Vibration of the dishwasher causes standing waves in a cup. crests form four concentric rings and the diameter of the cup is 6.0cm v=1.5m/x . What is the frequency of the vibrations?
To determine the frequency of the vibrations causing the formation of standing waves in the cup, we first need to understand the concept of standing waves.
Standing waves occur when two waves with the same frequency and amplitude traveling in opposite directions interfere with each other. In this case, the vibration from the dishwasher is causing the formation of standing waves in the cup.
Given that the crests of the standing waves form four concentric rings in the cup and the diameter of the cup is 6.0 cm, we can determine the wavelength of the standing waves.
The diameter of the cup can be used to find the circumference by using the formula C = πd, where C is the circumference and d is the diameter.
C = π * 6.0 cm
C ≈ 18.85 cm
Since the standing waves form four concentric rings, each ring represents half a wavelength. Therefore, the wavelength (λ) can be found by dividing the circumference by four since there are four rings.
λ = C/4
λ = 18.85 cm / 4
λ ≈ 4.71 cm
Now that we have the wavelength, we can use the wave equation v = fλ to find the frequency (f) of the vibrations. Here, v is the speed of the wave, and it is given as 1.5 m/s (which can also be expressed as 150 cm/s).
v = fλ
150 cm/s = f * 4.71 cm
Now, we can rearrange the equation to solve for the frequency:
f = v/λ
f = 150 cm/s / 4.71 cm
f ≈ 31.89 Hz
So, the frequency of the vibrations causing the standing waves in the cup is approximately 31.89 Hz.