The period of longitudinal sinusoidal wave is 0.16 seconds and its wavelength is 8.0 meters. Calculate the wave's speed, frequency, angular frequency and wave number.
T=0.16 s, λ=8 m
λ=vT
v= λ/T= 8/0.16 =50 m/s
f=1/T=1.0.16 =6.25 Hz
ω=2πf =…
k=2π/ λ=…
To calculate the wave's speed, frequency, angular frequency, and wave number, we can use the formulas relating these quantities. Let's break down the calculations step by step.
1. Speed (v): The speed of a wave can be calculated using the formula:
v = λ * f
where v is the speed, λ (lambda) is the wavelength, and f is the frequency.
Given:
λ = 8.0 meters
f = 1 / T (T is the period)
T = 0.16 seconds
f = 1 / 0.16 = 6.25 Hz
v = 8.0 * 6.25 = 50.0 meters per second
Therefore, the wave's speed is 50.0 m/s.
2. Frequency (f): We have already calculated the frequency above. It is 6.25 Hz.
3. Angular Frequency (ω): The angular frequency is the rate of change of the phase in radians per second. It can be calculated using the formula:
ω = 2πf
where ω (omega) is the angular frequency, and f is the frequency.
ω = 2π * 6.25 = 39.25 radians per second
Therefore, the wave's angular frequency is 39.25 rad/s.
4. Wave Number (k): The wave number represents the number of wavelengths per unit distance. It can be calculated using the formula:
k = 2π / λ
where k is the wave number, and λ (lambda) is the wavelength.
k = 2π / 8.0 = π / 4 ≈ 0.7854 per meter
Therefore, the wave's wave number is approximately 0.7854 per meter.