Answer to Question #231857 in Mechanics | Relativity for hassan

Question #231857

a sound wave has a wavelength of 0.20m. what is the phase difference between two points on wire which are 0.65m apart


1
Expert's answer
2021-09-03T08:24:56-0400

We can relate the wavelength λ\lambda with the displacement difference between the points Δx\Delta x and the phase difference Δϕ\Delta \phi with the following equation:


λ=2πΔxΔϕ    Δϕ=2πΔxλ\lambda=\cfrac{2\pi \Delta x}{\Delta \phi} \implies \Delta \phi=\cfrac{2\pi \Delta x}{\lambda}


We substitute and find the phase difference in radians:

Δϕ=2πΔxλ=2π(0.65m)0.20m=6.5πrad=1170\Delta \phi=\cfrac{2\pi \Delta x}{\lambda}=\cfrac{2\pi (0.65\,m)}{0.20\,m}= 6.5\pi\,rad=1170^{\circ}


In conclusion, the phase difference Δϕ\Delta \phi is 6.5π\pi radians or 1170°.


Reference:

  • Sears, F. W., & Zemansky, M. W. (1973). University physics.

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Comments

hassan
03.09.21, 23:02

great work thanks alot

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