Question

A wave disturbance in a medium is described by $y(x,t)=0.02cos(50\pi t+\frac{\pi }{2})cos\left(10\pi x\right)$where x and y are in meter and t is in second. Then

• A. First node occurs at x = 0.15m
• B. First antinode occurs at x = 0.3 m
• C. The speed of interfering waves is 5.0 m/s
• D. The wavelength is 0.2 m

Answer 1

Answer: (C), (D)

The correct options are
C The speed of interfering waves is 5.0 m/s
D The wavelength is 0.2 m

$y(x,t)=0.02cos(50\pi t+\frac{\pi }{2})cos\left(10\pi x\right)\equiv Acos(\omega t+\frac{\pi }{2})$

Node occurs when kx = $\frac{\pi }{2}\Rightarrow 10\pi x=\frac{\pi }{2}\Rightarrow$ x = 0.05 m

Antinode occurs when kx = $\pi \Rightarrow 10\pi x=\pi \Rightarrow$ x = 0.1 m

Speed of wave (v) = $\frac{\omega }{k}=\frac{50\pi }{10\pi }$ = 5 m/s

Wavelength $\left(\lambda \right)=\frac{2\pi }{k}$ = 0.2 m

$\therefore$ (C) and (D)