Answer
(a) The wavelength is $1.2~m$
(b) The next larger value of $L$ is $0.90~m$
(c) $v = 338.4~m/s$
Work Step by Step
(a) The smallest value of $L$ which produces resonance will be at the fundamental frequency. We can find the wavelength:
$\lambda = 4L = (4)(0.30~m) = 1.2~m$
The wavelength is $1.2~m$
(b) The next larger value that will produce resonance will be the third harmonic. We can find the next larger value of $L$:
$\frac{4L}{3} = 1.2~m$
$L = \frac{(3)(1.2~m)}{4}$
$L = 0.90~m$
The next larger value of $L$ is $0.90~m$
(c) We can find the speed of sound in the tube:
$v = \lambda~f$
$v = (1.2~m)(282~Hz)$
$v = 338.4~m/s$
