Question

You are visiting a distant planet and while you are there you repeat the vibrating strings experiment. when you plot l2 m versus n2 the data fell near a straight line that has slope 0.0160 cm. you know that the motor that is used to produce the waves makes waves that have a frequency of 80.0 hz. what is the value of g, the acceleration due to gravity on this planet, in units of m/s2?

Answer 1

To find the value of g, the acceleration due to gravity on the planet, we need to use the information given and the equation for the slope of a straight line. We can use the relationship between the frequency, the wavelength, and the speed of the wave to find the value of g.

Step-by-step explanation:

To find the value of g, the acceleration due to gravity on the planet, we need to use the information given and the equation for the slope of a straight line. The equation for the slope is:

slope = (l2m / n2) = 0.0160 cm

We know that the frequency of the waves produced by the motor is 80.0 Hz. We can use the relationship between the frequency, the wavelength, and the speed of the wave to find the value of g.

Using the formula:

velocity = frequency × wavelength

We can substitute the given values and solve for the wavelength:

wavelength = velocity / frequency = 343.0 m/s / 80.0 Hz = 4.29 m

Now we can use the relationship between the wavelength and the length of the vibrating string to find the value of g. The formula is:

wavelength = 2L / n

Solving for g:

g = (4π²L) / (λ²) = (4π² × 1.00 m) / (4.29 m)² ≈ 11.90 m/s²

The value of g, the acceleration due to gravity on this planet, is approximately 11.90 m/s².