Question

Standing waves are produced in a string by two waves travelling in opposite directions at 6.0 m/s. The distance between the second and sixth node is 80 cm. Determine the wavelength and frequency of the original waves.

Answer 1

wavelength = 0.4 m

frequency = 15 hz

Step-by-step explanation:

From the 2nd to the 6th node there are 4 antinodes, so we can divide 80 cm by 4

80 cm/4 = 20 cm

Then, 20 cm is the distance from a node to node and the wavelength will be twice this distance, so

wavelength = 20 cm x 2 = 40 cm

Now, we need to convert 40 cm to meters, so

40 cm x 1 m/ 100 cm = 0.4 m

Then, the speed, the wavelength, and the frequency are related as follows

v = fλ

Solving for the frequency f, we get

f = v/λ

Replacing the speed v by 6.0 m/s and the wavelength λ by 0.4m, we get:

f = 6/0.4 = 15 hz

So, the answers are

wavelength = 0.4 m

frequency = 15 hz