Two strings and have equal lengths and are made of the same material

PHYSICS · Multi-part · A Level · Physics · Waves · Waves

Problem

Two strings

A

and

B

have equal lengths and are made of the same material. String

A

has twice the diameter of string

B

. Both strings are stretched separately between identical rigid supports with the same tension. (i) Obtain the ratio of the linear mass densities

\mu_A : \mu_B

of the two strings. (ii) Deduce the ratio of their fundamental frequencies

f_A : f_B

. (iii) If the fundamental frequency of string

B

400\,\text{Hz}

, calculate the lowest frequency at which both strings can vibrate simultaneously without producing beats.