If the amplitude is 200, the intensity is 300. When the amplitude is increased to 800, then what will be the intensity?

Explanation

We know that The intensity of a wave is directly proportional to the square of its amplitude Mathematically-> I x a2HereI = intensitya = amplitudeAccording to the question, we are asked to find the new intensity given that If the amplitude is 200, the intensity is 300. When the amplitude is increased to 800HenceI = 300a = 200a' = 800Increase in amplitude (A)-> A = a'/aHence-> A = 800/200On further simplificationWe get-> A = 4Increase in amplitude (squared)-> A2 = 42-> A2 = 16Amplitude squared increases by a factor of 16-> I' = I x A2HereI' = new intensityI = initial intensityA² = squared amplitude factorIf the amplitude is 200, the intensity is 300. When the amplitude is increased to 800.HenceI = 300 We found out thatA² = 16Substituting the values-> I' = 300 x 16On further simplification-> I' = 4800HenceNew intensity = 4800When the amplitude is increased to 800 then the intensity will be 4800.