What are the wavelength (in meters) and frequency (in hertz) of a wave whose displacement is given by the equation y = 0.5 sin(0.20x + 120t), where x and y are in meters and t is in seconds?
A) 10 m, 0.50 Hz
B) 5.0 m, 10 Hz
C) 19 m, 120 Hz
D) 31 m, 19 Hz
E) 0.20 m, 120 $\sqrt { 2 \pi }$ Hz

Question

Quizplus · Accepted Answer

The equation for the wave can be written as:
y(x,t) = 0.5sin(0.20x + 120t)

Comparing with the standard equation for a sinusoidal wave:
y(x,t) = Asin(kx - ωt + φ)
where,
A = amplitude = 0.5 m
k = wave number = 0.20 m⁻¹
ω = angular frequency = 120 rad/s (since ωt = 120t)
φ = phase constant

The wavelength λ and frequency f of the wave can be calculated as:
λ = 2π/k = 2π/0.20 = 31.4 m
f = ω/2π = 120/2π = 19.1 Hz

Hence, the wavelength and frequency of the wave are 31 m and 19 Hz respectively. Therefore, the correct choice is D.

What Are the Wavelength (In Meters) and Frequency (In Hertz) 2π\sqrt { 2 \pi }2π​

What Are the Wavelength (In Meters) and Frequency (In Hertz) $\sqrt { 2 \pi }$