Question

The following two traveling waves are superposed to create a standing wave:

phi1 = (2.7 cm)sin((1.45 cm^-1)x - (9.7 s^-1)t)

phi2 = (2.7 cm)sin((1.45 cm^-1)x + (9.7 s^-1)t)

a) what is the resulting amplitude of the standing wave?

b) what is the resulting wavelength of the standing wave?

c) what is the resulting angular frequency of the standing wave?

Answer 1

apply trignometic relation

sinc +sind= 2*sin[( c+d) /2] *cos [(c-d)/2]

= (2.7 cm)sin((1.45 cm^-1)x - (9.7 s^-1)t) + (2.7 cm)sin((1.45 cm^-1)x + (9.7 s^-1)t)

= 2.7 [ sin((1.45 cm^-1)x - (9.7 s^-1)t) + sin((1.45 cm^-1)x + (9.7 s^-1)t) ]

= 2.7 [ 2* sin [ ( 1.45x-9.7t +1.45+9.7t) /2] *cos [ ( 1.45x-9.7t +1.45+9.7t) /2]

= 2.7 *[ 2 sin ( 1.45x )*cos( 9.7*t)  

Y = 5.4*sin ( 1.45x )*cos( 9.7*t)  

compare it with

Y= Asinkx*cosωt

a)

amplitude = 5.4 cm

b)

v= ω​​A

f*λ​ = ​ω​​A

f*λ​ = 2pi*f *A

λ​ = 2pi*A = 2pi *5.4 =33.9292007 cm answer

c)

ω​ = 9.7 rad/s

let me know in a comment if there is any problem or doubts