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

Answer:

1.9 m.

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.

Answer 2

Answer:

wavelength = 3.8 m

Explanation:

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

so here we have

$\mu = \frac{m}{L}$

$\mu = \frac{0.180}{5.70}$

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

$3\frac{\lambda}{2} = 5.70 m$

$\lambda = 3.8 m$

So wavelength of the wave on string is 3.8 m