A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along the rope in 10.0 s. What is the wavelength?

The wave speed is

V = (425 cm)/(10 s) = 4.25 cm/s

The frequency is
f = 40/30 = 1.333 cycles per second

The wavelength is the wave speed divided by the frequency.

Drwls is incorrect as 425/10 is 42.5 NOT 4.25!

Also the measure for wave speed MUST be in m/s. Other than that it is correct.

To find the wavelength of the harmonic wave, we can use the formula:

wavelength = (velocity) / (frequency)

Given that the oscillator completes 40.0 vibrations in 30.0s, the frequency can be calculated as:

frequency = (number of vibrations) / (time)
= 40.0 / 30.0
= 4/3 Hz

Now, we need to find the velocity of the wave. Since velocity is also equal to the product of frequency and wavelength, we can rearrange the equation to:

wavelength = (velocity) / (frequency)
= (velocity) / (4/3 Hz)

Next, we can find the velocity using the distance traveled in a given time.

velocity = (distance) / (time)
= 425 cm / 10.0 s
= 42.5 cm/s

Now we substitute the values into the wavelength equation:

wavelength = (velocity) / (4/3 Hz)
= (42.5 cm/s) / (4/3 Hz)
= (42.5 cm/s) * (3/4 Hz)
= 31.875 cm

Therefore, the wavelength of the harmonic wave is 31.875 cm.

To find the wavelength of the harmonic wave, we can use the formula:

wavelength = (velocity / frequency),

where velocity is the speed at which the wave travels and frequency is the number of complete oscillations or vibrations per unit of time.

In this case, we are given the number of vibrations completed by the oscillator in 30.0 seconds (40.0 vibrations) and the time it takes for a given maximum to travel along the rope (10.0 seconds). We need to calculate the velocity and frequency to find the wavelength.

First, let's calculate the frequency:
frequency = (number of vibrations / time) = (40.0 vibrations / 30.0 s).

Next, let's calculate the velocity:
velocity = (distance / time) = (425 cm / 10.0 s).

Before we proceed, it's important to note that we need to ensure that all the units for the calculations are consistent. In this case, it would be ideal to have velocity in cm/s instead of cm. So, let's convert the units:

velocity = (425 cm / 10.0 s) = 42.5 cm/s.

Now, we can substitute the calculated values into the wavelength formula:
wavelength = (velocity / frequency) = (42.5 cm/s) / (40.0 vibrations / 30.0 s).

To simplify the calculation, we can multiply the numerator and denominator by the reciprocal of the fraction in the denominator:

wavelength = (42.5 cm/s) * (30.0 s / 40.0 vibrations) = 31.875 cm.

Therefore, the wavelength of the harmonic wave is 31.875 cm.