A harmonic wave is traveling along a rope.
The oscillator that generates the wave com-
pletes 44.0 vibrations in 26.9 s. A given crest
of the wave travels 359 cm along the rope in a
time period of 11.6 s.
What is the wavelength?
Answer in units of m.
freq=44.26.9
v= 3.59m/11.6s
lambda= v/f
f=44/26.9
To find the wavelength of the harmonic wave, we need to know the velocity of the wave. The velocity of the wave can be calculated using the formula:
Velocity = Frequency × Wavelength
where the frequency is equal to the number of vibrations completed in a given time.
In this case, the wave completes 44.0 vibrations in 26.9 seconds. To find the frequency, we can use the formula:
Frequency = Number of Vibrations / Time
Frequency = 44.0 vibrations / 26.9 s
Frequency = 1.635 frequency
Next, we need to find the velocity of the wave. We know that a given crest of the wave travels 359 cm in a time period of 11.6 seconds. We can use the formula:
Velocity = Distance / Time
Convert the distance from cm to meters:
Distance = 359 cm × (1 m/100 cm)
Distance = 3.59 m
Now we have all the necessary information to find the wavelength. Rearrange the velocity formula to solve for wavelength:
Wavelength = Velocity / Frequency
Plug in the values:
Wavelength = 3.59 m / 1.635 frequency
Wavelength = 2.198 m
Therefore, the wavelength of the harmonic wave is 2.198 m.