Manipal MET2015PhysicsOscillations
A sinusoidal wave travelling in the positive direction on stretched string has amplitude 20 cm , wavelength 1 m and wave velocity 5 ~m / s . At x=0 and t=0 , it is given that y=0 and d y d t 0 . Find the wave function y(x, t) .
Options
- Ay(x, t)=(0.02 m) [ (2 ~m ⁻¹ ) x+ (10 ~s ⁻¹ ) t ] m
- By(x, t)=(0.02 m) [ (10 ~s ⁻¹ ) t+ (2 ~m ⁻¹ ) x ] m
- Cy(x, t)=(0.02 m) [ (2 ~m ⁻¹ ) x- (10 ~s ⁻¹ ) t ] m
- Dy(x, t)=(0.02 ~m ) [ ( m ⁻¹ ) x+ (5 ~s ⁻¹ ) t ] m
Correct answer
C. y(x, t)=(0.02 m) [ (2 ~m ⁻¹ ) x- (10 ~s ⁻¹ ) t ] m
Step-by-step solution
We start a general form for a rightward moving wave, y(x, t)=A (k x- t+ ) ...(i) The given amplitude is A=2 ~cm =0.02 ~m The wavelength is given as =1 ~m Wave number =k=2 / =2 ~m ⁻¹ Angular frequency, =v k=10 rad / s From Eq. (i), aligned y(x, t) & =(0.02) [2 (x-5 t)+ ] For x & =0, t=0 y & =0 and y t 0 aligned i.e. 0.02 =0 (as y=0 ) and -0.2 0 From these conditions, we may conclude that =2 n , where n=0,2,4,6, Therefore, y(x, t)=(0.02 ~m ) [ (2 ~m ⁻¹ ) x - (10 ~s ⁻¹ ) t ] m