Question

It is found that a 5.70 m segment of a long string contains three complete waves and has a mass of 180 g. The string is vibrating sinusoidally with a frequency of 55.0 Hz and a peak-to-valley distance of 19.0 cm. (The "peak-to-valley" distance is the vertical distance from the farthest positive position to the farthest negative position). Calculate the wavelenght.

Answer 1

wavelength = 3.8 m

Step-by-step explanation:

As we know that linear mass density is defined as the ratio of mass and length

so here we have

`\mu = (m)/(L)`

`\mu = (0.180)/(5.70)`

now we have

`\mu = 0.0315 kg/m`

Now it is given that string contains three complete waves

length of one segment on string is half of the wavelength

so here we have

`3(\lambda)/(2) = 5.70 m`

`\lambda = 3.8 m`

So wavelength of the wave on string is 3.8 m

Answer 2

1.9 m.

Step-by-step explanation:

Three complete waves in the length of 5.7 m

The distance traveled by one complete wave is called wavelength.

Thus, the distance traveled by one wave = 5.7 / 3 = 1.9 m

Thus, the wavelength is 1.9 m.