A 1.40-m long gas column that is open at one end and closed at the other end has a fundamental resonant frequency 80.0 Hz. What is the speed of sound in this gas? 28.0 m/s 228 m/s 448 m/s 112 m/s 57.1 m/s

The correct answer to the question is

448 m/s

Explanation:

The fundamental frequency is the lowest resonant frequency of a vibration. The nature of a standing wave in a tube with one end closed which is at the the fundamental frequency is to have the node of the wave at the closed end and the wave anti-node at the opened end making a quarter of the wavelength.

Therefore the length of the gas column, 1.40 m = λ/4

So that λ = 4 * 1.4 = 5.6 m

Therefore from v = fλ

Where

f = frequency = 80. o Hz

v = wave speed

we have the wave speed v = 5.6*80 = 448 m/s