A string in a musical instrument is 50 cm long and its fundamental frequency is 800 Hz. If a frequency of 1000 Hz is to be produced, then required length of string is

Question

A string in a musical instrument is 50 cm long and its fundamental frequency is 800 Hz. If a frequency of 1000 Hz is to be produced, then required length of string is (A) 62.5 cm (B) 40 cm (C) 50 cm (D) 37.5 cm

Tardigrade Admin · Accepted Answer

Fundamental frequency upsilon = (1/2L) √(T/μ) upsilon propto (1/L) ∴ (800/1000) = (L'/50) L' = (800 × 50/1000) = 40 cm

Q. A string in a musical instrument is $50 c m$ long and its fundamental frequency is $800 Hz$ . If a frequency of $1000 Hz$ is to be produced, then required length of string is

62.5 cm

40 cm

50 cm

37.5 cm

Fundamental frequency $υ = \frac{1}{2 L} \frac{T}{μ}$
$υ \propto \frac{1}{L} ∴ \frac{800}{1000} = \frac{L ^{'}}{50}$
$L^{'} = \frac{800 \times 50}{1000} = 40 c m$

Q. A string in a musical instrument is 50cm long and its fundamental frequency is 800Hz. If a frequency of 1000Hz is to be produced, then required length of string is