The equation of wave is given by
Y=10⁻² sin 2 π(160 t-0.5 x+π / 4)
where x and Y are in m and t in s. The speed of the wave is ________ km h⁻¹.

Solution

Physics sir · 4 steps

Read the coefficients of t and x, take their ratio for the speed, then convert m/s to km/h.

1. Open the bracket. Multiply the 2π into each term: Y = 10⁻²sin(320π t - π x + π²/2). Compare this with Y = A sin(ω t - kx + φ).
2. Read ω and k. The coefficient of t gives ω = 320π rad s⁻¹. The coefficient of x gives k = π rad m⁻¹. The phase constant does not affect the speed.

   v = ω/k = 320π/π = 320 m s⁻¹

3. Convert units. 1 m s⁻¹ = 3600/1000 km h⁻¹ = 3.6 km h⁻¹, so v = 320 × 3.6 km h⁻¹.
4. So. The speed of the wave is 1152 km h⁻¹.

The common slip: 320. Stopping at v = 320 m s⁻¹ gives 320. Multiply by 3.6 to get the speed in km h⁻¹.

The idea to keep. For any wave written as sin(ω t - kx), the speed is the coefficient of t divided by the coefficient of x. Always check which units the answer asks for.

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