A harmonic wave is traveling along a string. If the oscillator that generates the wave completes 23 vibrations in 18.50 seconds and if it takes a crest 20.21 seconds to travel 168 cm along the rope. What is the wavelength of the wave? Answer in cm.
period = T = 18.5/23 seconds
speed = 168 centi meters/ 20.21 seconds
distance = speed * time
= (168/20.21)(18.5/23)
To find the wavelength of the wave, we need to know the speed of the wave. The speed of a wave can be found using the formula:
Speed (v) = Frequency (f) × Wavelength (λ)
First, let's find the frequency of the wave. Frequency is the number of vibrations, or oscillations, completed in a given time. In this case, the oscillator completes 23 vibrations in 18.50 seconds. So, the frequency is:
Frequency (f) = Number of vibrations / Time
= 23 vibrations / 18.50 seconds
Next, we need to find the speed of the wave. Since the problem provides the time it takes for a crest to travel along the rope, we can calculate the speed using the distance traveled by the crest and the time:
Speed (v) = Distance (d) / Time (t)
= 168 cm / 20.21 seconds
Now that we have both the frequency and speed, we can rearrange the formula to solve for the wavelength:
Wavelength (λ) = Speed (v) / Frequency (f)
Substituting the values:
Wavelength (λ) = (168 cm / 20.21 seconds) / (23 vibrations / 18.50 seconds)
Finally, we can calculate the wavelength:
Wavelength (λ) = (168 cm / 20.21 seconds) * (18.50 seconds / 23 vibrations)
≈ 14.02 cm
Therefore, the wavelength of the wave is approximately 14.02 cm.