# How to graph a linear relationship between T and v of sound?

• Banker
In summary, the student conducted an experiment to measure the speed of sound at different temperatures. They used two microphones at a fixed distance and measured the time taken for sound to travel between them. They attempted to create a graph with a straight line relationship and used the equations v=d/t and v=331+0.6T to calculate the speed of sound. However, their results did not match the standard equation of v=331.4+0.6T and they question the accuracy of their experiment. After discussing possible sources of error, they have concluded that their equation is 164+3.07T with an uncertainty of plus or minus 1.30 for the gradient and plus or minus 44.8 for the y
Banker

## Homework Statement

I did an experiment involving the speed of sound at different temperatures. I placed two microphones at a fixed distance apart and I measured the time taken for a sound wave to travel between the two mics. I repeated this for different temperatures. I want to make a graph for my results, but I want a straight line relationship.

## Homework Equations

v=d/t , v = 331 + 0.6T

## The Attempt at a Solution

I could manually work out speed using v=d/t and plot v against the Temperature, T. However I do not know if this will give me a straight line. Or I can also plot the time against the temperature.
Extra question: in both cases, will the gradient be of any use to me?

Banker said:
I could manually work out speed using v=d/t and plot v against the Temperature
Why hesitate ? Make the plot and post if you have questions !

Alright, I plotted speed of sound against temperature in Kelvin. I tried to replicate the formula v = 331 +0.6T
Mine went horribly wrong. I got v = -675 + 3.07T

My telepathic capabilities are sufficient to suspect a mistake but to actually help out more information is necessary ...

I calculated the speed of sound using v=d/t where d is the fixed distance between each of the two mics and t is the time taken for the sound wave to travel between them(fast timer was used). I plotted this and their respective temperatures(in K).

So you measured 163 m/s at 0 ##^\circ##C, 224 at 20 ##^\circ##C and 286 at 40 ##^\circ##C ?

I only measured the speed at five intervals between 25 and 40 degrees celsius. The line I found is Excel's best fit line, but yes, I recorded something similar to 286 for 40 degrees.

Banker said:

## Homework Statement

I did an experiment involving the speed of sound at different temperatures. I placed two microphones at a fixed distance apart and I measured the time taken for a sound wave to travel between the two mics. I repeated this for different temperatures. I want to make a graph for my results, but I want a straight line relationship.

## Homework Equations

v=d/t , v = 331 + 0.6T

## The Attempt at a Solution

I could manually work out speed using v=d/t and plot v against the Temperature, T. However I do not know if this will give me a straight line. Or I can also plot the time against the temperature.
Extra question: in both cases, will the gradient be of any use to me?

Do you have any reason to suppose the relationship should be a straight line?

I found the equation online(v = 331.4 +0.6T). That is similar to y=mx + c, the equation of a straight line. So I am going under the assumption that that is what my results should mirror.

Banker said:
v = 331 + 0.6T
Yes, this is a common expression. But T is in ##^\circ##C, not Kelvin.

Ahh. I misinterpreted a graph I saw online and thought I had to convert into K.
I plot another graph and this time I got the result v = 164 + 3.07T

Yes, the slope doesn't change if you add a constant to the abscissa.

Banker
So how would I conclude my experiment? Because obviously my results don't fall in line with the standard. Is it scientifically accurate to call this experiment 'inaccurate'?

Banker said:
I recorded something similar to 286 for 40 degrees.
You don't show your observations -- at least from an earlier post I understand that the 'similar to 286 m/s' is the outcome of a calculation -- so it's hard to comment. For you it will also be hard to backtrack to find out if something went wrong.

In itself that is a very valuable learning experience: evaluate while doing the measurements so you can change things / do extra checks if results are not as expected.

Since the speed of sound is expected to be well above 300 m/s, a result below needs scrutinizing. Distance between microphones ? Time difference ? Path of the sound ?
It would be well worth it to place the microphones further apart to see if the calculated ##\Delta x\over \Delta t## is really independent of ##\Delta x##. If that isn''t the case the (much harder?) effort to vary the temperature isn't very useful.

Banker said:
Is it scientifically accurate to call this experiment 'inaccurate'
Hard to say without further info. If your distance measurement has an accuracy of 10% and your delta time measurement also, a deviation of the "litterature value" of 355 - 286 = 70 m/s is not exceptional, but if both are supposed to be about 1% you have a problem.

I worked out the uncertainty in my gradient and y-intercept using the parallelogram method and my final answer is 164+ 3.07T, with the uncertainty in gradient being plus or minus 1.30 and the uncertainty in the y-intercept being plus or minus 44.8. So the closest I could get to the actual equation is 208.8 + 1.77T.

## 1. What is the formula for graphing a linear relationship between T and v of sound?

The formula for graphing a linear relationship between T and v of sound is T = 1/v, where T represents the period of the sound wave and v represents the velocity of the sound wave. This formula can be rearranged to v = 1/T, depending on the desired orientation of the graph.

## 2. What units should be used when graphing a linear relationship between T and v of sound?

The units used for T and v will depend on the specific measurements being taken. T is typically measured in seconds, while v can be measured in meters per second or other units of distance per unit of time. It is important to ensure that the units for T and v are consistent in order to accurately graph the linear relationship.

## 3. What is the purpose of graphing a linear relationship between T and v of sound?

The purpose of graphing a linear relationship between T and v of sound is to visually represent the relationship between these two variables. This can help scientists to better understand and analyze the behavior of sound waves, and can also be used to make predictions or calculations based on the data.

## 4. How do you interpret a graph of a linear relationship between T and v of sound?

When graphing a linear relationship between T and v of sound, the slope of the line represents the inverse of the velocity of the sound wave. This means that a steeper slope indicates a higher velocity, while a shallower slope indicates a lower velocity. The y-intercept of the graph represents the period of the sound wave, or the time it takes for one complete cycle.

## 5. Are there any limitations to graphing a linear relationship between T and v of sound?

While graphing a linear relationship between T and v of sound can provide valuable insights and information, it is important to note that there may be other factors at play that could affect the relationship. For example, the medium through which the sound is traveling or the frequency of the sound wave may also impact the velocity and period. It is important to consider these potential limitations when interpreting the graph.

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