Question

A standing wave is set up in a 200-cm string fixed at both ends. the string vibrates in 5 distinct segments when driven by a 120-hz source. what is the wavelength?

Answer 1

`\lambda=80\ cm`

Step-by-step explanation:

It is given that,

Length of the string, L = 200 cm = 2 m

Frequency, f = 120 Hz

It vibrates in 5 distinct segments such that there is fifth harmonics. For a string fixed at both ends, the wavelength is given by :

`\lambda=(2)/(5)L`

`\lambda=(2)/(5)* 2`

`\lambda=0.8\ m`

`\lambda=80\ cm`

So, the wavelength of the string fixed at both ends is 80 cm. Hence, this is the required solution.

Answer 2

The wavelength of a standing wave is equivalent to:

wavelength = 2 l / n

Where l is the length of the string and n is the number of segments.

so, wavelength = 2 (0.2 m) / 5
wavelength = 0.08m (ANSWER)