Respuesta :
Answer:
The amplitude of the resultant wave are
(a). 0.0772 m
(b). 0.0692 m
Explanation:
Given that,
Frequency = 135 Hz
Wavelength = 2 cm
Amplitude = 0.04 m
We need to calculate the angular frequency
[tex]\omega=2\pi f[/tex]
[tex]\omega=2\times\pi\times135[/tex]
[tex]\omega=848.23\ rad/s[/tex]
As the two waves are identical except in their phase,
The amplitude of the resultant wave is given by
[tex]y+y=A\sin(kx-\omega t)+Asin(kx-\omega t+\phi)[/tex]
[tex]y+y=A[2\sin(kx-\omega t+\dfrac{\phi}{2})\cos\phi\dfrac{\phi}{2}[/tex]
[tex]y'=2A\cos(\dfrac{\phi}{2})\sin(kx-\omega t+\dfrac{\phi}{2})[/tex]
(a). We need to calculate the amplitude of the resultant wave
For [tex]\phi =\dfrac{\pi}{6}[/tex]
The amplitude of the resultant wave is
[tex]A'=2A\cos(\dfrac{\phi}{2})[/tex]
Put the value into the formula
[tex]A'=2\times0.04\cos(\dfrac{\pi}{12})[/tex]
[tex]A'=0.0772\ m[/tex]
(b), We need to calculate the amplitude of the resultant wave
For [tex]\phi =\dfrac{\pi}{3}[/tex]
[tex]A'=2\times0.04\cos(\dfrac{\pi}{6})[/tex]
[tex]A'=0.0692\ m[/tex]
Hence, The amplitude of the resultant wave are
(a). 0.0772 m
(b). 0.0692 m
