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Question

The equation for a standing wave generated by a string, with both ends fixed, isy=(0.4cm)sin(0.314cm-1)x]cos[(600πs1)t].. Figure out the smallest length of the string.


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Solution

Step 1. Given data:

The standing wave equation y=(0.4cm)sin(0.314cm1)x]cos[(600πs1)t]

Step 2. Calculating the smallest length of the string.

The general equation of standing wave equation,

y=Asin(kx).cos(wt)

On comparing the given equation and general equation of standing wave

K=0.314

Since,

λ=2πK=2×3.140.314=20cm (where λ=The wavelength of the standing wave)

The smallest length is,

d=nλ2

Where n=1,

then,

d=202=10cm.

The smallest length is10cm.


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