Question

a stretched string of length l vibrates in the third overtone .the wavelength of stationary wave formed is what?​

Answer 1

For a string vibrating in its n

th

overtone (n+1)

tj

harmonic)

y=2Asin(

L

(n+1)πx

)cosωt

For x=

3

l

.2A=a and n=3;

y=[asin(

l

4π

⋅

3

l

)]cosωt

=asin

3

4π

cosωt=−a(

2

3

)cosωt

i.e. at x=

3

l

, the amplitude is

2

3

a

.

hope it helps you

Answer 2

Given: a stretched string of length l vibrates in the third overtone

To find: wavelength of the stationary wave

Solution: Let the equation of the standing wave motion of the string be

y = a sin(kx)cos(wt)

here k will be propagation constant, w will be the angular velocity.

wavelength can be calculated with the formula as

λ = 2L/(n+1)

here L will be the length of the string and n will be 3 as the string is vibrating in 3rd overtone

so, λ = 2L/( 3+1) = 2L/4

λ will be L/2

Therefore, the wavelength of the stationary wave formed will be l/2.