A harmonic wave is traveling along a rope. It is observed that the oscillator that gener- ates the wave completes 44.9 in 30.4 s. Also, a given maximum travels 436 cm along the rope in 9.4 s.
What is the wavelength? Answer in units of cm
To find the wavelength of a harmonic wave, we can use the formula:
λ = v/f
where λ is the wavelength, v is the velocity of the wave, and f is the frequency of the wave.
In this case, we are given the time it takes for the oscillator to complete one cycle and the time it takes for a given maximum to travel a certain distance along the rope.
First, let's find the frequency of the wave.
Frequency (f) is the reciprocal of the time period (T):
f = 1/T
Given that the oscillator completes 44.9 cycles in 30.4 seconds, we can calculate the frequency as:
f = 1/30.4 s/cycle * 44.9 cycles = 0.0368 cycles/s
Next, let's find the velocity of the wave.
Velocity (v) can be calculated using the formula:
v = d/t
where v is the velocity, d is the distance traveled, and t is the time taken.
Given that the given maximum travels 436 cm in 9.4 seconds, we can calculate the velocity as:
v = 436 cm / 9.4 s = 46.38 cm/s
Now, we can calculate the wavelength using the formula:
λ = v/f
λ = 46.38 cm/s / 0.0368 cycles/s = 1260 cm
Therefore, the wavelength of the harmonic wave is 1260 cm.