A progressive wave travelling in a gas is given by y(x,t)=2.0 10^ -3

PHYSICS · Multi-part · A Level · Physics · Waves · Waves

Problem

A progressive wave travelling in a gas is given by y(x,t)=2.0×10−3 m  sin⁡(1.2×102 t+3.5x),y(x,t)=2.0\times10^{-3}\,\text{m}\;\sin\bigl(1.2\times10^{2}\,t+3.5x\bigr), with xx and yy in metres and tt in seconds. (i) Write down the numerical values of the angular frequency and the wave number. (ii) Using these values, calculate the wavelength, the frequency, the time period and the speed of the wave. (iii) From the mathematical form of the wave, state with justification whether it propagates along the positive or negative xx-direction. (iv) Evaluate the instantaneous displacement of the particle located at x=0.050 mx=0.050\,\text{m} at t=0.010 st=0.010\,\text{s}.

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