The length of the string of a musical instrument is 90 cm and has a fundamental frequency of 120 Hz. Where should it be pressed to produce fundamental frequency of 180 Hz ?

Question

The length of the string of a musical instrument is 90 cm and has a fundamental frequency of 120 Hz. Where should it be pressed to produce fundamental frequency of 180 Hz ? (A) 75 cm (B) 60 cm (C) 45 cm (D) 80 cm

Tardigrade Admin · Accepted Answer

The velocity of the travelling wave remains a constant.
Initially for fundamental mode,
the length of the string is half the wavelength.

λ = 180 c m v = 124 Hz

The new frequency is Given by:

v_{2} = 186 Hz

Using the fact that

v λ =

constant
we get

λ_{2} = 120 c m

The midpoint of this would be the node (where the string needs to be plucked).
The string needs to be plucked at

60 c m

.

Q. The length of the string of a musical instrument is $90 c m$ and has a fundamental frequency of $120 Hz$ . Where should it be pressed to produce fundamental frequency of $180 Hz$ ?

$75 c m$

$60 c m$

$45 c m$

$80 c m$

Q. The length of the string of a musical instrument is 90cm and has a fundamental frequency of 120Hz. Where should it be pressed to produce fundamental frequency of 180Hz ?

75cm

60cm

45cm

80cm

Q. The length of the string of a musical instrument is $90 c m$ and has a fundamental frequency of $120 Hz$ . Where should it be pressed to produce fundamental frequency of $180 Hz$ ?

$75 c m$

$60 c m$

$45 c m$

$80 c m$