Question

A string of length 4m is fixed at both ends and a tension is maintained in it. A standing wave described by y=(4mm) sin (3π/2). x cos 2400π t is established in the string. Then the string is oscillating in
(1) fundamental note
(2)4th overtone
(3)5th ,,
(4)6th ,,

Answer 1

Answer:

ANSWER

A standing wave is basically an equation of simple harmonic motion having amplitude as a function of x.

Similarly in the given equation of wave :

y=Asin(

3

20π

x)cos(1000πt)

Here the Amplitude A(x)=Asin(

3

20π

x)

where x is the distance of any point from the node

Now, The distance between the point oscillating with the amplitude A/2 above the node is equal to :

2

A

=Asin(

3

20π

x)

2

1

=sin(

3

20π

x)

sin

6

π

=sin(

3

20π

x)

6

π

=

3

20π

x

x=

40

1

m

In standing wave there are two such points with amplitude (

2

A

) one above the centre line and another below the centre line.

The distance between the successive points oscillating with the amplitude A/2 across a node is equal to =2×x

2×

40

1

=

20

1

m

or5cm

Hence option C is correct