Sound vibrations with frequency v = 0.2 kHz and amplitude of 0.5 mm are propagating in an elastic medium. A wave length is 50 cm. Find the velocity of the wave and maximum velocity of the particles of medium.
To find the velocity of the wave, we can use the formula:
velocity (v) = frequency (f) * wavelength (λ)
Given that the frequency (v) is 0.2 kHz and the wavelength (λ) is 50 cm, let's convert the frequency to Hz and the wavelength to meters:
0.2 kHz = 0.2 * 1000 Hz = 200 Hz
50 cm = 50 / 100 = 0.5 m (since 1 meter = 100 cm)
Now, we can substitute the values into the formula:
velocity (v) = 200 Hz * 0.5 m = 100 m/s
So, the velocity of the wave is 100 m/s.
To find the maximum velocity of the particles of the medium, we can use the formula:
maximum velocity = amplitude (A) * angular frequency (ω)
Given that the amplitude (A) is 0.5 mm, we need to convert it to meters:
0.5 mm = 0.5 / 1000 = 0.0005 m (since 1 meter = 1000 mm)
The angular frequency (ω) can be calculated using the formula:
angular frequency (ω) = 2π * frequency (f)
Let's calculate the angular frequency:
angular frequency (ω) = 2π * 200 Hz ≈ 1257.0 rad/s
Now, substitute the values into the formula:
maximum velocity = 0.0005 m * 1257.0 rad/s ≈ 0.6285 m/s
Therefore, the maximum velocity of the particles of the medium is approximately 0.6285 m/s.