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Question

Two identical transverse sinusoidal waves travel in opposite directions along a string. The speed of transverse waves in the string is 0.5 cm/s. Each has an amplitude of 3.0 cm and wavelength of 6.0 cm. The equation for the resultant wave is

A
y=6sin(πt6)cos(πx3)
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B
y=6sin(πx3)cos(πt6)
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C
Both (a) and (b) may be correct
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D
Both (a) and (b) are wrong
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Solution

The correct option is C Both (a) and (b) may be correct
Standing wave will be formed by their superposition.
So,
Wave number, k=2πλ=2π6=π3 cm1
Angular frequency,
ω=v×k=0.5×π3=π6 s1
Maximum amplitude of standing wave,
Amax=2A=6 cm
On putting above data in standard equations of standing wave,
y=2Asin(ωt)cos(kx)
y=2Acos(ωt)sin(kx), we get,
y=6sin(πt6)cos(πx3)
y=6sin(πx3)cos(πt6)
Both forms may be possible.
Exact form will depends on initial condition of string.

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