Answer
The temperature inside the pipe is $41.7^{\circ}C$
Work Step by Step
To find the correct harmonic, we can let the speed of sound in air be $343~m/s$:
$\lambda_n = \frac{v}{f_n}$
$\frac{2L}{n} = \frac{v}{f_n}$
$n = \frac{2L~f_n}{v}$
$n = \frac{(2)(2.0~m)(702~Hz)}{343~m/s}$
$n = 8.2$
Since this value is close to $8$, we can assume that the experiment uses the 8th harmonic. We can find the speed of sound inside the pipe:
$v = \lambda_8~f_8$
$v = \frac{2L}{8}~f_8$
$v = \frac{(2)(2.0~m)}{8}~(702~Hz)$
$v = 356~m/s$
We can find the temperature inside the pipe:
$331+0.6~T = 356$
$T = \frac{356-331}{0.6}$
$T = 41.7^{\circ}C$
The temperature inside the pipe is $41.7^{\circ}C$
