Question

A standing wave on a string 1.5 m long with both ends fixed has three antinodes. If the frequency of the wave is 200 Hz, what is the speed of the wave on the string?

Answer 1

Step-by-step explanation:

Length of the string, L = 1.5 m

number of antinodes, n = 3

Frequency, f 200 Hz

L = nλ/2

1.5 = 3 x λ / 2

λ = 1 m

v = f x λ

v = 200 x 1

v = 200 m/s

Answer 2

200 m/s

Step-by-step explanation:

We are given that

Length of string=L=1.5 m

Number of antinodes=n=3

Frequency of the wave=f=200 Hz

The relation between the length and wavelength

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

Using the formula

`1.5=(3)/(2)\lambda`

`\lambda=(1.5* 2)/(3)=1 m`

The relation between the velocity,frequency and wavelength

`v=f\lambda`

Using the formula

`v=200* 1=200m/s`

Hence, the speed of the wave on the string=200 m/s