A transverse harmonic wave on a string is given by
y(x,t) = 5 sin (6t + 0.003x)
where x and y are in cm and t in sec. The wave velocity is _______________ ms⁻¹.

Solution

Physics sir · 3 steps

Read ω off the t term and k off the x term, then v = ω/k. Just watch the centimetres.

1. Compare with standard form. A harmonic wave is y = A sin(ω t + kx). Matching terms gives ω = 6 rad s⁻¹ and k = 0.003 rad cm⁻¹, because x is in cm.

   v = ω/k = 6/0.003 cm s⁻¹ = 2000 cm s⁻¹

2. Convert units. Since 100 cm = 1 m, 2000 cm s⁻¹ = 20 m s⁻¹. The plus sign between the terms only tells you the wave moves along -x. It does not change the speed.
3. So. The wave velocity is 20 m s⁻¹.

The common slip: 2000. Leaving the answer in cm per second gives 2000, not 20. Divide by 100 to get m s⁻¹.

The idea to keep. Wave speed is the coefficient of t divided by the coefficient of x. Always check what unit x is in before you report the answer.

Answer from the NTA final answer key. Solution by PrepWiser.