The wave function for a travelling wave on a taut string is in SI units sx- t-0-350msin 10- t-3- x- -4- What is the maximum magnitude of the transverse speed of the string-

Equation of travelling wave is given by #160; #160; s(x,t) = Asin (wt kx+ ϕ) Transverse speed of wave #160; #160; V_y = dsdt V_y = 0. ...

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Standard XII

Physics

Speed in a Medium

The wave func...

Question

The wave function for a travelling wave on a taut string is (in SI units) $s (x, t) = (0.350 m) sin (10 π t - 3 π x + π / 4)$ . What is the maximum magnitude of the transverse speed of the string?

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Solution

Equation of travelling wave is given by $s (x, t) = A sin (w t - k x + ϕ)$
Transverse speed of wave $V_{y} = \frac{d s}{d t}$
$⟹ V_{y} = 0.350 \times (10 π) \times c o s (10 π t - 3 π x + \frac{π}{4})$
So maximum magnitude of transverse speed $V_{y} = 0.350 \times 10 π = 11 m / s$

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The wave function for a travelling wave on a taut string is (in SI units) s(x,t)=(0.350m)sin(10πt−3πx+π/4). What is the maximum magnitude of the transverse speed of the string?

Equation of travelling wave is given by s(x,t)=Asin(wt−kx+ϕ)Transverse speed of wave Vy=dsdt⟹ Vy=0.350×(10π)×cos(10πt−3πx+π4)So maximum magnitude of transverse speed Vy=0.350×10π=11 m/s

The wave function for a travelling wave on a taut string is (in SI units) $s (x, t) = (0.350 m) sin (10 π t - 3 π x + π / 4)$ . What is the maximum magnitude of the transverse speed of the string?

Equation of travelling wave is given by $s (x, t) = A sin (w t - k x + ϕ)$
Transverse speed of wave $V_{y} = \frac{d s}{d t}$
$⟹ V_{y} = 0.350 \times (10 π) \times c o s (10 π t - 3 π x + \frac{π}{4})$
So maximum magnitude of transverse speed $V_{y} = 0.350 \times 10 π = 11 m / s$