The equation of a simple harmonic wave is given by y = 5 sin (π /2) (100 t - x), where x and y are in metre and time is in second. The period of the wave in second will be

Question

The equation of a simple harmonic wave is given by y = 5 sin (π /2) (100 t - x), where x and y are in metre and time is in second. The period of the wave in second will be (A) 0.04 (B) 0.01 (C) 1 (D) 5

Tardigrade Admin · Accepted Answer

The given equation is y=5 sin (π /2)(100t-x) ...(i) Comparing Eq. (i) with standard wave equation, given by y=A sin (ω t-kx) ...(ii) we have ω =(100π /2)=50π ⇒ (2π /T)=50π ⇒ T=(2π /50 π )=0.04 s

Q. The equation of a simple harmonic wave is given by y = 5 sin $\frac{π}{2}$ (100 t - x), where x and y are in metre and time is in second. The period of the wave in second will be

0.04

0.01

1

5

The given equation is $y = 5 sin \frac{π}{2} (100 t - x)$ ...(i) Comparing Eq. (i) with standard wave equation, given by $y = A sin (ω t - k x)$ ...(ii) we have $ω = \frac{100 π}{2} = 50 π$ $\Rightarrow$ $\frac{2 π}{T} = 50 π$ $\Rightarrow$ $T = \frac{2 π}{50 π} = 0.04 s$

Q. The equation of a simple harmonic wave is given by y = 5 sin 2π​ (100 t - x), where x and y are in metre and time is in second. The period of the wave in second will be

0.04

0.01

1

5

The given equation is y=5sin2π​(100t−x) ...(i) Comparing Eq. (i) with standard wave equation, given by y=Asin(ωt−kx) ...(ii) we have ω=2100π​=50π ⇒ T2π​=50π ⇒ T=50π2π​=0.04s

Q. The equation of a simple harmonic wave is given by y = 5 sin $\frac{π}{2}$ (100 t - x), where x and y are in metre and time is in second. The period of the wave in second will be

The given equation is $y = 5 sin \frac{π}{2} (100 t - x)$ ...(i) Comparing Eq. (i) with standard wave equation, given by $y = A sin (ω t - k x)$ ...(ii) we have $ω = \frac{100 π}{2} = 50 π$ $\Rightarrow$ $\frac{2 π}{T} = 50 π$ $\Rightarrow$ $T = \frac{2 π}{50 π} = 0.04 s$