A harmonic wave is traveling along a rope.
The oscillator that generates the wave com-
pletes 48.0 vibrations in 25.8 s. A given crest
of the wave travels 413 cm along the rope in a
time period of 10.5 s.
What is the wavelength?
Answer in units of m
The wave speed is
V = 4.13m/10.5 s = 0.393 m/s
The frequency is
f = 48/25.8 = 1.86 s^-1
Use the relationship
L = V/f to get the wavelength, L , in meters
To find the wavelength of the harmonic wave, we can use the formula:
Wavelength = Speed / Frequency
First, let's find the speed of the wave. The speed of the wave is equal to the distance traveled by the crest divided by the time taken:
Speed = Distance / Time
Given that a given crest travels 413 cm (or 4.13 m) in a time of 10.5 s, we can calculate the speed as:
Speed = 4.13 m / 10.5 s = 0.393 m/s
Next, we need to find the frequency. The frequency is the number of oscillations (vibrations) completed by the oscillator in a given time period. In this case, the oscillator completes 48.0 vibrations in 25.8 s. We can calculate the frequency as:
Frequency = Number of Vibrations / Time
Frequency = 48.0 vibrations / 25.8 s = 1.86 Hz
Now that we have the speed (0.393 m/s) and the frequency (1.86 Hz), we can calculate the wavelength using the formula:
Wavelength = Speed / Frequency
Wavelength = 0.393 m/s / 1.86 Hz = 0.211 m
Therefore, the wavelength of the harmonic wave is 0.211 m.