A marine siren consists of a cylinder 72 cm in length closed at one end.for sound through air at 336 m/s. find the lowest frequency of the siren

.72 meters = (1/4) wavelength

but wavelength = c T = c/f
so
4(.72) = 336/f

f = 336/2.88

f = 117 Hz

see: http://www.physicsclassroom.com/class/sound/Lesson-5/Closed-End-Air-Columns

To find the lowest frequency of the siren, we need to consider the standing waves that can form in the cylinder.

In a closed cylinder, the lowest frequency corresponds to the longest wavelength that can fit within the cylinder length. This wavelength is twice the length of the cylinder (λ = 2L), as the wave needs to travel from one end of the cylinder to the other and back to form a standing wave pattern.

Given that the cylinder length (L) is 72 cm (or 0.72 m), we can use the formula to find the wavelength:

λ = 2L = 2 * 0.72 m = 1.44 m

The speed of sound through air is given as 336 m/s.

The frequency (f) of a wave is related to the speed of sound (v) and its wavelength (λ) by the formula: v = f * λ.

Rearranging the formula, we can solve for f:

f = v / λ = 336 m/s / 1.44 m = 233.3 Hz

Therefore, the lowest frequency of the marine siren is approximately 233.3 Hz.