Do high frequency non-dispersive waves travel faster in air than low frequency n

Question

Do high frequency non-dispersive waves travel faster in air than low frequency non-dispersive waves? What is the voltage reflection coefficient at the end of an open-circuited transmission line? The transverse displacement of a string as a function of time and distance along the string is given by, x= (2 m) sin( 2 pi / 3m z - 2 pi (300/s) t) What is the amplitude of this wave? What is the wavelength of this wave? What is the frequency (in Hz) of the source of this wave? What is the speed and direction of propagation of this wave?

Explanation / Answer

A) The waves traveling through non-dispersive medium will maintain a constant shape. for the pulse that is a Gaussian function, containing multiple frequencies. Since the wave speed is constant, all frequencies travel at the same speed and the pulse maintains constant shape.

B)  reflection coefficient is +1 for a open circuited transmission line

C) Comparing given equation by x=Asin[(2pi/lambda)x-2pi*f*t)], we get

i) Amplitude A=2 m

ii) Wavelength=lambda=3m

iii) frequency f=300 Hz

iv) Speed=f*lambda=300*3=900 m/s

direction of propagation=along z-direction

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