A sinusoidal wave travels along a string under tension. Figure 16-31 gives the slopes along the string at time t =0 .The scale of the x axis is set by .What is the amplitude of the wave?
The amplitude of the wave is 0.2 m
The sinusoidal wave exhibits different displacements at different positions .Thus, the slope at different points varies with the position. We use this concept along with the equation of the travelling wave to calculate amplitude.
The expression of wave equation, (i)
The wavenumber of a wave, (ii)
Here, is the angular velocity of the wave and is the amplitude of the oscillation
The scale of x axis is given as 0.80 m. This distance is equivalent to two wavelengths.
Hence, the wavelength is given as:
For x=0 and t=0 , equation (i) becomes-
From the graph, the value of y at x =0 is 0.2 . So, the above equation becomes-
Thus, the amplitude of the curve given in the graph is 0.2.
Figure 16-46 shows transverse accelerationversus time t of the point on a string at x=0, as a wave in the form ofpasses through that point. The scale of the vertical axis is set by. What is? (Caution: A calculator does not always give the proper inverse trig function, so check your answer by substituting it and an assumed value ofintoand then plotting the function.
A sinusoidal transverse wave of amplitude and wavelength travels on a stretched cord. (a) Find the ratio of the maximum particle speed (the speed with which a single particle in the cord moves transverse to the wave) to the wave speed. (b) Does this ratio depend on the material of which the cord is made?
A standing wave results from the sum of two transverse traveling waves given by and where, x, , and are in meters and t is in seconds. (a) What is the smallest positive value of x that corresponds to a node? Beginning at t=0, what is the value of the (b) first, (c) second, and (d) third time the particle at x=0 has zero velocity?
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