
1K
Is Velocity Equal to a*t in an Acceleration vs Time Graph?
    • Mechanics
Replies
3
Views
1K
Can I determine mass & spring k from graph of wave, t, a, & vectors?
    • Mechanics
Replies
1
Views
981

Hot Threads

Recent Insights

Back
Top