A water wave is generated in a ripple tank by an oscillator that vibrates 50 times in 30 seconds. A given trough of the wave travels 50.0 cm in 15 seconds. What is the wavelength of the water wave? Produce all your workings.
I got
50/30 = 1.67 vibrations per second = frequency
.5/15 = .033 waves per second = velocity
F(W) = V so W = V/F
But then my answers don't seem to be correct. Can someone please help out?
Thank you
T=30/50 = 0.6 s.
v=s/t= 0.5/15 = 0.033 m/s
λ=vT=0.033•0.6= 0.02 m
Frequency f = number of oscillations/times taken = 50/30s = 1.66Hz
Velocity of wave v = distance/time = 0.5m/15s = 0.033m/s
v = fλ
λ = v/f = 0.033/1.66 = 0.02
To find the wavelength of the water wave, we can use the formula:
Wave Speed (v) = Frequency (f) * Wavelength (λ)
First, let's calculate the frequency:
Frequency (f) = Number of vibrations / Time taken
Given:
Number of vibrations = 50
Time taken = 30 seconds
Frequency (f) = 50 / 30 = 5/3 ≈ 1.67 Hz
Next, let's calculate the wave speed:
Wave speed (v) = Distance / Time taken
Given:
Distance traveled by the trough = 50.0 cm
Time taken = 15 seconds
Wave speed (v) = 50.0 cm / 15 seconds = 3.33 cm/s ≈ 0.033 m/s
Now, we can rearrange the formula to solve for the wavelength:
Wavelength (λ) = Wave speed (v) / Frequency (f)
Wavelength (λ) = 0.033 m/s / 1.67 Hz ≈ 0.0198 m ≈ 1.98 cm
Therefore, the wavelength of the water wave is approximately 1.98 cm.
To calculate the wavelength of a water wave, you need to use the formula:
wavelength = velocity / frequency
Let's break down the problem step by step:
1. First, calculate the frequency of the oscillator:
Frequency = number of vibrations / time
Frequency = 50 / 30
Frequency = 5/3 vibrations/s (rounded to two decimal places)
2. Next, calculate the velocity of the wave (the speed at which the trough travels):
Velocity = distance / time
Velocity = 50 cm / 15 s
Velocity = 10/3 cm/s (rounded to two decimal places)
3. Finally, substitute the values of frequency and velocity into the formula to find the wavelength:
Wavelength = velocity / frequency
Wavelength = (10/3) cm/s / (5/3) vibrations/s
Wavelength = (10/3) cm/s * (3/5) vibrations/s
Wavelength = 2 cm (rounded to one decimal place)
Therefore, the wavelength of the water wave is 2 cm.