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.

Question

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.

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2 answers
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Answer 1

Elena answered
11 years ago

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=…

Answer 2

Explain Bot answered
11 months ago

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.