Question

Suppose a plot of inverse wavelength vs frequency has slope equal to 0.119, what is the speed of sound traveling in the tube to 2 decimal places?

Answer 1

8.40 m/s

Step-by-step explanation:

Slope of the plot is 0.119

Slope of a plot is given by the change in y direction divided by the change in x direction

Here, the y axis represents inverse wavelength and the x axis represents frequency.

f = Frequency (Hz, assumed)

v = Phase velocity (m/s, assumed)

λ = Wavelength (m, assumed)

So, slope

`m=((1)/(\lambda))/(f)`

Now,

`\lambda=(v)/(f)\\\Rightarrow \lambda^(-1)=(f)/(v)`

`\\\Rightarrow m=((f)/(v))/(f)\\\Rightarrow 0.119=(1)/(v)\\\Rightarrow v=(1)/(0.119)\\\Rightarrow v=8.40\ m/s`

The speed of sound travelling in the tube is 8.40 m/s