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Q.

A 100 Hz sinusoidal wave is travelling in the positive x-direction along a string with a linear mass density of $3.5 \times 10^{- 3} k g m^{- 1}$ and a tension of 35N. At time t=0, the point x=0 has zero displacement and the slope of the string is $\frac{π}{20} .$ Then select the wrong alternative.

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a

velocity of wave is 100m/s

b

angular frequency is $(200 π) r a d / s$

c

Amplitude of wave is 0.025m

d

propagation constant is $(4 π) m^{- 1}$

answer is D.

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Detailed Solution

$v = \sqrt{\frac{T}{μ}} = \sqrt{\frac{35}{3.5 \times 10^{- 3}}} = 100 m / s, λ = \frac{v}{f} = 1 m ∴ k = \frac{2 π}{λ} = (2 π) m^{- 1}$
And $ω = v \times k = (200 π) r a d / s$
At x=0, $v_{p} =maximum$
Particle velocity = wave velocity slope
$∴ A = \frac{s l o p e \times w a v e v e l o c i t y}{ω} = \frac{(\frac{π}{20}) \times (100)}{20 π} = 0.025 m$

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A 100 Hz sinusoidal wave is travelling in the positive x-direction along a string with a linear mass density of 3.5×10−3kgm−1 and a tension of 35N. At time t=0, the point x=0 has zero displacement and the slope of the string is π20. Then select the wrong alternative.