An air-filled cavity for producing electromagnetic standing waves has two parallel, highly conducting walls separated by a distance L. One standing-wave pattern in the cavity produces nodal planes of the electric field with a spacing of 1.50 cm. The next-higher-frequency standing wave in the cavity produces nodal planes with a spacing of 1.25 cm. What is the distance L between the walls of the cavity?



Answer :

The cavity produces nodal planes of the electric field with a spacing of 1.50 cm. The distance L between the walls of the cavity is 7.5cm.

The general formula for both ends closed is (n+1) λ/2

Let's say for n, [tex]\frac{\pi }{2} n = 1.5 = \pi = 3cm[/tex]

for (n+1), λ(n+1)/2 = 1.25 = λ(n+1) = 2.5cm

∴ (n+1) (1.5) = (n+2)(1.25) = n = 4

∴  L = (4+1)(3/2) = L = 7.5cm.

Electromagnetic waves, or EM waves, are waves produced by oscillations between electric and magnetic fields. In other words, EM waves consist of oscillating magnetic and electric fields. Gamma rays have the highest frequencies in the electromagnetic spectrum.

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